diff --git a/src/meson.build b/src/meson.build
index 6d6d59cca0f..5b4df8a8290 100644
--- a/src/meson.build
+++ b/src/meson.build
@@ -127,6 +127,7 @@ curl = declare_dependency(
     cc.find_library('curl'),
   ]
 )
+# Cannot be found via pkg-config
 ec = declare_dependency(
   dependencies: [
     cc.find_library('ec'),
diff --git a/src/sage/geometry/meson.build b/src/sage/geometry/meson.build
index ce70f0d691a..4964ad981a5 100644
--- a/src/sage/geometry/meson.build
+++ b/src/sage/geometry/meson.build
@@ -41,6 +41,6 @@ endforeach
 
 install_subdir('hyperbolic_space', install_dir: sage_install_dir / 'geometry')
 install_subdir('hyperplane_arrangement', install_dir: sage_install_dir / 'geometry')
-install_subdir('polyhedron', install_dir: sage_install_dir / 'geometry')
+subdir('polyhedron')
 install_subdir('riemannian_manifolds', install_dir: sage_install_dir / 'geometry')
 subdir('triangulation')
diff --git a/src/sage/geometry/polyhedron/combinatorial_polyhedron/meson.build b/src/sage/geometry/polyhedron/combinatorial_polyhedron/meson.build
new file mode 100644
index 00000000000..fcf98755cb1
--- /dev/null
+++ b/src/sage/geometry/polyhedron/combinatorial_polyhedron/meson.build
@@ -0,0 +1,25 @@
+py.install_sources(
+    'all.py',
+    subdir: 'sage/geometry/polyhedron/combinatorial_polyhedron',
+)
+
+extension_data = {
+    'base': files('base.pyx'),
+    'combinatorial_face': files('combinatorial_face.pyx'),
+    'conversions': files('conversions.pyx'),
+    'face_iterator': files('face_iterator.pyx'),
+    'face_list_data_structure': files('face_list_data_structure.pyx'),
+    'list_of_faces': files('list_of_faces.pyx'),
+    'polyhedron_face_lattice': files('polyhedron_face_lattice.pyx'),
+}
+
+foreach name, pyx : extension_data
+    py.extension_module(name,
+        sources: pyx,
+        subdir: 'sage/geometry/polyhedron/combinatorial_polyhedron',
+        install: true,
+        include_directories: [inc_cpython, inc_data_structures, inc_rings],
+        dependencies: [py_dep, cysignals, gmp],
+    )
+endforeach
+
diff --git a/src/sage/geometry/polyhedron/meson.build b/src/sage/geometry/polyhedron/meson.build
new file mode 100644
index 00000000000..3234e6b0167
--- /dev/null
+++ b/src/sage/geometry/polyhedron/meson.build
@@ -0,0 +1,43 @@
+py.install_sources(
+    'all.py',
+    'backend_cdd.py',
+    'backend_cdd_rdf.py',
+    'backend_field.py',
+    'backend_normaliz.py',
+    'backend_number_field.py',
+    'backend_polymake.py',
+    'backend_ppl.py',
+    'base.py',
+    'base0.py',
+    'base1.py',
+    'base2.py',
+    'base3.py',
+    'base4.py',
+    'base5.py',
+    'base6.py',
+    'base7.py',
+    'base_QQ.py',
+    'base_RDF.py',
+    'base_ZZ.py',
+    'base_mutable.py',
+    'base_number_field.py',
+    'cdd_file_format.py',
+    'constructor.py',
+    'double_description.py',
+    'double_description_inhomogeneous.py',
+    'face.py',
+    'generating_function.py',
+    'lattice_euclidean_group_element.py',
+    'library.py',
+    'misc.py',
+    'palp_database.py',
+    'parent.py',
+    'plot.py',
+    'ppl_lattice_polygon.py',
+    'ppl_lattice_polytope.py',
+    'representation.py',
+    subdir: 'sage/geometry/polyhedron',
+)
+
+subdir('combinatorial_polyhedron')
+install_subdir('modules', install_dir: sage_install_dir / 'geometry/polyhedron')
diff --git a/src/sage/libs/coxeter3/meson.build b/src/sage/libs/coxeter3/meson.build
index 877508d7916..8d9ea2019dc 100644
--- a/src/sage/libs/coxeter3/meson.build
+++ b/src/sage/libs/coxeter3/meson.build
@@ -1,3 +1,4 @@
+coxeter3 = cc.find_library('coxeter3', required: false)
 py.install_sources(
     '__init__.py',
     'all__sagemath_coxeter3.py',
@@ -6,18 +7,20 @@ py.install_sources(
 )
 
 
-extension_data_cpp = {
-    # 'coxeter': files('coxeter.pyx'), # not yet on conda
-}
+if coxeter3.found()
+    extension_data_cpp = {
+        'coxeter': files('coxeter.pyx'),
+    }
 
-foreach name, pyx : extension_data_cpp
-    py.extension_module(name,
-        sources: pyx,
-        subdir: 'sage/libs/coxeter3',
-        install: true,
-        override_options : ['cython_language=cpp'],
-        include_directories: [],
-        dependencies: [py_dep, cysignals, coxeter3],
-    )
-endforeach
+    foreach name, pyx : extension_data_cpp
+        py.extension_module(name,
+            sources: pyx,
+            subdir: 'sage/libs/coxeter3',
+            install: true,
+            override_options : ['cython_language=cpp'],
+            include_directories: [],
+            dependencies: [py_dep, cysignals, coxeter3],
+        )
+    endforeach
+endif
 
diff --git a/src/sage/libs/eclib/meson.build b/src/sage/libs/eclib/meson.build
index d47852e4d7b..5f5766801a3 100644
--- a/src/sage/libs/eclib/meson.build
+++ b/src/sage/libs/eclib/meson.build
@@ -20,7 +20,7 @@ foreach name, pyx : extension_data_cpp
         install: true,
         override_options : ['cython_language=cpp'],
         include_directories: [inc_cpython, inc_ext, inc_flint, inc_ntl, inc_rings],
-        dependencies: [py_dep, cysignals, flint, gmp],
+        dependencies: [py_dep, cysignals, flint, gmp, ec],
     )
 endforeach
 
diff --git a/src/sage/modular/arithgroup/farey.cpp b/src/sage/modular/arithgroup/farey.cpp
index 209391676de..5c912b46ca9 100644
--- a/src/sage/modular/arithgroup/farey.cpp
+++ b/src/sage/modular/arithgroup/farey.cpp
@@ -29,7 +29,7 @@
 #include <Python.h>
 
 #include "farey.hpp"
-#include "sage/modular/arithgroup/farey_symbol.h"
+#include "farey_symbol.h"
 
 
 using namespace std;
diff --git a/src/sage/modular/arithgroup/meson.build b/src/sage/modular/arithgroup/meson.build
index 50dca19bc89..23772d05a33 100644
--- a/src/sage/modular/arithgroup/meson.build
+++ b/src/sage/modular/arithgroup/meson.build
@@ -28,7 +28,7 @@ foreach name, pyx : extension_data
 endforeach
 
 extension_data_cpp = {
-    'farey_symbol': files('farey_symbol.pyx'),
+    'farey_symbol': files('farey_symbol.pyx', 'sl2z.cpp', 'farey.cpp'),
 }
 
 foreach name, pyx : extension_data_cpp
diff --git a/src/sage/rings/meson.build b/src/sage/rings/meson.build
index 442800e8eab..63438447097 100644
--- a/src/sage/rings/meson.build
+++ b/src/sage/rings/meson.build
@@ -101,7 +101,7 @@ foreach name, pyx : extension_data
 endforeach
 
 extension_data_cpp = {
-    'bernmm': files('bernmm.pyx'),
+    'bernmm': files('bernmm.pyx', 'bernmm/bern_modp.cpp', 'bernmm/bern_modp_util.cpp'),#, 'bernmm/bern_rat.cpp'), - TODO: Compilation error
     'bernoulli_mod_p': files('bernoulli_mod_p.pyx'),
     'fraction_field_FpT': files('fraction_field_FpT.pyx'),
     'rational': files('rational.pyx'),
diff --git a/src/sage/rings/polynomial/pbori/meson.build b/src/sage/rings/polynomial/pbori/meson.build
index c087b554e01..56482234dda 100644
--- a/src/sage/rings/polynomial/pbori/meson.build
+++ b/src/sage/rings/polynomial/pbori/meson.build
@@ -3,11 +3,8 @@ brial = declare_dependency(
     cc.find_library('brial', required: false),
   ]
 )
-brial_groebner = declare_dependency(
-  dependencies: [
-    cc.find_library('brial-groebner', required: false),
-  ]
-)
+# Cannot be found via pkg-config
+brial_groebner = cc.find_library('brial_groebner')
 
 py.install_sources(
     'PyPolyBoRi.py',
diff --git a/src/sage/schemes/hyperelliptic_curves/meson.build b/src/sage/schemes/hyperelliptic_curves/meson.build
index b64793152ec..35cdc5c72a8 100644
--- a/src/sage/schemes/hyperelliptic_curves/meson.build
+++ b/src/sage/schemes/hyperelliptic_curves/meson.build
@@ -20,7 +20,7 @@ py.install_sources(
 )
 
 extension_data_cpp = {
-    'hypellfrob': files('hypellfrob.pyx'),
+    'hypellfrob': files('hypellfrob.pyx', 'hypellfrob/hypellfrob.cpp', 'hypellfrob/recurrences_ntl.cpp'),
 }
 
 foreach name, pyx : extension_data_cpp
diff --git a/src/sage/stats/distributions/meson.build b/src/sage/stats/distributions/meson.build
index 1eb9d97f24f..b5b8a74e3bb 100644
--- a/src/sage/stats/distributions/meson.build
+++ b/src/sage/stats/distributions/meson.build
@@ -6,7 +6,7 @@ py.install_sources(
 )
 
 extension_data = {
-    'discrete_gaussian_integer': files('discrete_gaussian_integer.pyx'),
+    'discrete_gaussian_integer': files('discrete_gaussian_integer.pyx', 'dgs_gauss_mp.c', 'dgs_gauss_dp.c', 'dgs_bern.c'),
 }
 
 foreach name, pyx : extension_data