Number of states for twisty puzzles

Note

#states denotes the number of combinations of the puzzle, where permutations within identical pieces (e.g. centers of 4x4x4 cube with same color) are ignored, orientations of face centers are ignored.
#states_super denotes the number of combination of the super puzzle, where identical pieces are treated as distinguishable and the orientation of face centers are considered.
All puzzle definations are copied from cubing.js, which might be different from normal cognition, e.g. only 180-degree moves are available for pyramorphix.

2x2x2 (c f 0)

#states= 3674160
#states_super= 3674160

3x3x3 (c f 0.333333333333333)

#states= 4.33E+19 = 43252003274489856000
#states_super= 8.86E+22 = 88580102706155225088000

4x4x4 (c f 0.5 f 0)

#states= 7.4E+45 = 7401196841564901869874093974498574336000000000
#states_super= 7.07E+53 = 707195371192426622240452051915172831683411968000000000

5x5x5 (c f 0.6 f 0.2)

#states= 2.83E+74 = 282870942277741856536180333107150328293127731985672134721536000000000000000
#states_super= 5.29E+93 = 5289239086872492808525454741861751983960246149231077646632506991757159229816832000000000000000

6x6x6 (c f 0.666666666666667 f 0.333333333333333 f 0)

#states= 1.57E+116 = 157152858401024063281013959519483771508510790313968742344694684829502629887168573442107637760000000000000000000000000
#states_super= 1.31E+148 = 13100024355233283052810092676794378650621714232853978724635727939533635592901050796648498942325745447229267325774462304911360000000000000000000000000

7x7x7 (c f 0.714285714285714 f 0.428571428571429 f 0.142857142857143)

#states= 1.95E+160 = 19500551183731307835329126754019748794904992692043434567152132912323232706135469180065278712755853360682328551719137311299993600000000000000000000000000000000000
#states_super= 3.04E+211 = 30394959344628313725196721342080594178969399869254568458927606797888466511926167976029813263013109351048271452761427038626673512301072047453583839762885164901951680152889144115200000000000000000000000000000000000

8x8x8 (c f 0.75 f 0.5 f 0.25 f 0)

#states= 3.52E+217 = 35173780923109452777509592367006557398539936328978098352427605879843998663990903628634874024098344287402504043608416113016679717941937308041012307368528117622006727311360000000000000000000000000000000000000000000000000
#states_super= 2.33E+289 = 23353724131189876512168271318390516987450208930148898921181119386513499225982408507188446113843749245656482211219793230972657112414116278219439446278039837070296161265705342329444852531876787573949274076152634020567414684765443033593576161280000000000000000000000000000000000000000000000000

9x9x9 (c f 0.777777777777778 f 0.555555555555556 f 0.333333333333333 f 0.111111111111111)

#states= 1.42E+277 = 14170392390542612915246393916889970752732946384514830589276833655387444667609821068034079045039617216635075219765012566330942990302517903971787699783519265329288048603083134861573075573092224082416866010882486829056000000000000000000000000000000000000000000000000000000000000000
#states_super= 1.68E+376 = 16809751140223458272424760501777788523130938093911350611182390070359806658197328025195621690843332309548793029460267557905683379969958528553451303587768715930949136217737613888428518811944806263633543241734427383066486840465994695163996113388364992239184878972888538572079642014954645725674288344275031316525744128000000000000000000000000000000000000000000000000000000000000000

skewb (c v 0)

#states= 3149280
#states_super= 100776960

master skewb (c v 0.275)

#states= 4.22E+28 = 42250536084530912624640000000
#states_super= 1.38E+33 = 1384465566417908944884203520000000

professor skewb (c v 0 v 0.38)

#states= 3.17E+64 = 31751712428465834357338964143132445189189350195200000000000000000
#states_super= 1.09E+75 = 1090980531778059984144992228650164120672646334719001729433600000000000000000

compy cube (c v 0.915641442663986)

#states= 5.24E+11 = 523788249600
#states_super= 1.45E+10 = 14549673600

helicopter (c e 0.707106781186547)

#states= 1.18E+19 = 11848661611315200000
#states_super= 1.18E+19 = 11848661611315200000

curvy copter (c e 0.83)

#states= 6.32E+19 = 63192861927014400000
#states_super= 3.79E+20 = 379157171562086400000

dino (c v 0.577350269189626)

#states= 19958400
#states_super= 19958400

little chop (c e 0)

#states= 1.35E+14 = 135277939046250
#states_super= 1.29E+22 = 12926008369442488320000

pyramorphix (t e 0)

#states= 24
#states_super= 24

mastermorphix (t e 0.346184634065199)

#states= 5308416
#states_super= 5308416

pyraminx (t v 0.333333333333333 v 1.66666666666667)

#states= 75582720
#states_super= 75582720

tetraminx (t v 0.333333333333333)

#states= 933120
#states_super= 933120

master pyraminx (t v 0 v 1 v 2)

#states= 2.17E+17 = 217225462874112000
#states_super= 5.87E+18 = 5865087497601024000

master tetraminx (t v 0 v 1)

#states= 2.68E+15 = 2681795837952000
#states_super= 7.24E+16 = 72408487624704000

professor pyraminx (t v -0.2 v 0.6 v 1.4 v 2.2)

#states= 1.92E+31 = 19228688422470957567836160000000
#states_super= 3.36E+35 = 336425132639551873606861455360000000

professor tetraminx (t v -0.2 v 0.6 v 1.4)

#states= 2.37E+29 = 237391215092234044047360000000
#states_super= 4.15E+33 = 4153396699253726834652610560000000

royal pyraminx (t v -0.333333333333333 v 0.333333333333333 v 1 v 1.66666666666667 v 2.33333333333333)

#states= 5.24E+49 = 52425105093745505455227317179687895040000000000000
#states_super= 1.43E+58 = 14264755341376105044291307862676743489511751680000000000000

royal tetraminx (t v -0.333333333333333 v 0.333333333333333 v 1 v 1.66666666666667)

#states= 6.47E+47 = 647223519675870437718855767650467840000000000000
#states_super= 1.76E+56 = 176108090634272901781374171144157327031009280000000000000

emperor pyraminx (t v -0.428571428571429 v 0.142857142857143 v 0.714285714285714 v 1.28571428571429 v 1.85714285714286 v 2.42857142857143)

#states= 2.06E+70 = 20582183665033346731252760185588627707250626464317440000000000000000000
#states_super= 6.35E+85 = 63493642565300801642123248005585826168872066473591291524377571491840000000000000000000

emperor tetraminx (t v -0.428571428571429 v 0.142857142857143 v 0.714285714285714 v 1.28571428571429 v 1.85714285714286)

#states= 2.54E+68 = 254101032901646255941392101056649724780871931658240000000000000000000
#states_super= 7.84E+83 = 783872130435812365952138864266491681097186005846806068202192240640000000000000000000

Jing pyraminx (t f 0)

#states= 3732480
#states_super= 100776960

master pyramorphix (t e 0.866025403784437)

#states= 1327104
#states_super= 663552

megaminx (d f 0.7)

#states= 1.01E+68 = 100669616553523347122516032313645505168688116411019768627200000000000
#states_super= 4.92E+75 = 4915508620777507183716603140314721932064849434131824640000000000000000000000

gigaminx (d f 0.64 f 0.82)

#states= 3.65E+263 = 364790115307330759863081610372318101265506588175570326142504636524420418052012591965833824494002983141195363719832622599859321673282378258285548922759556475267223939167970310584246376631322981975599093194264275595527530658078092007833600000000000000000000000000000
#states_super= 1.77E+321 = 1769999026971081596626136210218664975727305679442738996896557803120073610269088872616782217187857449900174070287143671828412449753217392042540844562040392079111521059156483175283253597935863183559784599959429918940662260588730578953586271566355097719301734400000000000000000000000000000000000000000000000000000000000000000

pentultimate (d f 0)

#states= 5.64E+33 = 5643573414231758192239391539200000
#states_super= 1.38E+42 = 1377825540583925339902195200000000000000000

master pentultimate (d f 0.1)

#states= 3.75E+131 = 375019654400354707294669633353803254406934223608759102596973605814708295711798760960476283799591402976418152100501913600000000000000
#states_super= 4.08E+164 = 408168079675758399486743602420077681306164286932710494706151936097841953549054044822725584360936765008262429021066931129339084800000000000000000000000000000000000000

elite pentultimate (d f 0 f 0.145905)

#states= 1.91E+286 = 19085288228427121650439609770193914119589628690030202411929286187060684915502661143430065271127138951944479847678953128405351576427442301665945515719083162855213810611712986863456506119775904690101944001680763368203841916366437706170691711644379056683605148303360000000000000000000000000
#states_super= 4.13E+368 = 412832277860719168055227327183855728963127843891619830750034166184725822995600072437273903121095834513265745412404712671205049029008818491369231781086252553896782017229376386575503521502637367962999944984605967262116189091742335504930566257008635158089654200772699405199545083441054227896803000320000000000000000000000000000000000000000000000000000000000000000000000000

starminx (d v 0.937962370425399)

#states= 2.48E+50 = 248270459431215031814452911028288348886138880000000
#states_super= 8.28E+49 = 82756819810405010604817637009429449628712960000000

starminx 2 (d f 0.23606797749979)

#states= 2.65E+104 = 265250107370240367469162414694746375762242569590650060038924753298349372296676352306210867773440000000000
#states_super= 2.89E+137 = 288695874172821321990510884511315371379634080616088900725035437706502325786046417604536340030227920977920000000000000000000000000000000000

pyraminx crystal (d f 0.447213595499989)

#states= 1.68E+66 = 1677826942558722452041933871894091752811468606850329477120000000000
#states_super= 1.68E+66 = 1677826942558722452041933871894091752811468606850329477120000000000

chopasaurus (d v 0)

#states= 1.58E+91 = 15800663728104758909644418106446725732410808381024646912387887967512119371614031708160000000
#states_super= 3.36E+123 = 3357568651707114723890848010427580505412592679883579924191520615307429180657539536463643803648000000000000000000000000000000

big chop (d e 0)

#states= 1.45E+112 = 14516052935043314908425086486921095981497239833952164838015585093892581688832967020876755787637299754488037376000
#states_super= 5.77E+161 = 576990221086735801796034753752191543786610230415663802759437338529367082431389144856549058834900528204123296277839635969745972539424768000000000000000000000000000

skewb diamond (o f 0)

#states= 138240
#states_super= 100776960

FTO (o f 0.333333333333333)

#states= 3.14E+22 = 31408133379194880000000
#states_super= 1.32E+28 = 13188400838457446891520000000

master FTO (o f 0.5 f 0)

#states= 1.48E+44 = 147970626354794338756025552732160000000000000
#states_super= 1.71E+59 = 171177064096513260531495694352120921874141020160000000000000

Christopher's jewel (o v 0.577350269189626)

#states= 2.01E+15 = 2009078326886400
#states_super= 2.01E+15 = 2009078326886400

octastar (o e 0)

#states= 1.29E+22 = 12926008369442488320000
#states_super= 1.29E+22 = 12926008369442488320000

Trajber's octahedron (o v 0.433012701892219)

#states= 4.05E+19 = 40503019070029824000
#states_super= 8.86E+22 = 88580102706155225088000

radio chop (i f 0)

#states= 9.67E+113 = 967457895180780285952270515975606209946211361882723271959650922368017213678931673088000000000000000000000000000000
#states_super= 3.44E+123 = 3439460570041434595205258937511180029934851037929520897952289410802732331405284403206659506176000000000000000000000000000000

icosamate (i v 0)

#states= 1.19E+33 = 1185469517577945600000000000000000
#states_super= 1.38E+42 = 1377825540583925339902195200000000000000000

icosahedron 2 (i v 0.18759247376021)

#states= 1.58E+122 = 157923065373418904957539351074737544630583758186782014483622895529900508388034141319331840000000000000000000000000000000000
#states_super= 2.89E+137 = 288695874172821321990510884511315371379634080616088900725035437706502325786046417604536340030227920977920000000000000000000000000000000000

icosahedron 3 (i v 0.18759247376021 e 0)

#states= 2.32E+396 = 2316049301420563402622019094121817808649919261027764660300820734666969542073402766657452473402470512752594520726099285052905091451213533402350978624919468419707856115400350205964403580822973895744904033787022439641915310495461602212709310400193009145818552498488482495794930427982355505365839546302316335628655001600000000000000000000000000000000000000000000000000000000000000000000000000000000000
#states_super= 1.73E+488 = 172881239502678519142082581583416120426212419814819127630632369008962398056419425288748268528894084185689764583271135856071573284262394490470069249002602083336204358054874042285859400192450895000598622513811914367278747657726849479754550670967748843934214824207021869706602850856045617816972303653386045619350070506186522350722525359804257488182287792403356936279610655403935885889604047626128956419001548800000000000000000000000000000000000000000000000000000000000000000000000000000000000

icosahedron static faces (i v 0.84)

#states= 3.48E+48 = 3476722284130350643757822509056000000000000000000
#states_super= 6.95E+47 = 695344456826070128751564501811200000000000000000

icosahedron moving faces (i v 0.73)

#states= 2.11E+67 = 21146311567333012098028210464258305881119129600000000000000000000000
#states_super= 2.46E+76 = 24577543103887535918583015701573609660324247170659123200000000000000000000000

Eitan's star (i f 0.61803398874989)

#states= 2.24E+180 = 2244993471433157496895932168123233669700755234365187419849509622026846497302231883092088730046235053190997378990089032638895351209236889600000000000000000000000000000000000000000000
#states_super= 1.43E+205 = 14309853539048466370474851248867254196825108194060655872260229418585294590006490724868910777722309004840068133918957864342608932148921181272713242948349392112844800000000000000000000000000000000000000000000

2x2x2 + dino (c f 0 v 0.577350269189626)

#states= 2.58E+22 = 25852016738884976640000
#states_super= 2.58E+22 = 25852016738884976640000

2x2x2 + little chop (c f 0 e 0)

#states= 4.39E+29 = 439202899022422328631337500000
#states_super= 8.02E+45 = 8019921233611068269577854211520148275200000000

dino + little chop (c v 0.577350269189626 e 0)

#states= 1.35E+14 = 135277939046250
#states_super= 1.29E+22 = 12926008369442488320000

2x2x2 + dino + little chop (c f 0 v 0.577350269189626 e 0)

#states= 4.39E+29 = 439202899022422328631337500000
#states_super= 8.02E+45 = 8019921233611068269577854211520148275200000000

megaminx + chopasaurus (d f 0.61803398875 v 0)

#states= 1.58E+91 = 15800663728104758909644418106446725732410808381024646912387887967512119371614031708160000000
#states_super= 1.72E+124 = 17197302850207172976026294687555900149674255189647604489761447054013661657026422016033297530880000000000000000000000000000000

starminx combo (d f 0.23606797749979 v 0.937962370425399)

#states= 2.65E+104 = 265250107370240367469162414694746375762242569590650060038924753298349372296676352306210867773440000000000
#states_super= 2.89E+137 = 288695874172821321990510884511315371379634080616088900725035437706502325786046417604536340030227920977920000000000000000000000000000000000

Number of states for twisty puzzles

Note

2x2x2 (c f 0)

3x3x3 (c f 0.333333333333333)

4x4x4 (c f 0.5 f 0)

5x5x5 (c f 0.6 f 0.2)

6x6x6 (c f 0.666666666666667 f 0.333333333333333 f 0)

7x7x7 (c f 0.714285714285714 f 0.428571428571429 f 0.142857142857143)

8x8x8 (c f 0.75 f 0.5 f 0.25 f 0)

9x9x9 (c f 0.777777777777778 f 0.555555555555556 f 0.333333333333333 f 0.111111111111111)

skewb (c v 0)

master skewb (c v 0.275)

professor skewb (c v 0 v 0.38)

compy cube (c v 0.915641442663986)

helicopter (c e 0.707106781186547)

curvy copter (c e 0.83)

dino (c v 0.577350269189626)

little chop (c e 0)

pyramorphix (t e 0)

mastermorphix (t e 0.346184634065199)

pyraminx (t v 0.333333333333333 v 1.66666666666667)

tetraminx (t v 0.333333333333333)

master pyraminx (t v 0 v 1 v 2)

master tetraminx (t v 0 v 1)

professor pyraminx (t v -0.2 v 0.6 v 1.4 v 2.2)

professor tetraminx (t v -0.2 v 0.6 v 1.4)

royal pyraminx (t v -0.333333333333333 v 0.333333333333333 v 1 v 1.66666666666667 v 2.33333333333333)

royal tetraminx (t v -0.333333333333333 v 0.333333333333333 v 1 v 1.66666666666667)

emperor pyraminx (t v -0.428571428571429 v 0.142857142857143 v 0.714285714285714 v 1.28571428571429 v 1.85714285714286 v 2.42857142857143)

emperor tetraminx (t v -0.428571428571429 v 0.142857142857143 v 0.714285714285714 v 1.28571428571429 v 1.85714285714286)

Jing pyraminx (t f 0)

master pyramorphix (t e 0.866025403784437)

megaminx (d f 0.7)

gigaminx (d f 0.64 f 0.82)

pentultimate (d f 0)

master pentultimate (d f 0.1)

elite pentultimate (d f 0 f 0.145905)

starminx (d v 0.937962370425399)

starminx 2 (d f 0.23606797749979)

pyraminx crystal (d f 0.447213595499989)

chopasaurus (d v 0)

big chop (d e 0)

skewb diamond (o f 0)

FTO (o f 0.333333333333333)

master FTO (o f 0.5 f 0)

Christopher's jewel (o v 0.577350269189626)

octastar (o e 0)

Trajber's octahedron (o v 0.433012701892219)

radio chop (i f 0)

icosamate (i v 0)

icosahedron 2 (i v 0.18759247376021)

icosahedron 3 (i v 0.18759247376021 e 0)

icosahedron static faces (i v 0.84)

icosahedron moving faces (i v 0.73)

Eitan's star (i f 0.61803398874989)

2x2x2 + dino (c f 0 v 0.577350269189626)

2x2x2 + little chop (c f 0 e 0)

dino + little chop (c v 0.577350269189626 e 0)

2x2x2 + dino + little chop (c f 0 v 0.577350269189626 e 0)

megaminx + chopasaurus (d f 0.61803398875 v 0)

starminx combo (d f 0.23606797749979 v 0.937962370425399)

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