convex-hull-labels.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "35b903c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from skimage.morphology import convex_hull_image\n",
    "import tifffile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c204c9b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import napari"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6be8c670",
   "metadata": {},
   "outputs": [],
   "source": [
    "viewer = napari.Viewer()\n",
    "viewer.open_sample('napari', 'cells3d')\n",
    "membrane_layer = viewer.layers[0]\n",
    "nuclei_layer = viewer.layers[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d4b1b2b1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# numpy label data\n",
    "import tifffile\n",
    "label_data = tifffile.imread('criss-cross-labels.tif')\n",
    "viewer.add_labels(label_data)\n",
    "label_layer = viewer.layers[-1]\n",
    "labels = label_layer.data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e4b62ba4",
   "metadata": {},
   "outputs": [],
   "source": [
    "from skimage.morphology import convex_hull_image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "06571da6",
   "metadata": {},
   "outputs": [],
   "source": [
    "chull = convex_hull_image(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2f37da29",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.15 s ± 160 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "# The scikit-image convex hull implementation looks good\n",
    "# but is slow to compute (~10 seconds just for this tiny 3D image)\n",
    "# ...but it's also using the C++ qhull algorithm under the hood, so we may not be able to speed it up\n",
    "%timeit convex_hull_image(labels)\n",
    "# 9.15 s ± 160 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "140101d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x28996c250>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(chull[30,...])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "777e5b43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Labels layer 'chull' at 0x2961fe5b0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "viewer.add_labels(chull)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "822296d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x299d0c970>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skimage import filters\n",
    "\n",
    "edges = filters.sobel(label_data)  # canny and roberts are 2D only, sobel can handle 3d case\n",
    "edges = edges > 0\n",
    "\n",
    "plt.imshow(edges[30])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "8d046042",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x2999fbcd0>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(edges[30] > 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "7b7402ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "chull = convex_hull_image(edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a8a6ad16",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.imshow(chull[30,...])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "335c4cf1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20.8 s ± 1.34 s per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "# The scikit-image convex hull implementation looks good\n",
    "# but is slow to compute (~10 seconds just for this tiny 3D image)\n",
    "# ...but it's also using the C++ qhull algorithm under the hood, so we may not be able to speed it up\n",
    "%timeit convex_hull_image(edges)\n",
    "# 20.8 s ± 1.34 s per loop (mean ± std. dev. of 7 runs, 1 loop each)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d1a2845",
   "metadata": {},
   "source": [
    "How is it somehow EVEN SLOWER to run than before?\n",
    "\n",
    "...This approach is not going to be very practical for big datasets :("
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91e90ee3",
   "metadata": {},
   "source": [
    "### Qhull accelerated algorithm\n",
    "* \n",
    "* PyHull wrapper documentation: https://pythonhosted.org/pyhull/\n",
    "* Qhull is available from conda-forge: https://anaconda.org/conda-forge/qhull\n",
    "* Here's an explanation of how the quickhull algorithm works: https://www.youtube.com/watch?v=2EKIZrimeuk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "24654046",
   "metadata": {},
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'qhull'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "Input \u001b[0;32mIn [11]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mqhull\u001b[39;00m\n",
      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'qhull'"
     ]
    }
   ],
   "source": [
    "import qhull"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b80c616d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting pyhull\n",
      "  Downloading pyhull-2015.2.1.tar.gz (318 kB)\n",
      "\u001b[2K     \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m318.8/318.8 KB\u001b[0m \u001b[31m3.6 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0mm eta \u001b[36m0:00:01\u001b[0m0:01\u001b[0m\n",
      "\u001b[?25h  Preparing metadata (setup.py) ... \u001b[?25ldone\n",
      "\u001b[?25hRequirement already satisfied: numpy in /Users/genevieb/mambaforge/envs/zarpaint/lib/python3.9/site-packages (from pyhull) (1.22.3)\n",
      "Building wheels for collected packages: pyhull\n",
      "  Building wheel for pyhull (setup.py) ... \u001b[?25ldone\n",
      "\u001b[?25h  Created wheel for pyhull: filename=pyhull-2015.2.1-cp39-cp39-macosx_11_0_arm64.whl size=181110 sha256=310d66c1858778a63c93c18bdd08b25a726947f6e267e3ec91d1cab69b32bd79\n",
      "  Stored in directory: /Users/genevieb/Library/Caches/pip/wheels/24/4f/ce/68f0ec603d3be7e93d2fd7ca95a77d8191505e1055ae94406d\n",
      "Successfully built pyhull\n",
      "Installing collected packages: pyhull\n",
      "Successfully installed pyhull-2015.2.1\n"
     ]
    }
   ],
   "source": [
    "!pip install pyhull"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6fe0c40d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyhull\n",
    "from pyhull.convex_hull import ConvexHull\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "62bc7992",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pyhull.convex_hull.ConvexHull at 0x29a892a30>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pts = np.argwhere(labels)\n",
    "qhull = ConvexHull(pts)\n",
    "qhull"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "1c22df51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 19,  59, 108],\n",
       "       [ 19,  60, 108],\n",
       "       [ 19,  61, 108],\n",
       "       ...,\n",
       "       [ 49,  71, 108],\n",
       "       [ 49,  72, 108],\n",
       "       [ 49,  73, 108]])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qhull.points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "5a49c3d6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 62, 94)\n",
       " \t(24, 57, 94)\n",
       " \t(28, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(24, 53, 101)\n",
       " \t(22, 56, 101)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 56, 101)\n",
       " \t(24, 53, 101)\n",
       " \t(24, 57, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 97, 113)\n",
       " \t(30, 98, 110)\n",
       " \t(30, 96, 105),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 66, 94)\n",
       " \t(22, 62, 94)\n",
       " \t(28, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 72, 101)\n",
       " \t(21, 71, 94)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 80, 101)\n",
       " \t(46, 82, 108)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 59, 117)\n",
       " \t(23, 56, 112)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 52, 117)\n",
       " \t(41, 48, 108)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 53, 108)\n",
       " \t(41, 50, 100)\n",
       " \t(41, 48, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 60, 124)\n",
       " \t(41, 52, 117)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 52, 117)\n",
       " \t(41, 60, 124)\n",
       " \t(44, 55, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 53, 94)\n",
       " \t(41, 50, 100)\n",
       " \t(42, 56, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 50, 100)\n",
       " \t(39, 53, 94)\n",
       " \t(36, 51, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 48, 101)\n",
       " \t(41, 50, 100)\n",
       " \t(36, 51, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 50, 100)\n",
       " \t(37, 48, 101)\n",
       " \t(41, 48, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 91, 117)\n",
       " \t(22, 89, 103)\n",
       " \t(21, 93, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 89, 113)\n",
       " \t(42, 89, 109)\n",
       " \t(46, 82, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 82, 108)\n",
       " \t(42, 89, 109)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(42, 89, 109)\n",
       " \t(39, 89, 104)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 89, 104)\n",
       " \t(30, 95, 103)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 95, 103)\n",
       " \t(35, 97, 113)\n",
       " \t(30, 96, 105),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 95, 103)\n",
       " \t(39, 89, 104)\n",
       " \t(35, 97, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 98, 117)\n",
       " \t(30, 98, 110)\n",
       " \t(35, 97, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 87, 135)\n",
       " \t(37, 89, 133)\n",
       " \t(36, 84, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 89, 133)\n",
       " \t(35, 87, 135)\n",
       " \t(35, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 80, 101)\n",
       " \t(47, 76, 104)\n",
       " \t(46, 82, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 51, 94)\n",
       " \t(28, 49, 101)\n",
       " \t(30, 48, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 51, 94)\n",
       " \t(30, 57, 89)\n",
       " \t(24, 57, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(24, 57, 94)\n",
       " \t(30, 57, 89)\n",
       " \t(28, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 57, 89)\n",
       " \t(30, 51, 94)\n",
       " \t(36, 51, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 66, 94)\n",
       " \t(20, 60, 101)\n",
       " \t(22, 62, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 62, 94)\n",
       " \t(20, 60, 101)\n",
       " \t(24, 57, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 76, 104)\n",
       " \t(41, 76, 94)\n",
       " \t(43, 72, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 76, 94)\n",
       " \t(47, 76, 104)\n",
       " \t(43, 80, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 76, 94)\n",
       " \t(43, 80, 101)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 48, 108)\n",
       " \t(38, 47, 108)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 48, 101)\n",
       " \t(38, 47, 108)\n",
       " \t(41, 48, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 60, 124)\n",
       " \t(46, 58, 117)\n",
       " \t(44, 55, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 58, 117)\n",
       " \t(46, 53, 108)\n",
       " \t(44, 55, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 53, 108)\n",
       " \t(46, 58, 117)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 58, 117)\n",
       " \t(48, 76, 122)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 50, 115)\n",
       " \t(38, 47, 108)\n",
       " \t(34, 47, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(38, 47, 108)\n",
       " \t(30, 50, 115)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 59, 117)\n",
       " \t(30, 50, 115)\n",
       " \t(23, 56, 112),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 53, 94)\n",
       " \t(35, 61, 87)\n",
       " \t(36, 51, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 61, 87)\n",
       " \t(30, 57, 89)\n",
       " \t(36, 51, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 89, 108)\n",
       " \t(20, 91, 117)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 89, 103)\n",
       " \t(21, 89, 108)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 89, 108)\n",
       " \t(22, 89, 103)\n",
       " \t(20, 91, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 87, 128)\n",
       " \t(43, 89, 127)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 89, 127)\n",
       " \t(43, 87, 128)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 81, 96)\n",
       " \t(22, 89, 103)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 71, 94)\n",
       " \t(23, 81, 96)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 95, 103)\n",
       " \t(35, 87, 97)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 87, 97)\n",
       " \t(30, 95, 103)\n",
       " \t(32, 89, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 89, 97)\n",
       " \t(30, 95, 103)\n",
       " \t(26, 91, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 116)\n",
       " \t(36, 98, 117)\n",
       " \t(35, 97, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 89, 104)\n",
       " \t(37, 97, 116)\n",
       " \t(35, 97, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(42, 89, 109)\n",
       " \t(37, 97, 116)\n",
       " \t(39, 89, 104),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 116)\n",
       " \t(42, 89, 109)\n",
       " \t(44, 89, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 89, 123)\n",
       " \t(43, 89, 127)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 89, 123)\n",
       " \t(45, 88, 117)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 89, 127)\n",
       " \t(44, 89, 123)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(34, 93, 131)\n",
       " \t(37, 89, 133)\n",
       " \t(35, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 89, 133)\n",
       " \t(34, 93, 131)\n",
       " \t(36, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 89, 129)\n",
       " \t(27, 95, 128)\n",
       " \t(27, 93, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 89, 133)\n",
       " \t(39, 93, 128)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 93, 128)\n",
       " \t(37, 89, 133)\n",
       " \t(36, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 97, 123)\n",
       " \t(39, 93, 128)\n",
       " \t(36, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 63, 128)\n",
       " \t(41, 60, 124)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 66, 117)\n",
       " \t(22, 59, 117)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 80, 117)\n",
       " \t(20, 72, 101)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 91, 117)\n",
       " \t(19, 80, 117)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 80, 117)\n",
       " \t(19, 64, 108)\n",
       " \t(20, 72, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 69, 94)\n",
       " \t(43, 72, 94)\n",
       " \t(38, 68, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 69, 94)\n",
       " \t(47, 76, 104)\n",
       " \t(43, 72, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 58, 94)\n",
       " \t(38, 64, 87)\n",
       " \t(42, 56, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(38, 64, 87)\n",
       " \t(43, 58, 94)\n",
       " \t(44, 62, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 62, 94)\n",
       " \t(43, 58, 94)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 58, 94)\n",
       " \t(45, 56, 101)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 69, 128)\n",
       " \t(22, 75, 131)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 75, 131)\n",
       " \t(25, 87, 135)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 50, 100)\n",
       " \t(44, 54, 101)\n",
       " \t(42, 56, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 53, 108)\n",
       " \t(44, 54, 101)\n",
       " \t(41, 50, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 76, 126)\n",
       " \t(46, 58, 117)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 75, 128)\n",
       " \t(46, 76, 126)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 63, 128)\n",
       " \t(23, 69, 128)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 50, 115)\n",
       " \t(30, 49, 112)\n",
       " \t(23, 56, 112),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 49, 112)\n",
       " \t(30, 50, 115)\n",
       " \t(34, 47, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 95, 103)\n",
       " \t(27, 96, 108)\n",
       " \t(26, 91, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(27, 96, 108)\n",
       " \t(22, 89, 103)\n",
       " \t(26, 91, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(27, 96, 108)\n",
       " \t(30, 95, 103)\n",
       " \t(30, 96, 105),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 98, 110)\n",
       " \t(27, 96, 108)\n",
       " \t(30, 96, 105),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 76, 104)\n",
       " \t(48, 78, 108)\n",
       " \t(46, 82, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(45, 88, 117)\n",
       " \t(48, 78, 108)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(48, 78, 108)\n",
       " \t(44, 89, 113)\n",
       " \t(46, 82, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(48, 78, 108)\n",
       " \t(45, 88, 117)\n",
       " \t(44, 89, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 81, 96)\n",
       " \t(25, 82, 94)\n",
       " \t(22, 89, 103),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 120)\n",
       " \t(36, 97, 123)\n",
       " \t(36, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 120)\n",
       " \t(44, 89, 123)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 93, 128)\n",
       " \t(37, 97, 120)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 120)\n",
       " \t(39, 93, 128)\n",
       " \t(36, 97, 123),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(27, 95, 128)\n",
       " \t(29, 96, 128)\n",
       " \t(27, 93, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(34, 93, 131)\n",
       " \t(33, 96, 128)\n",
       " \t(36, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(27, 93, 131)\n",
       " \t(30, 91, 133)\n",
       " \t(26, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 91, 133)\n",
       " \t(34, 93, 131)\n",
       " \t(35, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 97, 123)\n",
       " \t(21, 93, 117)\n",
       " \t(26, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 97, 123)\n",
       " \t(23, 94, 122)\n",
       " \t(21, 93, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 98, 123)\n",
       " \t(26, 97, 123)\n",
       " \t(26, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 87, 128)\n",
       " \t(41, 84, 131)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 84, 131)\n",
       " \t(37, 89, 133)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 89, 133)\n",
       " \t(41, 84, 131)\n",
       " \t(36, 84, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 65, 127)\n",
       " \t(41, 67, 128)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 58, 117)\n",
       " \t(41, 65, 127)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 65, 127)\n",
       " \t(46, 58, 117)\n",
       " \t(41, 60, 124),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 63, 128)\n",
       " \t(41, 65, 127)\n",
       " \t(41, 60, 124),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 89, 127)\n",
       " \t(19, 80, 117)\n",
       " \t(20, 91, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 89, 127)\n",
       " \t(20, 91, 117)\n",
       " \t(21, 93, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 94, 122)\n",
       " \t(20, 89, 127)\n",
       " \t(21, 93, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 87, 132)\n",
       " \t(20, 89, 127)\n",
       " \t(21, 89, 129),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 97, 123)\n",
       " \t(20, 89, 127)\n",
       " \t(23, 94, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 63, 101)\n",
       " \t(44, 62, 94)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 73, 128)\n",
       " \t(19, 66, 117)\n",
       " \t(20, 76, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 66, 117)\n",
       " \t(21, 73, 128)\n",
       " \t(22, 59, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(42, 76, 130)\n",
       " \t(44, 75, 128)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(42, 76, 130)\n",
       " \t(36, 80, 135)\n",
       " \t(41, 79, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 50, 115)\n",
       " \t(31, 51, 117)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 68, 131)\n",
       " \t(29, 63, 128)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 52, 108)\n",
       " \t(30, 49, 112)\n",
       " \t(28, 49, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 48, 108)\n",
       " \t(34, 47, 108)\n",
       " \t(30, 48, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 48, 108)\n",
       " \t(30, 49, 112)\n",
       " \t(34, 47, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 49, 101)\n",
       " \t(31, 48, 108)\n",
       " \t(30, 48, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 49, 112)\n",
       " \t(31, 48, 108)\n",
       " \t(28, 49, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(27, 96, 108)\n",
       " \t(25, 97, 113)\n",
       " \t(22, 89, 103),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 89, 103)\n",
       " \t(25, 97, 113)\n",
       " \t(21, 93, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(25, 97, 113)\n",
       " \t(27, 96, 108)\n",
       " \t(30, 98, 110),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(25, 97, 113)\n",
       " \t(30, 98, 110)\n",
       " \t(26, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(48, 78, 108)\n",
       " \t(49, 73, 108)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 88, 101)\n",
       " \t(25, 82, 94)\n",
       " \t(28, 89, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(25, 82, 94)\n",
       " \t(23, 88, 101)\n",
       " \t(22, 89, 103),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(24, 80, 94)\n",
       " \t(25, 82, 94)\n",
       " \t(23, 81, 96),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 83, 91)\n",
       " \t(33, 85, 94)\n",
       " \t(32, 89, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 85, 94)\n",
       " \t(35, 87, 97)\n",
       " \t(32, 89, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 76, 88)\n",
       " \t(28, 68, 87)\n",
       " \t(31, 71, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 76, 88)\n",
       " \t(30, 83, 91)\n",
       " \t(25, 82, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 68, 87)\n",
       " \t(29, 76, 88)\n",
       " \t(21, 71, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(24, 80, 94)\n",
       " \t(29, 76, 88)\n",
       " \t(25, 82, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 76, 88)\n",
       " \t(24, 80, 94)\n",
       " \t(21, 71, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(45, 88, 117)\n",
       " \t(39, 95, 117)\n",
       " \t(44, 89, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 95, 117)\n",
       " \t(37, 97, 116)\n",
       " \t(44, 89, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 89, 123)\n",
       " \t(39, 95, 117)\n",
       " \t(45, 88, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 120)\n",
       " \t(39, 95, 117)\n",
       " \t(44, 89, 123),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 97, 126)\n",
       " \t(33, 96, 128)\n",
       " \t(30, 97, 127),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 98, 123)\n",
       " \t(33, 97, 126)\n",
       " \t(30, 97, 127),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 97, 126)\n",
       " \t(36, 97, 123)\n",
       " \t(36, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 96, 128)\n",
       " \t(33, 97, 126)\n",
       " \t(36, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 92, 127)\n",
       " \t(26, 97, 123)\n",
       " \t(27, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 89, 129)\n",
       " \t(23, 92, 127)\n",
       " \t(27, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 82, 128)\n",
       " \t(41, 84, 131)\n",
       " \t(43, 87, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 76, 126)\n",
       " \t(44, 82, 128)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 82, 128)\n",
       " \t(43, 87, 128)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 89, 127)\n",
       " \t(20, 80, 128)\n",
       " \t(19, 80, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 80, 128)\n",
       " \t(20, 89, 127)\n",
       " \t(22, 87, 132),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 73, 128)\n",
       " \t(21, 76, 130)\n",
       " \t(22, 75, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 76, 130)\n",
       " \t(21, 73, 128)\n",
       " \t(20, 76, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 76, 130)\n",
       " \t(22, 87, 132)\n",
       " \t(22, 75, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 76, 132)\n",
       " \t(42, 76, 130)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(42, 76, 130)\n",
       " \t(39, 76, 132)\n",
       " \t(36, 80, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 80, 135)\n",
       " \t(39, 76, 132)\n",
       " \t(34, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 67, 128)\n",
       " \t(39, 76, 132)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 76, 132)\n",
       " \t(41, 67, 128)\n",
       " \t(34, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 59, 125)\n",
       " \t(29, 63, 128)\n",
       " \t(35, 63, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 59, 125)\n",
       " \t(35, 63, 128)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(34, 68, 131)\n",
       " \t(41, 65, 127)\n",
       " \t(35, 63, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 69, 94)\n",
       " \t(47, 71, 101)\n",
       " \t(47, 76, 104),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 71, 101)\n",
       " \t(48, 78, 108)\n",
       " \t(47, 76, 104),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 71, 101)\n",
       " \t(49, 73, 108)\n",
       " \t(48, 78, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 85, 94)\n",
       " \t(36, 76, 89)\n",
       " \t(35, 87, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 76, 89)\n",
       " \t(33, 85, 94)\n",
       " \t(30, 83, 91),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 76, 89)\n",
       " \t(30, 83, 91)\n",
       " \t(33, 76, 88),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 52, 118)\n",
       " \t(31, 51, 117)\n",
       " \t(30, 50, 115),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 52, 117)\n",
       " \t(30, 52, 118)\n",
       " \t(30, 50, 115),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 53, 108)\n",
       " \t(41, 52, 117)\n",
       " \t(44, 55, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 52, 117)\n",
       " \t(46, 53, 108)\n",
       " \t(41, 48, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 51, 94)\n",
       " \t(37, 48, 101)\n",
       " \t(36, 51, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 48, 101)\n",
       " \t(30, 51, 94)\n",
       " \t(30, 48, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 66, 94)\n",
       " \t(28, 68, 87)\n",
       " \t(21, 71, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 68, 87)\n",
       " \t(21, 66, 94)\n",
       " \t(28, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 49, 101)\n",
       " \t(30, 51, 94)\n",
       " \t(24, 57, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(24, 53, 101)\n",
       " \t(28, 49, 101)\n",
       " \t(24, 57, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 56, 101)\n",
       " \t(20, 60, 101)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 60, 101)\n",
       " \t(22, 56, 101)\n",
       " \t(24, 57, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(38, 47, 108)\n",
       " \t(37, 48, 101)\n",
       " \t(30, 48, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(34, 47, 108)\n",
       " \t(38, 47, 108)\n",
       " \t(30, 48, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 61, 87)\n",
       " \t(39, 53, 94)\n",
       " \t(42, 56, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(38, 64, 87)\n",
       " \t(35, 61, 87)\n",
       " \t(42, 56, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 98, 117)\n",
       " \t(30, 98, 123)\n",
       " \t(30, 98, 110),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 98, 110)\n",
       " \t(30, 98, 123)\n",
       " \t(26, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 87, 135)\n",
       " \t(36, 80, 135)\n",
       " \t(25, 87, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(25, 87, 135)\n",
       " \t(36, 80, 135)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 80, 135)\n",
       " \t(35, 87, 135)\n",
       " \t(36, 84, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 80, 135)\n",
       " \t(34, 76, 135)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 61, 87)\n",
       " \t(35, 71, 87)\n",
       " \t(31, 71, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 68, 87)\n",
       " \t(31, 61, 87)\n",
       " \t(31, 71, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 61, 87)\n",
       " \t(28, 68, 87)\n",
       " \t(28, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 61, 87)\n",
       " \t(35, 61, 87)\n",
       " \t(38, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 61, 87)\n",
       " \t(38, 64, 87)\n",
       " \t(38, 68, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 71, 87)\n",
       " \t(31, 61, 87)\n",
       " \t(38, 68, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 57, 89)\n",
       " \t(31, 61, 87)\n",
       " \t(28, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 61, 87)\n",
       " \t(31, 61, 87)\n",
       " \t(30, 57, 89),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 64, 108)\n",
       " \t(21, 66, 94)\n",
       " \t(21, 71, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 72, 101)\n",
       " \t(19, 64, 108)\n",
       " \t(21, 71, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 64, 108)\n",
       " \t(20, 60, 101)\n",
       " \t(21, 66, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 60, 101)\n",
       " \t(19, 64, 108)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 64, 108)\n",
       " \t(19, 80, 117)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 80, 117)\n",
       " \t(19, 66, 117)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(38, 64, 87)\n",
       " \t(44, 69, 94)\n",
       " \t(38, 68, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 69, 94)\n",
       " \t(38, 64, 87)\n",
       " \t(44, 62, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 58, 94)\n",
       " \t(44, 54, 101)\n",
       " \t(45, 56, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 54, 101)\n",
       " \t(43, 58, 94)\n",
       " \t(42, 56, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 54, 101)\n",
       " \t(46, 53, 108)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(45, 56, 101)\n",
       " \t(44, 54, 101)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 58, 117)\n",
       " \t(46, 76, 126)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 89, 97)\n",
       " \t(30, 83, 91)\n",
       " \t(30, 95, 103),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 95, 103)\n",
       " \t(30, 83, 91)\n",
       " \t(32, 89, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(25, 82, 94)\n",
       " \t(30, 83, 91)\n",
       " \t(28, 89, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 91, 133)\n",
       " \t(25, 87, 135)\n",
       " \t(26, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 91, 133)\n",
       " \t(35, 87, 135)\n",
       " \t(25, 87, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 87, 135)\n",
       " \t(30, 91, 133)\n",
       " \t(35, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 91, 133)\n",
       " \t(33, 96, 128)\n",
       " \t(34, 93, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 96, 128)\n",
       " \t(30, 91, 133)\n",
       " \t(27, 93, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 91, 133)\n",
       " \t(29, 96, 128)\n",
       " \t(30, 97, 127),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 96, 128)\n",
       " \t(30, 91, 133)\n",
       " \t(30, 97, 127),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(25, 87, 135)\n",
       " \t(22, 87, 132)\n",
       " \t(26, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 87, 132)\n",
       " \t(27, 93, 131)\n",
       " \t(26, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 87, 132)\n",
       " \t(21, 89, 129)\n",
       " \t(27, 93, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 75, 131)\n",
       " \t(22, 87, 132)\n",
       " \t(25, 87, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 96, 128)\n",
       " \t(26, 97, 123)\n",
       " \t(30, 97, 127),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 97, 123)\n",
       " \t(29, 96, 128)\n",
       " \t(27, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 97, 123)\n",
       " \t(30, 98, 123)\n",
       " \t(30, 97, 127),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 84, 131)\n",
       " \t(36, 80, 135)\n",
       " \t(36, 84, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 80, 135)\n",
       " \t(41, 84, 131)\n",
       " \t(41, 79, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 73, 128)\n",
       " \t(22, 75, 131)\n",
       " \t(23, 69, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 73, 128)\n",
       " \t(23, 69, 128)\n",
       " \t(22, 59, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 52, 108)\n",
       " \t(28, 49, 101)\n",
       " \t(24, 53, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 52, 108)\n",
       " \t(24, 53, 101)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 56, 112)\n",
       " \t(26, 52, 108)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 49, 112)\n",
       " \t(26, 52, 108)\n",
       " \t(23, 56, 112),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 93, 117)\n",
       " \t(25, 97, 113)\n",
       " \t(26, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(48, 76, 122)\n",
       " \t(49, 73, 108)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 88, 101)\n",
       " \t(28, 89, 97)\n",
       " \t(26, 91, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 89, 103)\n",
       " \t(23, 88, 101)\n",
       " \t(26, 91, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(24, 80, 94)\n",
       " \t(23, 81, 96)\n",
       " \t(21, 71, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 83, 91)\n",
       " \t(29, 76, 88)\n",
       " \t(33, 76, 88),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 71, 87)\n",
       " \t(29, 76, 88)\n",
       " \t(31, 71, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 76, 88)\n",
       " \t(35, 71, 87)\n",
       " \t(33, 76, 88),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 95, 117)\n",
       " \t(37, 97, 120)\n",
       " \t(36, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 116)\n",
       " \t(39, 95, 117)\n",
       " \t(36, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 97, 126)\n",
       " \t(30, 98, 123)\n",
       " \t(36, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 97, 123)\n",
       " \t(33, 97, 126)\n",
       " \t(36, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 92, 127)\n",
       " \t(20, 89, 127)\n",
       " \t(26, 97, 123),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 89, 127)\n",
       " \t(23, 92, 127)\n",
       " \t(21, 89, 129),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 82, 128)\n",
       " \t(46, 76, 126)\n",
       " \t(44, 75, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(42, 76, 130)\n",
       " \t(44, 82, 128)\n",
       " \t(44, 75, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 84, 131)\n",
       " \t(44, 82, 128)\n",
       " \t(41, 79, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 82, 128)\n",
       " \t(42, 76, 130)\n",
       " \t(41, 79, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 80, 117)\n",
       " \t(20, 80, 128)\n",
       " \t(19, 66, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 66, 117)\n",
       " \t(20, 80, 128)\n",
       " \t(20, 76, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 80, 128)\n",
       " \t(21, 76, 130)\n",
       " \t(20, 76, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 76, 130)\n",
       " \t(20, 80, 128)\n",
       " \t(22, 87, 132),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(34, 76, 135)\n",
       " \t(34, 68, 131)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(34, 68, 131)\n",
       " \t(29, 68, 131)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 63, 128)\n",
       " \t(34, 68, 131)\n",
       " \t(35, 63, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 68, 131)\n",
       " \t(34, 68, 131)\n",
       " \t(29, 63, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 67, 128)\n",
       " \t(34, 68, 131)\n",
       " \t(34, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 65, 127)\n",
       " \t(34, 68, 131)\n",
       " \t(41, 67, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(49, 73, 108)\n",
       " \t(47, 71, 101)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 71, 101)\n",
       " \t(47, 63, 101)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 71, 101)\n",
       " \t(44, 69, 94)\n",
       " \t(44, 62, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 63, 101)\n",
       " \t(47, 71, 101)\n",
       " \t(44, 62, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 76, 89)\n",
       " \t(41, 76, 94)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 87, 97)\n",
       " \t(36, 76, 89)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 72, 94)\n",
       " \t(36, 76, 89)\n",
       " \t(38, 68, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 76, 94)\n",
       " \t(36, 76, 89)\n",
       " \t(43, 72, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 76, 89)\n",
       " \t(35, 71, 87)\n",
       " \t(38, 68, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 71, 87)\n",
       " \t(36, 76, 89)\n",
       " \t(33, 76, 88),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 51, 117)\n",
       " \t(30, 52, 118)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 52, 118)\n",
       " \t(30, 59, 125)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 69, 128)\n",
       " \t(29, 52, 117)\n",
       " \t(22, 59, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 63, 128)\n",
       " \t(29, 52, 117)\n",
       " \t(23, 69, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 59, 125)\n",
       " \t(29, 52, 117)\n",
       " \t(29, 63, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 52, 118)\n",
       " \t(29, 52, 117)\n",
       " \t(30, 59, 125),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 52, 117)\n",
       " \t(30, 50, 115)\n",
       " \t(22, 59, 117)]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qhull.simplices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "ba67af16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[314, 1604, 2894],\n",
       " [1597, 299, 0],\n",
       " [299, 1597, 1604],\n",
       " [6940, 5061, 5017],\n",
       " [143, 314, 2894],\n",
       " [55, 163, 241],\n",
       " [9914, 10335, 7832],\n",
       " [307, 538, 0],\n",
       " [8496, 8449, 7918],\n",
       " [10244, 8451, 8449],\n",
       " [8715, 8496, 7918],\n",
       " [8496, 8715, 9981],\n",
       " [7922, 8451, 9578],\n",
       " [8451, 7922, 6960],\n",
       " [7297, 8451, 6960],\n",
       " [8451, 7297, 8449],\n",
       " [121, 490, 298],\n",
       " [10124, 9756, 10335],\n",
       " [10335, 9756, 7832],\n",
       " [9756, 8151, 7832],\n",
       " [8151, 4990, 7832],\n",
       " [4990, 6940, 5017],\n",
       " [4990, 8151, 6940],\n",
       " [7295, 5061, 6940],\n",
       " [6879, 7593, 7182],\n",
       " [7593, 6879, 6919],\n",
       " [9914, 10593, 10335],\n",
       " [3616, 2844, 3583],\n",
       " [3616, 3784, 1604],\n",
       " [1604, 3784, 2894],\n",
       " [3784, 3616, 6960],\n",
       " [143, 23, 314],\n",
       " [314, 23, 1604],\n",
       " [10593, 9132, 9853],\n",
       " [9132, 10593, 9914],\n",
       " [9132, 9914, 7832],\n",
       " [8449, 7614, 7918],\n",
       " [7297, 7614, 8449],\n",
       " [8715, 10250, 9981],\n",
       " [10250, 10244, 9981],\n",
       " [10244, 10250, 10664],\n",
       " [10250, 10661, 10664],\n",
       " [3615, 7614, 6222],\n",
       " [7614, 3615, 7918],\n",
       " [307, 3615, 538],\n",
       " [7922, 6640, 6960],\n",
       " [6640, 3784, 6960],\n",
       " [273, 121, 241],\n",
       " [490, 273, 241],\n",
       " [273, 490, 121],\n",
       " [9954, 9972, 10661],\n",
       " [9972, 9954, 9777],\n",
       " [1217, 490, 241],\n",
       " [163, 1217, 241],\n",
       " [4990, 6841, 7832],\n",
       " [6841, 4990, 5759],\n",
       " [3126, 4990, 2469],\n",
       " [7609, 7295, 6940],\n",
       " [8151, 7609, 6940],\n",
       " [9756, 7609, 8151],\n",
       " [7609, 9756, 10124],\n",
       " [10134, 9972, 9777],\n",
       " [10134, 10243, 10661],\n",
       " [9972, 10134, 10661],\n",
       " [6571, 7593, 6919],\n",
       " [7593, 6571, 7284],\n",
       " [294, 2826, 2820],\n",
       " [7593, 8187, 9777],\n",
       " [8187, 7593, 7284],\n",
       " [7294, 8187, 7284],\n",
       " [6655, 8715, 7918],\n",
       " [6, 307, 0],\n",
       " [20, 55, 241],\n",
       " [121, 20, 241],\n",
       " [20, 5, 55],\n",
       " [10028, 9853, 7692],\n",
       " [10028, 10593, 9853],\n",
       " [9796, 7670, 9578],\n",
       " [7670, 9796, 10000],\n",
       " [10000, 9796, 10664],\n",
       " [9796, 10139, 10664],\n",
       " [876, 373, 2322],\n",
       " [373, 2108, 2322],\n",
       " [8451, 9977, 9578],\n",
       " [10244, 9977, 8451],\n",
       " [10324, 10250, 9852],\n",
       " [10050, 10324, 9852],\n",
       " [3262, 876, 2322],\n",
       " [3615, 3597, 538],\n",
       " [3597, 3615, 6222],\n",
       " [4990, 2827, 2469],\n",
       " [2827, 490, 2469],\n",
       " [2827, 4990, 5017],\n",
       " [5061, 2827, 5017],\n",
       " [10593, 10663, 10335],\n",
       " [10243, 10663, 10661],\n",
       " [10663, 10124, 10335],\n",
       " [10663, 10243, 10124],\n",
       " [1217, 2046, 490],\n",
       " [7613, 7294, 7295],\n",
       " [7613, 10134, 9777],\n",
       " [8187, 7613, 9777],\n",
       " [7613, 8187, 7294],\n",
       " [2826, 3564, 2820],\n",
       " [6571, 6204, 7284],\n",
       " [2820, 4896, 2463],\n",
       " [4896, 6571, 6919],\n",
       " [2498, 298, 2499],\n",
       " [2498, 1595, 298],\n",
       " [5074, 2498, 2499],\n",
       " [9954, 9410, 9777],\n",
       " [9410, 7593, 9777],\n",
       " [7593, 9410, 7182],\n",
       " [8857, 8910, 9852],\n",
       " [10250, 8857, 9852],\n",
       " [8857, 10250, 8715],\n",
       " [6655, 8857, 8715],\n",
       " [119, 20, 121],\n",
       " [119, 121, 298],\n",
       " [1595, 119, 298],\n",
       " [486, 119, 294],\n",
       " [2498, 119, 1595],\n",
       " [10395, 10000, 10664],\n",
       " [173, 6, 87],\n",
       " [6, 173, 307],\n",
       " [9697, 10050, 9852],\n",
       " [9697, 7156, 9257],\n",
       " [3615, 5084, 7918],\n",
       " [3293, 3262, 2322],\n",
       " [2174, 3597, 2844],\n",
       " [5076, 6222, 3583],\n",
       " [5076, 3597, 6222],\n",
       " [2844, 5076, 3583],\n",
       " [3597, 5076, 2844],\n",
       " [2827, 2167, 490],\n",
       " [490, 2167, 298],\n",
       " [2167, 2827, 5061],\n",
       " [2167, 5061, 2499],\n",
       " [10663, 10678, 10661],\n",
       " [1454, 2046, 3126],\n",
       " [2046, 1454, 490],\n",
       " [1750, 2046, 1217],\n",
       " [4586, 6085, 5759],\n",
       " [6085, 6841, 5759],\n",
       " [3337, 2918, 5182],\n",
       " [3337, 4586, 2046],\n",
       " [2918, 3337, 163],\n",
       " [1750, 3337, 2046],\n",
       " [3337, 1750, 163],\n",
       " [10243, 8189, 10124],\n",
       " [8189, 7609, 10124],\n",
       " [10134, 8189, 10243],\n",
       " [7613, 8189, 10134],\n",
       " [6220, 6204, 5060],\n",
       " [5074, 6220, 5060],\n",
       " [6220, 7294, 7284],\n",
       " [6204, 6220, 7284],\n",
       " [1571, 2498, 2826],\n",
       " [294, 1571, 2826],\n",
       " [10100, 9410, 9954],\n",
       " [10324, 10100, 10661],\n",
       " [10100, 9954, 10661],\n",
       " [119, 99, 20],\n",
       " [99, 119, 486],\n",
       " [173, 212, 373],\n",
       " [212, 173, 87],\n",
       " [212, 486, 373],\n",
       " [8067, 9697, 9852],\n",
       " [9697, 8067, 7156],\n",
       " [7156, 8067, 6407],\n",
       " [8910, 8067, 9852],\n",
       " [8067, 8910, 6407],\n",
       " [3891, 3262, 6655],\n",
       " [3891, 6655, 7918],\n",
       " [6315, 8857, 6655],\n",
       " [10028, 10528, 10593],\n",
       " [10528, 10663, 10593],\n",
       " [10528, 10678, 10663],\n",
       " [6085, 7087, 6841],\n",
       " [7087, 6085, 4586],\n",
       " [7087, 4586, 5981],\n",
       " [3663, 5084, 3615],\n",
       " [3216, 3663, 3615],\n",
       " [10244, 8496, 9981],\n",
       " [8496, 10244, 8449],\n",
       " [3616, 7297, 6960],\n",
       " [7297, 3616, 3583],\n",
       " [143, 2918, 163],\n",
       " [2918, 143, 2894],\n",
       " [2844, 3616, 1604],\n",
       " [1597, 2844, 1604],\n",
       " [299, 23, 0],\n",
       " [23, 299, 1604],\n",
       " [7614, 7297, 3583],\n",
       " [6222, 7614, 3583],\n",
       " [6640, 7922, 9578],\n",
       " [7670, 6640, 9578],\n",
       " [7295, 5074, 5061],\n",
       " [5061, 5074, 2499],\n",
       " [6879, 7156, 2108],\n",
       " [2108, 7156, 2322],\n",
       " [7156, 6879, 7182],\n",
       " [7156, 6407, 2322],\n",
       " [5121, 6700, 5182],\n",
       " [2918, 5121, 5182],\n",
       " [5121, 2918, 2894],\n",
       " [5121, 6640, 7670],\n",
       " [5121, 7670, 7692],\n",
       " [6700, 5121, 7692],\n",
       " [3784, 5121, 2894],\n",
       " [6640, 5121, 3784],\n",
       " [5, 143, 163],\n",
       " [55, 5, 163],\n",
       " [5, 23, 143],\n",
       " [23, 5, 0],\n",
       " [5, 20, 0],\n",
       " [20, 6, 0],\n",
       " [7670, 10028, 7692],\n",
       " [10028, 7670, 10000],\n",
       " [9796, 9977, 10139],\n",
       " [9977, 9796, 9578],\n",
       " [9977, 10244, 10664],\n",
       " [10139, 9977, 10664],\n",
       " [10250, 10324, 10661],\n",
       " [3126, 4586, 4990],\n",
       " [4990, 4586, 5759],\n",
       " [2046, 4586, 3126],\n",
       " [4896, 2108, 2463],\n",
       " [4896, 6879, 2108],\n",
       " [6879, 4896, 6919],\n",
       " [4896, 6204, 6571],\n",
       " [3564, 4896, 2820],\n",
       " [4896, 3564, 5060],\n",
       " [6204, 4896, 5060],\n",
       " [2108, 486, 2463],\n",
       " [486, 2820, 2463],\n",
       " [486, 294, 2820],\n",
       " [373, 486, 2108],\n",
       " [3564, 2498, 5060],\n",
       " [2498, 3564, 2826],\n",
       " [2498, 5074, 5060],\n",
       " [9410, 7156, 7182],\n",
       " [7156, 9410, 9257],\n",
       " [173, 373, 876],\n",
       " [173, 876, 307],\n",
       " [2174, 2844, 1597],\n",
       " [2174, 1597, 0],\n",
       " [538, 2174, 0],\n",
       " [3597, 2174, 538],\n",
       " [298, 2167, 2499],\n",
       " [10661, 10678, 10664],\n",
       " [1454, 3126, 2469],\n",
       " [490, 1454, 2469],\n",
       " [1750, 1217, 163],\n",
       " [4586, 3337, 5981],\n",
       " [6700, 3337, 5182],\n",
       " [3337, 6700, 5981],\n",
       " [8189, 7613, 7295],\n",
       " [7609, 8189, 7295],\n",
       " [6220, 5074, 7295],\n",
       " [7294, 6220, 7295],\n",
       " [1571, 119, 2498],\n",
       " [119, 1571, 294],\n",
       " [10100, 10324, 10050],\n",
       " [9697, 10100, 10050],\n",
       " [9410, 10100, 9257],\n",
       " [10100, 9697, 9257],\n",
       " [20, 99, 6],\n",
       " [6, 99, 87],\n",
       " [99, 212, 87],\n",
       " [212, 99, 486],\n",
       " [6407, 6315, 2322],\n",
       " [6315, 3293, 2322],\n",
       " [3262, 6315, 6655],\n",
       " [3293, 6315, 3262],\n",
       " [8910, 6315, 6407],\n",
       " [8857, 6315, 8910],\n",
       " [10678, 10528, 10664],\n",
       " [10528, 10395, 10664],\n",
       " [10528, 10028, 10000],\n",
       " [10395, 10528, 10000],\n",
       " [7087, 9132, 7832],\n",
       " [6841, 7087, 7832],\n",
       " [9853, 7087, 7692],\n",
       " [9132, 7087, 9853],\n",
       " [7087, 6700, 7692],\n",
       " [6700, 7087, 5981],\n",
       " [5084, 3663, 7918],\n",
       " [3663, 3891, 7918],\n",
       " [876, 3216, 307],\n",
       " [3262, 3216, 876],\n",
       " [3891, 3216, 3262],\n",
       " [3663, 3216, 3891],\n",
       " [3216, 3615, 307]]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qhull.vertices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "766d4360",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10679\n",
      "294\n",
      "294\n"
     ]
    }
   ],
   "source": [
    "print(len(qhull.points))\n",
    "print(len(qhull.simplices))\n",
    "print(len(qhull.vertices))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "0b830fba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__class__',\n",
       " '__delattr__',\n",
       " '__dict__',\n",
       " '__dir__',\n",
       " '__doc__',\n",
       " '__eq__',\n",
       " '__format__',\n",
       " '__ge__',\n",
       " '__getattribute__',\n",
       " '__gt__',\n",
       " '__hash__',\n",
       " '__init__',\n",
       " '__init_subclass__',\n",
       " '__le__',\n",
       " '__lt__',\n",
       " '__module__',\n",
       " '__ne__',\n",
       " '__new__',\n",
       " '__reduce__',\n",
       " '__reduce_ex__',\n",
       " '__repr__',\n",
       " '__setattr__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__subclasshook__',\n",
       " '__weakref__',\n",
       " 'dim',\n",
       " 'points',\n",
       " 'simplices',\n",
       " 'vertices']"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(qhull)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "c8a5746a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__class__',\n",
       " '__delattr__',\n",
       " '__dict__',\n",
       " '__dir__',\n",
       " '__doc__',\n",
       " '__eq__',\n",
       " '__format__',\n",
       " '__ge__',\n",
       " '__getattribute__',\n",
       " '__gt__',\n",
       " '__hash__',\n",
       " '__init__',\n",
       " '__init_subclass__',\n",
       " '__le__',\n",
       " '__lt__',\n",
       " '__module__',\n",
       " '__ne__',\n",
       " '__new__',\n",
       " '__reduce__',\n",
       " '__reduce_ex__',\n",
       " '__repr__',\n",
       " '__setattr__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__subclasshook__',\n",
       " '__weakref__',\n",
       " '_coords',\n",
       " 'bary_coords',\n",
       " 'coords',\n",
       " 'in_simplex',\n",
       " 'origin',\n",
       " 'simplex_dim',\n",
       " 'space_dim',\n",
       " 'volume']"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(face)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "894ec167",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 29,  52, 117],\n",
       "       [ 30,  50, 115],\n",
       "       [ 22,  59, 117]])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "face.coords"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "fed13829",
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'Simplex' object has no attribute 'T'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "Input \u001b[0;32mIn [52]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mface\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvolume\u001b[49m\n",
      "File \u001b[0;32m~/mambaforge/envs/zarpaint/lib/python3.9/site-packages/pyhull/simplex.py:55\u001b[0m, in \u001b[0;36mSimplex.volume\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m     50\u001b[0m \u001b[38;5;129m@property\u001b[39m\n\u001b[1;32m     51\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvolume\u001b[39m(\u001b[38;5;28mself\u001b[39m):\n\u001b[1;32m     52\u001b[0m     \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     53\u001b[0m \u001b[38;5;124;03m    Volume of the simplex.\u001b[39;00m\n\u001b[1;32m     54\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m---> 55\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mabs\u001b[39m(np\u001b[38;5;241m.\u001b[39mlinalg\u001b[38;5;241m.\u001b[39mdet(\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mT\u001b[49m)) \u001b[38;5;241m/\u001b[39m math\u001b[38;5;241m.\u001b[39mfactorial(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mspace_dim)\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'Simplex' object has no attribute 'T'"
     ]
    }
   ],
   "source": [
    "face.volume"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "18caab78",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 62, 94)\n",
      "\t(24, 57, 94)\n",
      "\t(28, 64, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(24, 53, 101)\n",
      "\t(22, 56, 101)\n",
      "\t(19, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 56, 101)\n",
      "\t(24, 53, 101)\n",
      "\t(24, 57, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 97, 113)\n",
      "\t(30, 98, 110)\n",
      "\t(30, 96, 105)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 66, 94)\n",
      "\t(22, 62, 94)\n",
      "\t(28, 64, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(20, 72, 101)\n",
      "\t(21, 71, 94)\n",
      "\t(21, 84, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(43, 80, 101)\n",
      "\t(46, 82, 108)\n",
      "\t(38, 87, 100)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 59, 117)\n",
      "\t(23, 56, 112)\n",
      "\t(19, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 52, 117)\n",
      "\t(41, 48, 108)\n",
      "\t(39, 51, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(46, 53, 108)\n",
      "\t(41, 50, 100)\n",
      "\t(41, 48, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 60, 124)\n",
      "\t(41, 52, 117)\n",
      "\t(39, 51, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 52, 117)\n",
      "\t(41, 60, 124)\n",
      "\t(44, 55, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(39, 53, 94)\n",
      "\t(41, 50, 100)\n",
      "\t(42, 56, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 50, 100)\n",
      "\t(39, 53, 94)\n",
      "\t(36, 51, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 48, 101)\n",
      "\t(41, 50, 100)\n",
      "\t(36, 51, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 50, 100)\n",
      "\t(37, 48, 101)\n",
      "\t(41, 48, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(20, 91, 117)\n",
      "\t(22, 89, 103)\n",
      "\t(21, 93, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 89, 113)\n",
      "\t(42, 89, 109)\n",
      "\t(46, 82, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(46, 82, 108)\n",
      "\t(42, 89, 109)\n",
      "\t(38, 87, 100)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(42, 89, 109)\n",
      "\t(39, 89, 104)\n",
      "\t(38, 87, 100)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(39, 89, 104)\n",
      "\t(30, 95, 103)\n",
      "\t(38, 87, 100)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 95, 103)\n",
      "\t(35, 97, 113)\n",
      "\t(30, 96, 105)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 95, 103)\n",
      "\t(39, 89, 104)\n",
      "\t(35, 97, 113)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(36, 98, 117)\n",
      "\t(30, 98, 110)\n",
      "\t(35, 97, 113)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 87, 135)\n",
      "\t(37, 89, 133)\n",
      "\t(36, 84, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 89, 133)\n",
      "\t(35, 87, 135)\n",
      "\t(35, 89, 134)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(43, 80, 101)\n",
      "\t(47, 76, 104)\n",
      "\t(46, 82, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 51, 94)\n",
      "\t(28, 49, 101)\n",
      "\t(30, 48, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 51, 94)\n",
      "\t(30, 57, 89)\n",
      "\t(24, 57, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(24, 57, 94)\n",
      "\t(30, 57, 89)\n",
      "\t(28, 64, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 57, 89)\n",
      "\t(30, 51, 94)\n",
      "\t(36, 51, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 66, 94)\n",
      "\t(20, 60, 101)\n",
      "\t(22, 62, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 62, 94)\n",
      "\t(20, 60, 101)\n",
      "\t(24, 57, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(47, 76, 104)\n",
      "\t(41, 76, 94)\n",
      "\t(43, 72, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 76, 94)\n",
      "\t(47, 76, 104)\n",
      "\t(43, 80, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 76, 94)\n",
      "\t(43, 80, 101)\n",
      "\t(38, 87, 100)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 48, 108)\n",
      "\t(38, 47, 108)\n",
      "\t(39, 51, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 48, 101)\n",
      "\t(38, 47, 108)\n",
      "\t(41, 48, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 60, 124)\n",
      "\t(46, 58, 117)\n",
      "\t(44, 55, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(46, 58, 117)\n",
      "\t(46, 53, 108)\n",
      "\t(44, 55, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(46, 53, 108)\n",
      "\t(46, 58, 117)\n",
      "\t(49, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(46, 58, 117)\n",
      "\t(48, 76, 122)\n",
      "\t(49, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 50, 115)\n",
      "\t(38, 47, 108)\n",
      "\t(34, 47, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(38, 47, 108)\n",
      "\t(30, 50, 115)\n",
      "\t(39, 51, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 59, 117)\n",
      "\t(30, 50, 115)\n",
      "\t(23, 56, 112)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(39, 53, 94)\n",
      "\t(35, 61, 87)\n",
      "\t(36, 51, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 61, 87)\n",
      "\t(30, 57, 89)\n",
      "\t(36, 51, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 89, 108)\n",
      "\t(20, 91, 117)\n",
      "\t(21, 84, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 89, 103)\n",
      "\t(21, 89, 108)\n",
      "\t(21, 84, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 89, 108)\n",
      "\t(22, 89, 103)\n",
      "\t(20, 91, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(43, 87, 128)\n",
      "\t(43, 89, 127)\n",
      "\t(48, 76, 122)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(43, 89, 127)\n",
      "\t(43, 87, 128)\n",
      "\t(42, 90, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(23, 81, 96)\n",
      "\t(22, 89, 103)\n",
      "\t(21, 84, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 71, 94)\n",
      "\t(23, 81, 96)\n",
      "\t(21, 84, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 95, 103)\n",
      "\t(35, 87, 97)\n",
      "\t(38, 87, 100)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 87, 97)\n",
      "\t(30, 95, 103)\n",
      "\t(32, 89, 97)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(28, 89, 97)\n",
      "\t(30, 95, 103)\n",
      "\t(26, 91, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 97, 116)\n",
      "\t(36, 98, 117)\n",
      "\t(35, 97, 113)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(39, 89, 104)\n",
      "\t(37, 97, 116)\n",
      "\t(35, 97, 113)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(42, 89, 109)\n",
      "\t(37, 97, 116)\n",
      "\t(39, 89, 104)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 97, 116)\n",
      "\t(42, 89, 109)\n",
      "\t(44, 89, 113)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 89, 123)\n",
      "\t(43, 89, 127)\n",
      "\t(42, 90, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 89, 123)\n",
      "\t(45, 88, 117)\n",
      "\t(48, 76, 122)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(43, 89, 127)\n",
      "\t(44, 89, 123)\n",
      "\t(48, 76, 122)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(34, 93, 131)\n",
      "\t(37, 89, 133)\n",
      "\t(35, 89, 134)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 89, 133)\n",
      "\t(34, 93, 131)\n",
      "\t(36, 95, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 89, 129)\n",
      "\t(27, 95, 128)\n",
      "\t(27, 93, 131)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 89, 133)\n",
      "\t(39, 93, 128)\n",
      "\t(42, 90, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(39, 93, 128)\n",
      "\t(37, 89, 133)\n",
      "\t(36, 95, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(36, 97, 123)\n",
      "\t(39, 93, 128)\n",
      "\t(36, 95, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 63, 128)\n",
      "\t(41, 60, 124)\n",
      "\t(39, 51, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(19, 66, 117)\n",
      "\t(22, 59, 117)\n",
      "\t(19, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(19, 80, 117)\n",
      "\t(20, 72, 101)\n",
      "\t(21, 84, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(20, 91, 117)\n",
      "\t(19, 80, 117)\n",
      "\t(21, 84, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(19, 80, 117)\n",
      "\t(19, 64, 108)\n",
      "\t(20, 72, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 69, 94)\n",
      "\t(43, 72, 94)\n",
      "\t(38, 68, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 69, 94)\n",
      "\t(47, 76, 104)\n",
      "\t(43, 72, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(43, 58, 94)\n",
      "\t(38, 64, 87)\n",
      "\t(42, 56, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(38, 64, 87)\n",
      "\t(43, 58, 94)\n",
      "\t(44, 62, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 62, 94)\n",
      "\t(43, 58, 94)\n",
      "\t(49, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(43, 58, 94)\n",
      "\t(45, 56, 101)\n",
      "\t(49, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(23, 69, 128)\n",
      "\t(22, 75, 131)\n",
      "\t(26, 76, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 75, 131)\n",
      "\t(25, 87, 135)\n",
      "\t(26, 76, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 50, 100)\n",
      "\t(44, 54, 101)\n",
      "\t(42, 56, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(46, 53, 108)\n",
      "\t(44, 54, 101)\n",
      "\t(41, 50, 100)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(46, 76, 126)\n",
      "\t(46, 58, 117)\n",
      "\t(43, 71, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 75, 128)\n",
      "\t(46, 76, 126)\n",
      "\t(43, 71, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 63, 128)\n",
      "\t(23, 69, 128)\n",
      "\t(26, 76, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 50, 115)\n",
      "\t(30, 49, 112)\n",
      "\t(23, 56, 112)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 49, 112)\n",
      "\t(30, 50, 115)\n",
      "\t(34, 47, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 95, 103)\n",
      "\t(27, 96, 108)\n",
      "\t(26, 91, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(27, 96, 108)\n",
      "\t(22, 89, 103)\n",
      "\t(26, 91, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(27, 96, 108)\n",
      "\t(30, 95, 103)\n",
      "\t(30, 96, 105)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 98, 110)\n",
      "\t(27, 96, 108)\n",
      "\t(30, 96, 105)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(47, 76, 104)\n",
      "\t(48, 78, 108)\n",
      "\t(46, 82, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(45, 88, 117)\n",
      "\t(48, 78, 108)\n",
      "\t(48, 76, 122)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(48, 78, 108)\n",
      "\t(44, 89, 113)\n",
      "\t(46, 82, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(48, 78, 108)\n",
      "\t(45, 88, 117)\n",
      "\t(44, 89, 113)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(23, 81, 96)\n",
      "\t(25, 82, 94)\n",
      "\t(22, 89, 103)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 97, 120)\n",
      "\t(36, 97, 123)\n",
      "\t(36, 98, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 97, 120)\n",
      "\t(44, 89, 123)\n",
      "\t(42, 90, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(39, 93, 128)\n",
      "\t(37, 97, 120)\n",
      "\t(42, 90, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 97, 120)\n",
      "\t(39, 93, 128)\n",
      "\t(36, 97, 123)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(27, 95, 128)\n",
      "\t(29, 96, 128)\n",
      "\t(27, 93, 131)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(34, 93, 131)\n",
      "\t(33, 96, 128)\n",
      "\t(36, 95, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(27, 93, 131)\n",
      "\t(30, 91, 133)\n",
      "\t(26, 89, 134)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 91, 133)\n",
      "\t(34, 93, 131)\n",
      "\t(35, 89, 134)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(26, 97, 123)\n",
      "\t(21, 93, 117)\n",
      "\t(26, 98, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(26, 97, 123)\n",
      "\t(23, 94, 122)\n",
      "\t(21, 93, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 98, 123)\n",
      "\t(26, 97, 123)\n",
      "\t(26, 98, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(43, 87, 128)\n",
      "\t(41, 84, 131)\n",
      "\t(42, 90, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 84, 131)\n",
      "\t(37, 89, 133)\n",
      "\t(42, 90, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 89, 133)\n",
      "\t(41, 84, 131)\n",
      "\t(36, 84, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 65, 127)\n",
      "\t(41, 67, 128)\n",
      "\t(43, 71, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(46, 58, 117)\n",
      "\t(41, 65, 127)\n",
      "\t(43, 71, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 65, 127)\n",
      "\t(46, 58, 117)\n",
      "\t(41, 60, 124)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 63, 128)\n",
      "\t(41, 65, 127)\n",
      "\t(41, 60, 124)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(20, 89, 127)\n",
      "\t(19, 80, 117)\n",
      "\t(20, 91, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(20, 89, 127)\n",
      "\t(20, 91, 117)\n",
      "\t(21, 93, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(23, 94, 122)\n",
      "\t(20, 89, 127)\n",
      "\t(21, 93, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 87, 132)\n",
      "\t(20, 89, 127)\n",
      "\t(21, 89, 129)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(26, 97, 123)\n",
      "\t(20, 89, 127)\n",
      "\t(23, 94, 122)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(47, 63, 101)\n",
      "\t(44, 62, 94)\n",
      "\t(49, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 73, 128)\n",
      "\t(19, 66, 117)\n",
      "\t(20, 76, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(19, 66, 117)\n",
      "\t(21, 73, 128)\n",
      "\t(22, 59, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(42, 76, 130)\n",
      "\t(44, 75, 128)\n",
      "\t(43, 71, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(42, 76, 130)\n",
      "\t(36, 80, 135)\n",
      "\t(41, 79, 131)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 50, 115)\n",
      "\t(31, 51, 117)\n",
      "\t(39, 51, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 68, 131)\n",
      "\t(29, 63, 128)\n",
      "\t(26, 76, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(26, 52, 108)\n",
      "\t(30, 49, 112)\n",
      "\t(28, 49, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(31, 48, 108)\n",
      "\t(34, 47, 108)\n",
      "\t(30, 48, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(31, 48, 108)\n",
      "\t(30, 49, 112)\n",
      "\t(34, 47, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(28, 49, 101)\n",
      "\t(31, 48, 108)\n",
      "\t(30, 48, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 49, 112)\n",
      "\t(31, 48, 108)\n",
      "\t(28, 49, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(27, 96, 108)\n",
      "\t(25, 97, 113)\n",
      "\t(22, 89, 103)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 89, 103)\n",
      "\t(25, 97, 113)\n",
      "\t(21, 93, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(25, 97, 113)\n",
      "\t(27, 96, 108)\n",
      "\t(30, 98, 110)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(25, 97, 113)\n",
      "\t(30, 98, 110)\n",
      "\t(26, 98, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(48, 78, 108)\n",
      "\t(49, 73, 108)\n",
      "\t(48, 76, 122)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(23, 88, 101)\n",
      "\t(25, 82, 94)\n",
      "\t(28, 89, 97)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(25, 82, 94)\n",
      "\t(23, 88, 101)\n",
      "\t(22, 89, 103)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(24, 80, 94)\n",
      "\t(25, 82, 94)\n",
      "\t(23, 81, 96)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 83, 91)\n",
      "\t(33, 85, 94)\n",
      "\t(32, 89, 97)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(33, 85, 94)\n",
      "\t(35, 87, 97)\n",
      "\t(32, 89, 97)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 76, 88)\n",
      "\t(28, 68, 87)\n",
      "\t(31, 71, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 76, 88)\n",
      "\t(30, 83, 91)\n",
      "\t(25, 82, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(28, 68, 87)\n",
      "\t(29, 76, 88)\n",
      "\t(21, 71, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(24, 80, 94)\n",
      "\t(29, 76, 88)\n",
      "\t(25, 82, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 76, 88)\n",
      "\t(24, 80, 94)\n",
      "\t(21, 71, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(45, 88, 117)\n",
      "\t(39, 95, 117)\n",
      "\t(44, 89, 113)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(39, 95, 117)\n",
      "\t(37, 97, 116)\n",
      "\t(44, 89, 113)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 89, 123)\n",
      "\t(39, 95, 117)\n",
      "\t(45, 88, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 97, 120)\n",
      "\t(39, 95, 117)\n",
      "\t(44, 89, 123)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(33, 97, 126)\n",
      "\t(33, 96, 128)\n",
      "\t(30, 97, 127)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 98, 123)\n",
      "\t(33, 97, 126)\n",
      "\t(30, 97, 127)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(33, 97, 126)\n",
      "\t(36, 97, 123)\n",
      "\t(36, 95, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(33, 96, 128)\n",
      "\t(33, 97, 126)\n",
      "\t(36, 95, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(23, 92, 127)\n",
      "\t(26, 97, 123)\n",
      "\t(27, 95, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 89, 129)\n",
      "\t(23, 92, 127)\n",
      "\t(27, 95, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 82, 128)\n",
      "\t(41, 84, 131)\n",
      "\t(43, 87, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(46, 76, 126)\n",
      "\t(44, 82, 128)\n",
      "\t(48, 76, 122)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 82, 128)\n",
      "\t(43, 87, 128)\n",
      "\t(48, 76, 122)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(20, 89, 127)\n",
      "\t(20, 80, 128)\n",
      "\t(19, 80, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(20, 80, 128)\n",
      "\t(20, 89, 127)\n",
      "\t(22, 87, 132)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 73, 128)\n",
      "\t(21, 76, 130)\n",
      "\t(22, 75, 131)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 76, 130)\n",
      "\t(21, 73, 128)\n",
      "\t(20, 76, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 76, 130)\n",
      "\t(22, 87, 132)\n",
      "\t(22, 75, 131)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(39, 76, 132)\n",
      "\t(42, 76, 130)\n",
      "\t(43, 71, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(42, 76, 130)\n",
      "\t(39, 76, 132)\n",
      "\t(36, 80, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(36, 80, 135)\n",
      "\t(39, 76, 132)\n",
      "\t(34, 76, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 67, 128)\n",
      "\t(39, 76, 132)\n",
      "\t(43, 71, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(39, 76, 132)\n",
      "\t(41, 67, 128)\n",
      "\t(34, 76, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 59, 125)\n",
      "\t(29, 63, 128)\n",
      "\t(35, 63, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 59, 125)\n",
      "\t(35, 63, 128)\n",
      "\t(39, 51, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(34, 68, 131)\n",
      "\t(41, 65, 127)\n",
      "\t(35, 63, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 69, 94)\n",
      "\t(47, 71, 101)\n",
      "\t(47, 76, 104)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(47, 71, 101)\n",
      "\t(48, 78, 108)\n",
      "\t(47, 76, 104)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(47, 71, 101)\n",
      "\t(49, 73, 108)\n",
      "\t(48, 78, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(33, 85, 94)\n",
      "\t(36, 76, 89)\n",
      "\t(35, 87, 97)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(36, 76, 89)\n",
      "\t(33, 85, 94)\n",
      "\t(30, 83, 91)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(36, 76, 89)\n",
      "\t(30, 83, 91)\n",
      "\t(33, 76, 88)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 52, 118)\n",
      "\t(31, 51, 117)\n",
      "\t(30, 50, 115)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 52, 117)\n",
      "\t(30, 52, 118)\n",
      "\t(30, 50, 115)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(46, 53, 108)\n",
      "\t(41, 52, 117)\n",
      "\t(44, 55, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 52, 117)\n",
      "\t(46, 53, 108)\n",
      "\t(41, 48, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 51, 94)\n",
      "\t(37, 48, 101)\n",
      "\t(36, 51, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 48, 101)\n",
      "\t(30, 51, 94)\n",
      "\t(30, 48, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 66, 94)\n",
      "\t(28, 68, 87)\n",
      "\t(21, 71, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(28, 68, 87)\n",
      "\t(21, 66, 94)\n",
      "\t(28, 64, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(28, 49, 101)\n",
      "\t(30, 51, 94)\n",
      "\t(24, 57, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(24, 53, 101)\n",
      "\t(28, 49, 101)\n",
      "\t(24, 57, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 56, 101)\n",
      "\t(20, 60, 101)\n",
      "\t(19, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(20, 60, 101)\n",
      "\t(22, 56, 101)\n",
      "\t(24, 57, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(38, 47, 108)\n",
      "\t(37, 48, 101)\n",
      "\t(30, 48, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(34, 47, 108)\n",
      "\t(38, 47, 108)\n",
      "\t(30, 48, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 61, 87)\n",
      "\t(39, 53, 94)\n",
      "\t(42, 56, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(38, 64, 87)\n",
      "\t(35, 61, 87)\n",
      "\t(42, 56, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(36, 98, 117)\n",
      "\t(30, 98, 123)\n",
      "\t(30, 98, 110)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 98, 110)\n",
      "\t(30, 98, 123)\n",
      "\t(26, 98, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 87, 135)\n",
      "\t(36, 80, 135)\n",
      "\t(25, 87, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(25, 87, 135)\n",
      "\t(36, 80, 135)\n",
      "\t(26, 76, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(36, 80, 135)\n",
      "\t(35, 87, 135)\n",
      "\t(36, 84, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(36, 80, 135)\n",
      "\t(34, 76, 135)\n",
      "\t(26, 76, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(31, 61, 87)\n",
      "\t(35, 71, 87)\n",
      "\t(31, 71, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(28, 68, 87)\n",
      "\t(31, 61, 87)\n",
      "\t(31, 71, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(31, 61, 87)\n",
      "\t(28, 68, 87)\n",
      "\t(28, 64, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(31, 61, 87)\n",
      "\t(35, 61, 87)\n",
      "\t(38, 64, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(31, 61, 87)\n",
      "\t(38, 64, 87)\n",
      "\t(38, 68, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 71, 87)\n",
      "\t(31, 61, 87)\n",
      "\t(38, 68, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 57, 89)\n",
      "\t(31, 61, 87)\n",
      "\t(28, 64, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 61, 87)\n",
      "\t(31, 61, 87)\n",
      "\t(30, 57, 89)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(19, 64, 108)\n",
      "\t(21, 66, 94)\n",
      "\t(21, 71, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(20, 72, 101)\n",
      "\t(19, 64, 108)\n",
      "\t(21, 71, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(19, 64, 108)\n",
      "\t(20, 60, 101)\n",
      "\t(21, 66, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(20, 60, 101)\n",
      "\t(19, 64, 108)\n",
      "\t(19, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(19, 64, 108)\n",
      "\t(19, 80, 117)\n",
      "\t(19, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(19, 80, 117)\n",
      "\t(19, 66, 117)\n",
      "\t(19, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(38, 64, 87)\n",
      "\t(44, 69, 94)\n",
      "\t(38, 68, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 69, 94)\n",
      "\t(38, 64, 87)\n",
      "\t(44, 62, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(43, 58, 94)\n",
      "\t(44, 54, 101)\n",
      "\t(45, 56, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 54, 101)\n",
      "\t(43, 58, 94)\n",
      "\t(42, 56, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 54, 101)\n",
      "\t(46, 53, 108)\n",
      "\t(49, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(45, 56, 101)\n",
      "\t(44, 54, 101)\n",
      "\t(49, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(46, 58, 117)\n",
      "\t(46, 76, 126)\n",
      "\t(48, 76, 122)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(28, 89, 97)\n",
      "\t(30, 83, 91)\n",
      "\t(30, 95, 103)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 95, 103)\n",
      "\t(30, 83, 91)\n",
      "\t(32, 89, 97)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(25, 82, 94)\n",
      "\t(30, 83, 91)\n",
      "\t(28, 89, 97)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 91, 133)\n",
      "\t(25, 87, 135)\n",
      "\t(26, 89, 134)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 91, 133)\n",
      "\t(35, 87, 135)\n",
      "\t(25, 87, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 87, 135)\n",
      "\t(30, 91, 133)\n",
      "\t(35, 89, 134)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 91, 133)\n",
      "\t(33, 96, 128)\n",
      "\t(34, 93, 131)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 96, 128)\n",
      "\t(30, 91, 133)\n",
      "\t(27, 93, 131)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 91, 133)\n",
      "\t(29, 96, 128)\n",
      "\t(30, 97, 127)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(33, 96, 128)\n",
      "\t(30, 91, 133)\n",
      "\t(30, 97, 127)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(25, 87, 135)\n",
      "\t(22, 87, 132)\n",
      "\t(26, 89, 134)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 87, 132)\n",
      "\t(27, 93, 131)\n",
      "\t(26, 89, 134)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 87, 132)\n",
      "\t(21, 89, 129)\n",
      "\t(27, 93, 131)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 75, 131)\n",
      "\t(22, 87, 132)\n",
      "\t(25, 87, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 96, 128)\n",
      "\t(26, 97, 123)\n",
      "\t(30, 97, 127)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(26, 97, 123)\n",
      "\t(29, 96, 128)\n",
      "\t(27, 95, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(26, 97, 123)\n",
      "\t(30, 98, 123)\n",
      "\t(30, 97, 127)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 84, 131)\n",
      "\t(36, 80, 135)\n",
      "\t(36, 84, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(36, 80, 135)\n",
      "\t(41, 84, 131)\n",
      "\t(41, 79, 131)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 73, 128)\n",
      "\t(22, 75, 131)\n",
      "\t(23, 69, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 73, 128)\n",
      "\t(23, 69, 128)\n",
      "\t(22, 59, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(26, 52, 108)\n",
      "\t(28, 49, 101)\n",
      "\t(24, 53, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(26, 52, 108)\n",
      "\t(24, 53, 101)\n",
      "\t(19, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(23, 56, 112)\n",
      "\t(26, 52, 108)\n",
      "\t(19, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 49, 112)\n",
      "\t(26, 52, 108)\n",
      "\t(23, 56, 112)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 93, 117)\n",
      "\t(25, 97, 113)\n",
      "\t(26, 98, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(48, 76, 122)\n",
      "\t(49, 73, 108)\n",
      "\t(49, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(23, 88, 101)\n",
      "\t(28, 89, 97)\n",
      "\t(26, 91, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(22, 89, 103)\n",
      "\t(23, 88, 101)\n",
      "\t(26, 91, 101)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(24, 80, 94)\n",
      "\t(23, 81, 96)\n",
      "\t(21, 71, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 83, 91)\n",
      "\t(29, 76, 88)\n",
      "\t(33, 76, 88)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 71, 87)\n",
      "\t(29, 76, 88)\n",
      "\t(31, 71, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 76, 88)\n",
      "\t(35, 71, 87)\n",
      "\t(33, 76, 88)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(39, 95, 117)\n",
      "\t(37, 97, 120)\n",
      "\t(36, 98, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(37, 97, 116)\n",
      "\t(39, 95, 117)\n",
      "\t(36, 98, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(33, 97, 126)\n",
      "\t(30, 98, 123)\n",
      "\t(36, 98, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(36, 97, 123)\n",
      "\t(33, 97, 126)\n",
      "\t(36, 98, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(23, 92, 127)\n",
      "\t(20, 89, 127)\n",
      "\t(26, 97, 123)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(20, 89, 127)\n",
      "\t(23, 92, 127)\n",
      "\t(21, 89, 129)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 82, 128)\n",
      "\t(46, 76, 126)\n",
      "\t(44, 75, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(42, 76, 130)\n",
      "\t(44, 82, 128)\n",
      "\t(44, 75, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 84, 131)\n",
      "\t(44, 82, 128)\n",
      "\t(41, 79, 131)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(44, 82, 128)\n",
      "\t(42, 76, 130)\n",
      "\t(41, 79, 131)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(19, 80, 117)\n",
      "\t(20, 80, 128)\n",
      "\t(19, 66, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(19, 66, 117)\n",
      "\t(20, 80, 128)\n",
      "\t(20, 76, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(20, 80, 128)\n",
      "\t(21, 76, 130)\n",
      "\t(20, 76, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(21, 76, 130)\n",
      "\t(20, 80, 128)\n",
      "\t(22, 87, 132)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(34, 76, 135)\n",
      "\t(34, 68, 131)\n",
      "\t(26, 76, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(34, 68, 131)\n",
      "\t(29, 68, 131)\n",
      "\t(26, 76, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 63, 128)\n",
      "\t(34, 68, 131)\n",
      "\t(35, 63, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 68, 131)\n",
      "\t(34, 68, 131)\n",
      "\t(29, 63, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 67, 128)\n",
      "\t(34, 68, 131)\n",
      "\t(34, 76, 135)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 65, 127)\n",
      "\t(34, 68, 131)\n",
      "\t(41, 67, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(49, 73, 108)\n",
      "\t(47, 71, 101)\n",
      "\t(49, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(47, 71, 101)\n",
      "\t(47, 63, 101)\n",
      "\t(49, 59, 108)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(47, 71, 101)\n",
      "\t(44, 69, 94)\n",
      "\t(44, 62, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(47, 63, 101)\n",
      "\t(47, 71, 101)\n",
      "\t(44, 62, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(36, 76, 89)\n",
      "\t(41, 76, 94)\n",
      "\t(38, 87, 100)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 87, 97)\n",
      "\t(36, 76, 89)\n",
      "\t(38, 87, 100)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(43, 72, 94)\n",
      "\t(36, 76, 89)\n",
      "\t(38, 68, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(41, 76, 94)\n",
      "\t(36, 76, 89)\n",
      "\t(43, 72, 94)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(36, 76, 89)\n",
      "\t(35, 71, 87)\n",
      "\t(38, 68, 87)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(35, 71, 87)\n",
      "\t(36, 76, 89)\n",
      "\t(33, 76, 88)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(31, 51, 117)\n",
      "\t(30, 52, 118)\n",
      "\t(39, 51, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 52, 118)\n",
      "\t(30, 59, 125)\n",
      "\t(39, 51, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(23, 69, 128)\n",
      "\t(29, 52, 117)\n",
      "\t(22, 59, 117)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 63, 128)\n",
      "\t(29, 52, 117)\n",
      "\t(23, 69, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 59, 125)\n",
      "\t(29, 52, 117)\n",
      "\t(29, 63, 128)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(30, 52, 118)\n",
      "\t(29, 52, 117)\n",
      "\t(30, 59, 125)\n",
      "3-simplex in 3D space\n",
      "Vertices:\n",
      "\t(29, 52, 117)\n",
      "\t(30, 50, 115)\n",
      "\t(22, 59, 117)\n"
     ]
    }
   ],
   "source": [
    "for face in qhull.simplices:\n",
    "    print(face)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "1a60b1f5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 62, 94)\n",
       " \t(24, 57, 94)\n",
       " \t(28, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(24, 53, 101)\n",
       " \t(22, 56, 101)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 56, 101)\n",
       " \t(24, 53, 101)\n",
       " \t(24, 57, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 97, 113)\n",
       " \t(30, 98, 110)\n",
       " \t(30, 96, 105),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 66, 94)\n",
       " \t(22, 62, 94)\n",
       " \t(28, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 72, 101)\n",
       " \t(21, 71, 94)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 80, 101)\n",
       " \t(46, 82, 108)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 59, 117)\n",
       " \t(23, 56, 112)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 52, 117)\n",
       " \t(41, 48, 108)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 53, 108)\n",
       " \t(41, 50, 100)\n",
       " \t(41, 48, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 60, 124)\n",
       " \t(41, 52, 117)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 52, 117)\n",
       " \t(41, 60, 124)\n",
       " \t(44, 55, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 53, 94)\n",
       " \t(41, 50, 100)\n",
       " \t(42, 56, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 50, 100)\n",
       " \t(39, 53, 94)\n",
       " \t(36, 51, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 48, 101)\n",
       " \t(41, 50, 100)\n",
       " \t(36, 51, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 50, 100)\n",
       " \t(37, 48, 101)\n",
       " \t(41, 48, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 91, 117)\n",
       " \t(22, 89, 103)\n",
       " \t(21, 93, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 89, 113)\n",
       " \t(42, 89, 109)\n",
       " \t(46, 82, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 82, 108)\n",
       " \t(42, 89, 109)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(42, 89, 109)\n",
       " \t(39, 89, 104)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 89, 104)\n",
       " \t(30, 95, 103)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 95, 103)\n",
       " \t(35, 97, 113)\n",
       " \t(30, 96, 105),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 95, 103)\n",
       " \t(39, 89, 104)\n",
       " \t(35, 97, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 98, 117)\n",
       " \t(30, 98, 110)\n",
       " \t(35, 97, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 87, 135)\n",
       " \t(37, 89, 133)\n",
       " \t(36, 84, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 89, 133)\n",
       " \t(35, 87, 135)\n",
       " \t(35, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 80, 101)\n",
       " \t(47, 76, 104)\n",
       " \t(46, 82, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 51, 94)\n",
       " \t(28, 49, 101)\n",
       " \t(30, 48, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 51, 94)\n",
       " \t(30, 57, 89)\n",
       " \t(24, 57, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(24, 57, 94)\n",
       " \t(30, 57, 89)\n",
       " \t(28, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 57, 89)\n",
       " \t(30, 51, 94)\n",
       " \t(36, 51, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 66, 94)\n",
       " \t(20, 60, 101)\n",
       " \t(22, 62, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 62, 94)\n",
       " \t(20, 60, 101)\n",
       " \t(24, 57, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 76, 104)\n",
       " \t(41, 76, 94)\n",
       " \t(43, 72, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 76, 94)\n",
       " \t(47, 76, 104)\n",
       " \t(43, 80, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 76, 94)\n",
       " \t(43, 80, 101)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 48, 108)\n",
       " \t(38, 47, 108)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 48, 101)\n",
       " \t(38, 47, 108)\n",
       " \t(41, 48, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 60, 124)\n",
       " \t(46, 58, 117)\n",
       " \t(44, 55, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 58, 117)\n",
       " \t(46, 53, 108)\n",
       " \t(44, 55, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 53, 108)\n",
       " \t(46, 58, 117)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 58, 117)\n",
       " \t(48, 76, 122)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 50, 115)\n",
       " \t(38, 47, 108)\n",
       " \t(34, 47, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(38, 47, 108)\n",
       " \t(30, 50, 115)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 59, 117)\n",
       " \t(30, 50, 115)\n",
       " \t(23, 56, 112),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 53, 94)\n",
       " \t(35, 61, 87)\n",
       " \t(36, 51, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 61, 87)\n",
       " \t(30, 57, 89)\n",
       " \t(36, 51, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 89, 108)\n",
       " \t(20, 91, 117)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 89, 103)\n",
       " \t(21, 89, 108)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 89, 108)\n",
       " \t(22, 89, 103)\n",
       " \t(20, 91, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 87, 128)\n",
       " \t(43, 89, 127)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 89, 127)\n",
       " \t(43, 87, 128)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 81, 96)\n",
       " \t(22, 89, 103)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 71, 94)\n",
       " \t(23, 81, 96)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 95, 103)\n",
       " \t(35, 87, 97)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 87, 97)\n",
       " \t(30, 95, 103)\n",
       " \t(32, 89, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 89, 97)\n",
       " \t(30, 95, 103)\n",
       " \t(26, 91, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 116)\n",
       " \t(36, 98, 117)\n",
       " \t(35, 97, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 89, 104)\n",
       " \t(37, 97, 116)\n",
       " \t(35, 97, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(42, 89, 109)\n",
       " \t(37, 97, 116)\n",
       " \t(39, 89, 104),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 116)\n",
       " \t(42, 89, 109)\n",
       " \t(44, 89, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 89, 123)\n",
       " \t(43, 89, 127)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 89, 123)\n",
       " \t(45, 88, 117)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 89, 127)\n",
       " \t(44, 89, 123)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(34, 93, 131)\n",
       " \t(37, 89, 133)\n",
       " \t(35, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 89, 133)\n",
       " \t(34, 93, 131)\n",
       " \t(36, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 89, 129)\n",
       " \t(27, 95, 128)\n",
       " \t(27, 93, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 89, 133)\n",
       " \t(39, 93, 128)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 93, 128)\n",
       " \t(37, 89, 133)\n",
       " \t(36, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 97, 123)\n",
       " \t(39, 93, 128)\n",
       " \t(36, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 63, 128)\n",
       " \t(41, 60, 124)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 66, 117)\n",
       " \t(22, 59, 117)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 80, 117)\n",
       " \t(20, 72, 101)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 91, 117)\n",
       " \t(19, 80, 117)\n",
       " \t(21, 84, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 80, 117)\n",
       " \t(19, 64, 108)\n",
       " \t(20, 72, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 69, 94)\n",
       " \t(43, 72, 94)\n",
       " \t(38, 68, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 69, 94)\n",
       " \t(47, 76, 104)\n",
       " \t(43, 72, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 58, 94)\n",
       " \t(38, 64, 87)\n",
       " \t(42, 56, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(38, 64, 87)\n",
       " \t(43, 58, 94)\n",
       " \t(44, 62, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 62, 94)\n",
       " \t(43, 58, 94)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 58, 94)\n",
       " \t(45, 56, 101)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 69, 128)\n",
       " \t(22, 75, 131)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 75, 131)\n",
       " \t(25, 87, 135)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 50, 100)\n",
       " \t(44, 54, 101)\n",
       " \t(42, 56, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 53, 108)\n",
       " \t(44, 54, 101)\n",
       " \t(41, 50, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 76, 126)\n",
       " \t(46, 58, 117)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 75, 128)\n",
       " \t(46, 76, 126)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 63, 128)\n",
       " \t(23, 69, 128)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 50, 115)\n",
       " \t(30, 49, 112)\n",
       " \t(23, 56, 112),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 49, 112)\n",
       " \t(30, 50, 115)\n",
       " \t(34, 47, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 95, 103)\n",
       " \t(27, 96, 108)\n",
       " \t(26, 91, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(27, 96, 108)\n",
       " \t(22, 89, 103)\n",
       " \t(26, 91, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(27, 96, 108)\n",
       " \t(30, 95, 103)\n",
       " \t(30, 96, 105),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 98, 110)\n",
       " \t(27, 96, 108)\n",
       " \t(30, 96, 105),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 76, 104)\n",
       " \t(48, 78, 108)\n",
       " \t(46, 82, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(45, 88, 117)\n",
       " \t(48, 78, 108)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(48, 78, 108)\n",
       " \t(44, 89, 113)\n",
       " \t(46, 82, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(48, 78, 108)\n",
       " \t(45, 88, 117)\n",
       " \t(44, 89, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 81, 96)\n",
       " \t(25, 82, 94)\n",
       " \t(22, 89, 103),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 120)\n",
       " \t(36, 97, 123)\n",
       " \t(36, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 120)\n",
       " \t(44, 89, 123)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 93, 128)\n",
       " \t(37, 97, 120)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 120)\n",
       " \t(39, 93, 128)\n",
       " \t(36, 97, 123),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(27, 95, 128)\n",
       " \t(29, 96, 128)\n",
       " \t(27, 93, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(34, 93, 131)\n",
       " \t(33, 96, 128)\n",
       " \t(36, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(27, 93, 131)\n",
       " \t(30, 91, 133)\n",
       " \t(26, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 91, 133)\n",
       " \t(34, 93, 131)\n",
       " \t(35, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 97, 123)\n",
       " \t(21, 93, 117)\n",
       " \t(26, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 97, 123)\n",
       " \t(23, 94, 122)\n",
       " \t(21, 93, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 98, 123)\n",
       " \t(26, 97, 123)\n",
       " \t(26, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 87, 128)\n",
       " \t(41, 84, 131)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 84, 131)\n",
       " \t(37, 89, 133)\n",
       " \t(42, 90, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 89, 133)\n",
       " \t(41, 84, 131)\n",
       " \t(36, 84, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 65, 127)\n",
       " \t(41, 67, 128)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 58, 117)\n",
       " \t(41, 65, 127)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 65, 127)\n",
       " \t(46, 58, 117)\n",
       " \t(41, 60, 124),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 63, 128)\n",
       " \t(41, 65, 127)\n",
       " \t(41, 60, 124),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 89, 127)\n",
       " \t(19, 80, 117)\n",
       " \t(20, 91, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 89, 127)\n",
       " \t(20, 91, 117)\n",
       " \t(21, 93, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 94, 122)\n",
       " \t(20, 89, 127)\n",
       " \t(21, 93, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 87, 132)\n",
       " \t(20, 89, 127)\n",
       " \t(21, 89, 129),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 97, 123)\n",
       " \t(20, 89, 127)\n",
       " \t(23, 94, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 63, 101)\n",
       " \t(44, 62, 94)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 73, 128)\n",
       " \t(19, 66, 117)\n",
       " \t(20, 76, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 66, 117)\n",
       " \t(21, 73, 128)\n",
       " \t(22, 59, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(42, 76, 130)\n",
       " \t(44, 75, 128)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(42, 76, 130)\n",
       " \t(36, 80, 135)\n",
       " \t(41, 79, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 50, 115)\n",
       " \t(31, 51, 117)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 68, 131)\n",
       " \t(29, 63, 128)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 52, 108)\n",
       " \t(30, 49, 112)\n",
       " \t(28, 49, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 48, 108)\n",
       " \t(34, 47, 108)\n",
       " \t(30, 48, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 48, 108)\n",
       " \t(30, 49, 112)\n",
       " \t(34, 47, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 49, 101)\n",
       " \t(31, 48, 108)\n",
       " \t(30, 48, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 49, 112)\n",
       " \t(31, 48, 108)\n",
       " \t(28, 49, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(27, 96, 108)\n",
       " \t(25, 97, 113)\n",
       " \t(22, 89, 103),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 89, 103)\n",
       " \t(25, 97, 113)\n",
       " \t(21, 93, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(25, 97, 113)\n",
       " \t(27, 96, 108)\n",
       " \t(30, 98, 110),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(25, 97, 113)\n",
       " \t(30, 98, 110)\n",
       " \t(26, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(48, 78, 108)\n",
       " \t(49, 73, 108)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 88, 101)\n",
       " \t(25, 82, 94)\n",
       " \t(28, 89, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(25, 82, 94)\n",
       " \t(23, 88, 101)\n",
       " \t(22, 89, 103),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(24, 80, 94)\n",
       " \t(25, 82, 94)\n",
       " \t(23, 81, 96),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 83, 91)\n",
       " \t(33, 85, 94)\n",
       " \t(32, 89, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 85, 94)\n",
       " \t(35, 87, 97)\n",
       " \t(32, 89, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 76, 88)\n",
       " \t(28, 68, 87)\n",
       " \t(31, 71, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 76, 88)\n",
       " \t(30, 83, 91)\n",
       " \t(25, 82, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 68, 87)\n",
       " \t(29, 76, 88)\n",
       " \t(21, 71, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(24, 80, 94)\n",
       " \t(29, 76, 88)\n",
       " \t(25, 82, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 76, 88)\n",
       " \t(24, 80, 94)\n",
       " \t(21, 71, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(45, 88, 117)\n",
       " \t(39, 95, 117)\n",
       " \t(44, 89, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 95, 117)\n",
       " \t(37, 97, 116)\n",
       " \t(44, 89, 113),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 89, 123)\n",
       " \t(39, 95, 117)\n",
       " \t(45, 88, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 120)\n",
       " \t(39, 95, 117)\n",
       " \t(44, 89, 123),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 97, 126)\n",
       " \t(33, 96, 128)\n",
       " \t(30, 97, 127),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 98, 123)\n",
       " \t(33, 97, 126)\n",
       " \t(30, 97, 127),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 97, 126)\n",
       " \t(36, 97, 123)\n",
       " \t(36, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 96, 128)\n",
       " \t(33, 97, 126)\n",
       " \t(36, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 92, 127)\n",
       " \t(26, 97, 123)\n",
       " \t(27, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 89, 129)\n",
       " \t(23, 92, 127)\n",
       " \t(27, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 82, 128)\n",
       " \t(41, 84, 131)\n",
       " \t(43, 87, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 76, 126)\n",
       " \t(44, 82, 128)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 82, 128)\n",
       " \t(43, 87, 128)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 89, 127)\n",
       " \t(20, 80, 128)\n",
       " \t(19, 80, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 80, 128)\n",
       " \t(20, 89, 127)\n",
       " \t(22, 87, 132),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 73, 128)\n",
       " \t(21, 76, 130)\n",
       " \t(22, 75, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 76, 130)\n",
       " \t(21, 73, 128)\n",
       " \t(20, 76, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 76, 130)\n",
       " \t(22, 87, 132)\n",
       " \t(22, 75, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 76, 132)\n",
       " \t(42, 76, 130)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(42, 76, 130)\n",
       " \t(39, 76, 132)\n",
       " \t(36, 80, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 80, 135)\n",
       " \t(39, 76, 132)\n",
       " \t(34, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 67, 128)\n",
       " \t(39, 76, 132)\n",
       " \t(43, 71, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 76, 132)\n",
       " \t(41, 67, 128)\n",
       " \t(34, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 59, 125)\n",
       " \t(29, 63, 128)\n",
       " \t(35, 63, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 59, 125)\n",
       " \t(35, 63, 128)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(34, 68, 131)\n",
       " \t(41, 65, 127)\n",
       " \t(35, 63, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 69, 94)\n",
       " \t(47, 71, 101)\n",
       " \t(47, 76, 104),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 71, 101)\n",
       " \t(48, 78, 108)\n",
       " \t(47, 76, 104),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 71, 101)\n",
       " \t(49, 73, 108)\n",
       " \t(48, 78, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 85, 94)\n",
       " \t(36, 76, 89)\n",
       " \t(35, 87, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 76, 89)\n",
       " \t(33, 85, 94)\n",
       " \t(30, 83, 91),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 76, 89)\n",
       " \t(30, 83, 91)\n",
       " \t(33, 76, 88),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 52, 118)\n",
       " \t(31, 51, 117)\n",
       " \t(30, 50, 115),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 52, 117)\n",
       " \t(30, 52, 118)\n",
       " \t(30, 50, 115),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 53, 108)\n",
       " \t(41, 52, 117)\n",
       " \t(44, 55, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 52, 117)\n",
       " \t(46, 53, 108)\n",
       " \t(41, 48, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 51, 94)\n",
       " \t(37, 48, 101)\n",
       " \t(36, 51, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 48, 101)\n",
       " \t(30, 51, 94)\n",
       " \t(30, 48, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 66, 94)\n",
       " \t(28, 68, 87)\n",
       " \t(21, 71, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 68, 87)\n",
       " \t(21, 66, 94)\n",
       " \t(28, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 49, 101)\n",
       " \t(30, 51, 94)\n",
       " \t(24, 57, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(24, 53, 101)\n",
       " \t(28, 49, 101)\n",
       " \t(24, 57, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 56, 101)\n",
       " \t(20, 60, 101)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 60, 101)\n",
       " \t(22, 56, 101)\n",
       " \t(24, 57, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(38, 47, 108)\n",
       " \t(37, 48, 101)\n",
       " \t(30, 48, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(34, 47, 108)\n",
       " \t(38, 47, 108)\n",
       " \t(30, 48, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 61, 87)\n",
       " \t(39, 53, 94)\n",
       " \t(42, 56, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(38, 64, 87)\n",
       " \t(35, 61, 87)\n",
       " \t(42, 56, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 98, 117)\n",
       " \t(30, 98, 123)\n",
       " \t(30, 98, 110),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 98, 110)\n",
       " \t(30, 98, 123)\n",
       " \t(26, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 87, 135)\n",
       " \t(36, 80, 135)\n",
       " \t(25, 87, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(25, 87, 135)\n",
       " \t(36, 80, 135)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 80, 135)\n",
       " \t(35, 87, 135)\n",
       " \t(36, 84, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 80, 135)\n",
       " \t(34, 76, 135)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 61, 87)\n",
       " \t(35, 71, 87)\n",
       " \t(31, 71, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 68, 87)\n",
       " \t(31, 61, 87)\n",
       " \t(31, 71, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 61, 87)\n",
       " \t(28, 68, 87)\n",
       " \t(28, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 61, 87)\n",
       " \t(35, 61, 87)\n",
       " \t(38, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 61, 87)\n",
       " \t(38, 64, 87)\n",
       " \t(38, 68, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 71, 87)\n",
       " \t(31, 61, 87)\n",
       " \t(38, 68, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 57, 89)\n",
       " \t(31, 61, 87)\n",
       " \t(28, 64, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 61, 87)\n",
       " \t(31, 61, 87)\n",
       " \t(30, 57, 89),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 64, 108)\n",
       " \t(21, 66, 94)\n",
       " \t(21, 71, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 72, 101)\n",
       " \t(19, 64, 108)\n",
       " \t(21, 71, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 64, 108)\n",
       " \t(20, 60, 101)\n",
       " \t(21, 66, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 60, 101)\n",
       " \t(19, 64, 108)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 64, 108)\n",
       " \t(19, 80, 117)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 80, 117)\n",
       " \t(19, 66, 117)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(38, 64, 87)\n",
       " \t(44, 69, 94)\n",
       " \t(38, 68, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 69, 94)\n",
       " \t(38, 64, 87)\n",
       " \t(44, 62, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 58, 94)\n",
       " \t(44, 54, 101)\n",
       " \t(45, 56, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 54, 101)\n",
       " \t(43, 58, 94)\n",
       " \t(42, 56, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 54, 101)\n",
       " \t(46, 53, 108)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(45, 56, 101)\n",
       " \t(44, 54, 101)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(46, 58, 117)\n",
       " \t(46, 76, 126)\n",
       " \t(48, 76, 122),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(28, 89, 97)\n",
       " \t(30, 83, 91)\n",
       " \t(30, 95, 103),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 95, 103)\n",
       " \t(30, 83, 91)\n",
       " \t(32, 89, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(25, 82, 94)\n",
       " \t(30, 83, 91)\n",
       " \t(28, 89, 97),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 91, 133)\n",
       " \t(25, 87, 135)\n",
       " \t(26, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 91, 133)\n",
       " \t(35, 87, 135)\n",
       " \t(25, 87, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 87, 135)\n",
       " \t(30, 91, 133)\n",
       " \t(35, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 91, 133)\n",
       " \t(33, 96, 128)\n",
       " \t(34, 93, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 96, 128)\n",
       " \t(30, 91, 133)\n",
       " \t(27, 93, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 91, 133)\n",
       " \t(29, 96, 128)\n",
       " \t(30, 97, 127),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 96, 128)\n",
       " \t(30, 91, 133)\n",
       " \t(30, 97, 127),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(25, 87, 135)\n",
       " \t(22, 87, 132)\n",
       " \t(26, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 87, 132)\n",
       " \t(27, 93, 131)\n",
       " \t(26, 89, 134),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 87, 132)\n",
       " \t(21, 89, 129)\n",
       " \t(27, 93, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 75, 131)\n",
       " \t(22, 87, 132)\n",
       " \t(25, 87, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 96, 128)\n",
       " \t(26, 97, 123)\n",
       " \t(30, 97, 127),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 97, 123)\n",
       " \t(29, 96, 128)\n",
       " \t(27, 95, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 97, 123)\n",
       " \t(30, 98, 123)\n",
       " \t(30, 97, 127),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 84, 131)\n",
       " \t(36, 80, 135)\n",
       " \t(36, 84, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 80, 135)\n",
       " \t(41, 84, 131)\n",
       " \t(41, 79, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 73, 128)\n",
       " \t(22, 75, 131)\n",
       " \t(23, 69, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 73, 128)\n",
       " \t(23, 69, 128)\n",
       " \t(22, 59, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 52, 108)\n",
       " \t(28, 49, 101)\n",
       " \t(24, 53, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(26, 52, 108)\n",
       " \t(24, 53, 101)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 56, 112)\n",
       " \t(26, 52, 108)\n",
       " \t(19, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 49, 112)\n",
       " \t(26, 52, 108)\n",
       " \t(23, 56, 112),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 93, 117)\n",
       " \t(25, 97, 113)\n",
       " \t(26, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(48, 76, 122)\n",
       " \t(49, 73, 108)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 88, 101)\n",
       " \t(28, 89, 97)\n",
       " \t(26, 91, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(22, 89, 103)\n",
       " \t(23, 88, 101)\n",
       " \t(26, 91, 101),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(24, 80, 94)\n",
       " \t(23, 81, 96)\n",
       " \t(21, 71, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 83, 91)\n",
       " \t(29, 76, 88)\n",
       " \t(33, 76, 88),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 71, 87)\n",
       " \t(29, 76, 88)\n",
       " \t(31, 71, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 76, 88)\n",
       " \t(35, 71, 87)\n",
       " \t(33, 76, 88),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(39, 95, 117)\n",
       " \t(37, 97, 120)\n",
       " \t(36, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(37, 97, 116)\n",
       " \t(39, 95, 117)\n",
       " \t(36, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(33, 97, 126)\n",
       " \t(30, 98, 123)\n",
       " \t(36, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 97, 123)\n",
       " \t(33, 97, 126)\n",
       " \t(36, 98, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 92, 127)\n",
       " \t(20, 89, 127)\n",
       " \t(26, 97, 123),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 89, 127)\n",
       " \t(23, 92, 127)\n",
       " \t(21, 89, 129),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 82, 128)\n",
       " \t(46, 76, 126)\n",
       " \t(44, 75, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(42, 76, 130)\n",
       " \t(44, 82, 128)\n",
       " \t(44, 75, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 84, 131)\n",
       " \t(44, 82, 128)\n",
       " \t(41, 79, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(44, 82, 128)\n",
       " \t(42, 76, 130)\n",
       " \t(41, 79, 131),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 80, 117)\n",
       " \t(20, 80, 128)\n",
       " \t(19, 66, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(19, 66, 117)\n",
       " \t(20, 80, 128)\n",
       " \t(20, 76, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(20, 80, 128)\n",
       " \t(21, 76, 130)\n",
       " \t(20, 76, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(21, 76, 130)\n",
       " \t(20, 80, 128)\n",
       " \t(22, 87, 132),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(34, 76, 135)\n",
       " \t(34, 68, 131)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(34, 68, 131)\n",
       " \t(29, 68, 131)\n",
       " \t(26, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 63, 128)\n",
       " \t(34, 68, 131)\n",
       " \t(35, 63, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 68, 131)\n",
       " \t(34, 68, 131)\n",
       " \t(29, 63, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 67, 128)\n",
       " \t(34, 68, 131)\n",
       " \t(34, 76, 135),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 65, 127)\n",
       " \t(34, 68, 131)\n",
       " \t(41, 67, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(49, 73, 108)\n",
       " \t(47, 71, 101)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 71, 101)\n",
       " \t(47, 63, 101)\n",
       " \t(49, 59, 108),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 71, 101)\n",
       " \t(44, 69, 94)\n",
       " \t(44, 62, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(47, 63, 101)\n",
       " \t(47, 71, 101)\n",
       " \t(44, 62, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 76, 89)\n",
       " \t(41, 76, 94)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 87, 97)\n",
       " \t(36, 76, 89)\n",
       " \t(38, 87, 100),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(43, 72, 94)\n",
       " \t(36, 76, 89)\n",
       " \t(38, 68, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(41, 76, 94)\n",
       " \t(36, 76, 89)\n",
       " \t(43, 72, 94),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(36, 76, 89)\n",
       " \t(35, 71, 87)\n",
       " \t(38, 68, 87),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(35, 71, 87)\n",
       " \t(36, 76, 89)\n",
       " \t(33, 76, 88),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(31, 51, 117)\n",
       " \t(30, 52, 118)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 52, 118)\n",
       " \t(30, 59, 125)\n",
       " \t(39, 51, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(23, 69, 128)\n",
       " \t(29, 52, 117)\n",
       " \t(22, 59, 117),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 63, 128)\n",
       " \t(29, 52, 117)\n",
       " \t(23, 69, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 59, 125)\n",
       " \t(29, 52, 117)\n",
       " \t(29, 63, 128),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(30, 52, 118)\n",
       " \t(29, 52, 117)\n",
       " \t(30, 59, 125),\n",
       " 3-simplex in 3D space\n",
       " Vertices:\n",
       " \t(29, 52, 117)\n",
       " \t(30, 50, 115)\n",
       " \t(22, 59, 117)]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qhull.simplices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "d5676f6a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(294, 3)"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(qhull.vertices).shape\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39e11b95",
   "metadata": {},
   "source": [
    "The data for a surface layer is defined by a 3-tuple of its:\n",
    "\n",
    "1. vertices, \n",
    "2. faces, and \n",
    "3. vertex values. \n",
    "\n",
    "* The vertices are an NxD array of N vertices in D coordinates.\n",
    "\n",
    "* The faces are an Mx3 integer array of the indices of the triangles making up the faces of the surface.\n",
    "\n",
    "* The vertex values are a length N list of values to associate with each vertex to use alongside a colormap.\n",
    "\n",
    "This 3-tuple is accessible through the layer.data property.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "da078cb2",
   "metadata": {},
   "outputs": [],
   "source": [
    "vertices = np.array(qhull.vertices)\n",
    "values = np.ones(len(vertices))\n",
    "surface = (qhull.vertices, faces, values)\n",
    "viewer.add_surface(surface)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "04b48a96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Viewer(axes=Axes(visible=False, labels=True, colored=True, dashed=False, arrows=True), camera=Camera(center=(0.0, 5.0, 10.0), zoom=16.435, angles=(0.0, 0.0, 90.0), perspective=0, interactive=True), cursor=Cursor(position=(1, 1), scaled=True, size=1, style=<CursorStyle.STANDARD: 'standard'>), dims=Dims(ndim=2, ndisplay=2, last_used=0, range=((0.0, 11.0, 1.0), (0.0, 21.0, 1.0)), current_step=(5, 10), order=(0, 1), axis_labels=('0', '1')), grid=GridCanvas(stride=1, shape=(-1, -1), enabled=False), layers=[<Surface layer 'surface' at 0x28c7bd6a0>], scale_bar=ScaleBar(visible=False, colored=False, ticks=True, position=<Position.BOTTOM_RIGHT: 'bottom_right'>, font_size=10, unit=None), text_overlay=TextOverlay(visible=False, color=(0.5, 0.5, 0.5, 1.0), font_size=10, position=<TextOverlayPosition.TOP_LEFT: 'top_left'>, text=''), overlays=Overlays(interaction_box=InteractionBox(points=None, show=False, show_handle=False, show_vertices=False, selection_box_drag=None, selection_box_final=None, transform_start=<napari.utils.transforms.transforms.Affine object at 0x2b0524e50>, transform_drag=<napari.utils.transforms.transforms.Affine object at 0x2b0524eb0>, transform_final=<napari.utils.transforms.transforms.Affine object at 0x2b0524f10>, transform=<napari.utils.transforms.transforms.Affine object at 0x2b0524f70>, allow_new_selection=True, selected_vertex=None)), help='', status='Ready', tooltip=Tooltip(visible=False, text=''), theme='dark', title='napari', mouse_move_callbacks=[<function InteractionBoxMouseBindings.initialize_mouse_events.<locals>.mouse_move at 0x28c7c5940>], mouse_drag_callbacks=[<function InteractionBoxMouseBindings.initialize_mouse_events.<locals>.mouse_drag at 0x28c7c5820>], mouse_double_click_callbacks=[], mouse_wheel_callbacks=[<function dims_scroll at 0x283967dc0>], _persisted_mouse_event={}, _mouse_drag_gen={}, _mouse_wheel_gen={}, keymap={'Shift': <function InteractionBoxMouseBindings.initialize_key_events.<locals>.hold_to_lock_aspect_ratio at 0x28c7c5430>, 'Control-Shift-R': <function InteractionBoxMouseBindings._reset_active_layer_affine at 0x28c7c5700>, 'Control-Shift-A': <function InteractionBoxMouseBindings._transform_active_layer at 0x28c7c5670>})"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vertices = np.array([[0, 0], [0, 20], [10, 0], [10, 10]])\n",
    "faces = np.array([[0, 1, 2], [1, 2, 3]])\n",
    "values = np.ones(len(vertices))#np.linspace(0, 1, len(vertices))\n",
    "surface = (vertices, faces, values)\n",
    "\n",
    "napari.view_surface(surface)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "1e978291",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "vertices.shape (4, 2)\n",
      "faces.shape (2, 3)\n",
      "values.shape (4,)\n"
     ]
    }
   ],
   "source": [
    "print(\"vertices.shape\", vertices.shape)\n",
    "print(\"faces.shape\", faces.shape)\n",
    "print(\"values.shape\", values.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "cfbd1fd1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(vertices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "d3a9f80f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0,  0],\n",
       "       [ 0, 20],\n",
       "       [10,  0],\n",
       "       [10, 10],\n",
       "       [ 5,  5]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "verts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "7b63cbc8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x297928c40>"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "verts = np.array([[0, 0], [0, 20], [10, 0], [10, 10], [5, 5]])\n",
    "img = np.zeros((21,21))\n",
    "img[0, 0] = 1\n",
    "img[0, 20] = 1\n",
    "img[10, 0] = 1\n",
    "img[10, 10] = 1\n",
    "img[5, 5] = 1\n",
    "plt.imshow(img)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "fd9b0e31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<pyhull.convex_hull.ConvexHull at 0x29dfca550>"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_pts = np.argwhere(img)\n",
    "test_qhull = ConvexHull(test_pts)\n",
    "test_qhull"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "7b70d488",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n",
      "4\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "print(len(test_qhull.points))\n",
    "print(len(test_qhull.vertices))\n",
    "print(len(test_qhull.simplices))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "ee125dad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  0]\n",
      " [ 0 20]\n",
      " [ 5  5]\n",
      " [10  0]\n",
      " [10 10]]\n"
     ]
    }
   ],
   "source": [
    "print(test_qhull.points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "aceec13b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 3], [1, 0], [3, 4], [4, 1]]\n"
     ]
    }
   ],
   "source": [
    "print(test_qhull.vertices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "e32fa430",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[ 0  0]\n",
      "  [10  0]]\n",
      "\n",
      " [[ 0 20]\n",
      "  [ 0  0]]\n",
      "\n",
      " [[10  0]\n",
      "  [10 10]]\n",
      "\n",
      " [[10 10]\n",
      "  [ 0 20]]]\n"
     ]
    }
   ],
   "source": [
    "real_vertices = np.array([[test_qhull.points[pt1], test_qhull.points[pt2]] for pt1, pt2 in test_qhull.vertices])\n",
    "print(real_vertices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "8e4619d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2-simplex in 2D space\n",
      "Vertices:\n",
      "\t(0, 0)\n",
      "\t(10, 0), 2-simplex in 2D space\n",
      "Vertices:\n",
      "\t(0, 20)\n",
      "\t(0, 0), 2-simplex in 2D space\n",
      "Vertices:\n",
      "\t(10, 0)\n",
      "\t(10, 10), 2-simplex in 2D space\n",
      "Vertices:\n",
      "\t(10, 10)\n",
      "\t(0, 20)]\n"
     ]
    }
   ],
   "source": [
    "print(test_qhull.simplices)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f1550d9",
   "metadata": {},
   "source": [
    "## Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "a10681d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x2aa5e3550>"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jyD+izttYIr+jnpMqHf1ek/7Nx+6jon8DlgGbquqfF3dEo0vyxwyuEgBOAb601M4nyW3AJQz+lHc/g/IAXwf+C3gZgz+Xf8dSmZBnhvO5hMFtRAG7gXdPuUefWEkuBr4LPAA81zV/kMFzhuP6/Ux8MEhaeJN+KyFpERgMkhoGg6SGwSCpYTBIahgMkhoGg6TG/wPE2KDqRpZIKgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "pts = np.array([[0, 0], [0, 20], [10, 0], [10, 10], [5, 5]])\n",
    "img = np.zeros((21, 21))\n",
    "img[0, 0] = 1\n",
    "img[0, 20] = 1\n",
    "img[10, 0] = 1\n",
    "img[10, 10] = 1\n",
    "img[5, 5] = 1\n",
    "\n",
    "plt.imshow(img)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "79df5a57",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "vertices\n",
      "[[0, 2], [1, 0], [2, 3], [3, 1]]\n",
      "points\n",
      "[[ 0  0]\n",
      " [ 0 20]\n",
      " [10  0]\n",
      " [10 10]\n",
      " [ 5  5]]\n",
      "simplices\n",
      "[2-simplex in 2D space\n",
      "Vertices:\n",
      "\t(0, 0)\n",
      "\t(10, 0), 2-simplex in 2D space\n",
      "Vertices:\n",
      "\t(0, 20)\n",
      "\t(0, 0), 2-simplex in 2D space\n",
      "Vertices:\n",
      "\t(10, 0)\n",
      "\t(10, 10), 2-simplex in 2D space\n",
      "Vertices:\n",
      "\t(10, 10)\n",
      "\t(0, 20)]\n"
     ]
    }
   ],
   "source": [
    "from pyhull.convex_hull import ConvexHull\n",
    "\n",
    "hull = ConvexHull(pts)\n",
    "print(\"vertices\")\n",
    "print(hull.vertices)\n",
    "print(\"points\")\n",
    "print(hull.points)\n",
    "print(\"simplices\")\n",
    "print(hull.simplices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "2401203d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vertices\n",
      "[[2, 4, 0], [3, 4, 2], [4, 1, 0], [4, 3, 1]]\n",
      "Points\n",
      "[[ 0  0]\n",
      " [ 0 20]\n",
      " [10  0]\n",
      " [10 10]\n",
      " [ 5  5]]\n"
     ]
    }
   ],
   "source": [
    "from pyhull.delaunay import DelaunayTri\n",
    "\n",
    "tri = DelaunayTri(pts)\n",
    "print(\"Vertices\")\n",
    "print(tri.vertices)\n",
    "print(\"Points\")\n",
    "print(tri.points)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "47cc0aa9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__class__',\n",
       " '__delattr__',\n",
       " '__dict__',\n",
       " '__dir__',\n",
       " '__doc__',\n",
       " '__eq__',\n",
       " '__format__',\n",
       " '__ge__',\n",
       " '__getattribute__',\n",
       " '__gt__',\n",
       " '__hash__',\n",
       " '__init__',\n",
       " '__init_subclass__',\n",
       " '__le__',\n",
       " '__lt__',\n",
       " '__module__',\n",
       " '__ne__',\n",
       " '__new__',\n",
       " '__reduce__',\n",
       " '__reduce_ex__',\n",
       " '__repr__',\n",
       " '__setattr__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__subclasshook__',\n",
       " '__weakref__',\n",
       " 'dim',\n",
       " 'points',\n",
       " 'simplices',\n",
       " 'vertices']"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(tri)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "74d9a0f8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}