Play with this polytope as a twisty puzzle
This page is part of the Atlas of Small Regular Polytopess0 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 12, 67)( 13, 77)( 14, 76)( 15, 75)( 16, 74)( 17, 73)( 18, 72)( 19, 71)( 20, 70)( 21, 69)( 22, 68)( 23, 56)( 24, 66)( 25, 65)( 26, 64)( 27, 63)( 28, 62)( 29, 61)( 30, 60)( 31, 59)( 32, 58)( 33, 57)( 34, 45)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)( 40, 50)( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)( 89,144)( 90,154)( 91,153)( 92,152)( 93,151)( 94,150)( 95,149)( 96,148)( 97,147)( 98,146)( 99,145)(100,133)(101,143)(102,142)(103,141)(104,140)(105,139)(106,138)(107,137)(108,136)(109,135)(110,134)(111,122)(112,132)(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124)(121,123)(156,165)(157,164)(158,163)(159,162)(160,161)(166,221)(167,231)(168,230)(169,229)(170,228)(171,227)(172,226)(173,225)(174,224)(175,223)(176,222)(177,210)(178,220)(179,219)(180,218)(181,217)(182,216)(183,215)(184,214)(185,213)(186,212)(187,211)(188,199)(189,209)(190,208)(191,207)(192,206)(193,205)(194,204)(195,203)(196,202)(197,201)(198,200)(233,242)(234,241)(235,240)(236,239)(237,238)(243,298)(244,308)(245,307)(246,306)(247,305)(248,304)(249,303)(250,302)(251,301)(252,300)(253,299)(254,287)(255,297)(256,296)(257,295)(258,294)(259,293)(260,292)(261,291)(262,290)(263,289)(264,288)(265,276)(266,286)(267,285)(268,284)(269,283)(270,282)(271,281)(272,280)(273,279)(274,278)(275,277)(310,319)(311,318)(312,317)(313,316)(314,315)(320,375)(321,385)(322,384)(323,383)(324,382)(325,381)(326,380)(327,379)(328,378)(329,377)(330,376)(331,364)(332,374)(333,373)(334,372)(335,371)(336,370)(337,369)(338,368)(339,367)(340,366)(341,365)(342,353)(343,363)(344,362)(345,361)(346,360)(347,359)(348,358)(349,357)(350,356)(351,355)(352,354)(387,396)(388,395)(389,394)(390,393)(391,392)(397,452)(398,462)(399,461)(400,460)(401,459)(402,458)(403,457)(404,456)(405,455)(406,454)(407,453)(408,441)(409,451)(410,450)(411,449)(412,448)(413,447)(414,446)(415,445)(416,444)(417,443)(418,442)(419,430)(420,440)(421,439)(422,438)(423,437)(424,436)(425,435)(426,434)(427,433)(428,432)(429,431);; s1 := ( 1, 13)( 2, 12)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 23, 68)( 24, 67)( 25, 77)( 26, 76)( 27, 75)( 28, 74)( 29, 73)( 30, 72)( 31, 71)( 32, 70)( 33, 69)( 34, 57)( 35, 56)( 36, 66)( 37, 65)( 38, 64)( 39, 63)( 40, 62)( 41, 61)( 42, 60)( 43, 59)( 44, 58)( 45, 46)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 78,167)( 79,166)( 80,176)( 81,175)( 82,174)( 83,173)( 84,172)( 85,171)( 86,170)( 87,169)( 88,168)( 89,156)( 90,155)( 91,165)( 92,164)( 93,163)( 94,162)( 95,161)( 96,160)( 97,159)( 98,158)( 99,157)(100,222)(101,221)(102,231)(103,230)(104,229)(105,228)(106,227)(107,226)(108,225)(109,224)(110,223)(111,211)(112,210)(113,220)(114,219)(115,218)(116,217)(117,216)(118,215)(119,214)(120,213)(121,212)(122,200)(123,199)(124,209)(125,208)(126,207)(127,206)(128,205)(129,204)(130,203)(131,202)(132,201)(133,189)(134,188)(135,198)(136,197)(137,196)(138,195)(139,194)(140,193)(141,192)(142,191)(143,190)(144,178)(145,177)(146,187)(147,186)(148,185)(149,184)(150,183)(151,182)(152,181)(153,180)(154,179)(232,244)(233,243)(234,253)(235,252)(236,251)(237,250)(238,249)(239,248)(240,247)(241,246)(242,245)(254,299)(255,298)(256,308)(257,307)(258,306)(259,305)(260,304)(261,303)(262,302)(263,301)(264,300)(265,288)(266,287)(267,297)(268,296)(269,295)(270,294)(271,293)(272,292)(273,291)(274,290)(275,289)(276,277)(278,286)(279,285)(280,284)(281,283)(309,398)(310,397)(311,407)(312,406)(313,405)(314,404)(315,403)(316,402)(317,401)(318,400)(319,399)(320,387)(321,386)(322,396)(323,395)(324,394)(325,393)(326,392)(327,391)(328,390)(329,389)(330,388)(331,453)(332,452)(333,462)(334,461)(335,460)(336,459)(337,458)(338,457)(339,456)(340,455)(341,454)(342,442)(343,441)(344,451)(345,450)(346,449)(347,448)(348,447)(349,446)(350,445)(351,444)(352,443)(353,431)(354,430)(355,440)(356,439)(357,438)(358,437)(359,436)(360,435)(361,434)(362,433)(363,432)(364,420)(365,419)(366,429)(367,428)(368,427)(369,426)(370,425)(371,424)(372,423)(373,422)(374,421)(375,409)(376,408)(377,418)(378,417)(379,416)(380,415)(381,414)(382,413)(383,412)(384,411)(385,410);; s2 := ( 1,309)( 2,310)( 3,311)( 4,312)( 5,313)( 6,314)( 7,315)( 8,316)( 9,317)( 10,318)( 11,319)( 12,320)( 13,321)( 14,322)( 15,323)( 16,324)( 17,325)( 18,326)( 19,327)( 20,328)( 21,329)( 22,330)( 23,331)( 24,332)( 25,333)( 26,334)( 27,335)( 28,336)( 29,337)( 30,338)( 31,339)( 32,340)( 33,341)( 34,342)( 35,343)( 36,344)( 37,345)( 38,346)( 39,347)( 40,348)( 41,349)( 42,350)( 43,351)( 44,352)( 45,353)( 46,354)( 47,355)( 48,356)( 49,357)( 50,358)( 51,359)( 52,360)( 53,361)( 54,362)( 55,363)( 56,364)( 57,365)( 58,366)( 59,367)( 60,368)( 61,369)( 62,370)( 63,371)( 64,372)( 65,373)( 66,374)( 67,375)( 68,376)( 69,377)( 70,378)( 71,379)( 72,380)( 73,381)( 74,382)( 75,383)( 76,384)( 77,385)( 78,232)( 79,233)( 80,234)( 81,235)( 82,236)( 83,237)( 84,238)( 85,239)( 86,240)( 87,241)( 88,242)( 89,243)( 90,244)( 91,245)( 92,246)( 93,247)( 94,248)( 95,249)( 96,250)( 97,251)( 98,252)( 99,253)(100,254)(101,255)(102,256)(103,257)(104,258)(105,259)(106,260)(107,261)(108,262)(109,263)(110,264)(111,265)(112,266)(113,267)(114,268)(115,269)(116,270)(117,271)(118,272)(119,273)(120,274)(121,275)(122,276)(123,277)(124,278)(125,279)(126,280)(127,281)(128,282)(129,283)(130,284)(131,285)(132,286)(133,287)(134,288)(135,289)(136,290)(137,291)(138,292)(139,293)(140,294)(141,295)(142,296)(143,297)(144,298)(145,299)(146,300)(147,301)(148,302)(149,303)(150,304)(151,305)(152,306)(153,307)(154,308)(155,386)(156,387)(157,388)(158,389)(159,390)(160,391)(161,392)(162,393)(163,394)(164,395)(165,396)(166,397)(167,398)(168,399)(169,400)(170,401)(171,402)(172,403)(173,404)(174,405)(175,406)(176,407)(177,408)(178,409)(179,410)(180,411)(181,412)(182,413)(183,414)(184,415)(185,416)(186,417)(187,418)(188,419)(189,420)(190,421)(191,422)(192,423)(193,424)(194,425)(195,426)(196,427)(197,428)(198,429)(199,430)(200,431)(201,432)(202,433)(203,434)(204,435)(205,436)(206,437)(207,438)(208,439)(209,440)(210,441)(211,442)(212,443)(213,444)(214,445)(215,446)(216,447)(217,448)(218,449)(219,450)(220,451)(221,452)(222,453)(223,454)(224,455)(225,456)(226,457)(227,458)(228,459)(229,460)(230,461)(231,462);; poly := Group([s0,s1,s2]);;Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : s0 := Sym(462)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 12, 67)( 13, 77)( 14, 76)( 15, 75)( 16, 74)( 17, 73)( 18, 72)( 19, 71)( 20, 70)( 21, 69)( 22, 68)( 23, 56)( 24, 66)( 25, 65)( 26, 64)( 27, 63)( 28, 62)( 29, 61)( 30, 60)( 31, 59)( 32, 58)( 33, 57)( 34, 45)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)( 40, 50)( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 79, 88)( 80, 87)( 81, 86)( 82, 85)( 83, 84)( 89,144)( 90,154)( 91,153)( 92,152)( 93,151)( 94,150)( 95,149)( 96,148)( 97,147)( 98,146)( 99,145)(100,133)(101,143)(102,142)(103,141)(104,140)(105,139)(106,138)(107,137)(108,136)(109,135)(110,134)(111,122)(112,132)(113,131)(114,130)(115,129)(116,128)(117,127)(118,126)(119,125)(120,124)(121,123)(156,165)(157,164)(158,163)(159,162)(160,161)(166,221)(167,231)(168,230)(169,229)(170,228)(171,227)(172,226)(173,225)(174,224)(175,223)(176,222)(177,210)(178,220)(179,219)(180,218)(181,217)(182,216)(183,215)(184,214)(185,213)(186,212)(187,211)(188,199)(189,209)(190,208)(191,207)(192,206)(193,205)(194,204)(195,203)(196,202)(197,201)(198,200)(233,242)(234,241)(235,240)(236,239)(237,238)(243,298)(244,308)(245,307)(246,306)(247,305)(248,304)(249,303)(250,302)(251,301)(252,300)(253,299)(254,287)(255,297)(256,296)(257,295)(258,294)(259,293)(260,292)(261,291)(262,290)(263,289)(264,288)(265,276)(266,286)(267,285)(268,284)(269,283)(270,282)(271,281)(272,280)(273,279)(274,278)(275,277)(310,319)(311,318)(312,317)(313,316)(314,315)(320,375)(321,385)(322,384)(323,383)(324,382)(325,381)(326,380)(327,379)(328,378)(329,377)(330,376)(331,364)(332,374)(333,373)(334,372)(335,371)(336,370)(337,369)(338,368)(339,367)(340,366)(341,365)(342,353)(343,363)(344,362)(345,361)(346,360)(347,359)(348,358)(349,357)(350,356)(351,355)(352,354)(387,396)(388,395)(389,394)(390,393)(391,392)(397,452)(398,462)(399,461)(400,460)(401,459)(402,458)(403,457)(404,456)(405,455)(406,454)(407,453)(408,441)(409,451)(410,450)(411,449)(412,448)(413,447)(414,446)(415,445)(416,444)(417,443)(418,442)(419,430)(420,440)(421,439)(422,438)(423,437)(424,436)(425,435)(426,434)(427,433)(428,432)(429,431); s1 := Sym(462)!( 1, 13)( 2, 12)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 23, 68)( 24, 67)( 25, 77)( 26, 76)( 27, 75)( 28, 74)( 29, 73)( 30, 72)( 31, 71)( 32, 70)( 33, 69)( 34, 57)( 35, 56)( 36, 66)( 37, 65)( 38, 64)( 39, 63)( 40, 62)( 41, 61)( 42, 60)( 43, 59)( 44, 58)( 45, 46)( 47, 55)( 48, 54)( 49, 53)( 50, 52)( 78,167)( 79,166)( 80,176)( 81,175)( 82,174)( 83,173)( 84,172)( 85,171)( 86,170)( 87,169)( 88,168)( 89,156)( 90,155)( 91,165)( 92,164)( 93,163)( 94,162)( 95,161)( 96,160)( 97,159)( 98,158)( 99,157)(100,222)(101,221)(102,231)(103,230)(104,229)(105,228)(106,227)(107,226)(108,225)(109,224)(110,223)(111,211)(112,210)(113,220)(114,219)(115,218)(116,217)(117,216)(118,215)(119,214)(120,213)(121,212)(122,200)(123,199)(124,209)(125,208)(126,207)(127,206)(128,205)(129,204)(130,203)(131,202)(132,201)(133,189)(134,188)(135,198)(136,197)(137,196)(138,195)(139,194)(140,193)(141,192)(142,191)(143,190)(144,178)(145,177)(146,187)(147,186)(148,185)(149,184)(150,183)(151,182)(152,181)(153,180)(154,179)(232,244)(233,243)(234,253)(235,252)(236,251)(237,250)(238,249)(239,248)(240,247)(241,246)(242,245)(254,299)(255,298)(256,308)(257,307)(258,306)(259,305)(260,304)(261,303)(262,302)(263,301)(264,300)(265,288)(266,287)(267,297)(268,296)(269,295)(270,294)(271,293)(272,292)(273,291)(274,290)(275,289)(276,277)(278,286)(279,285)(280,284)(281,283)(309,398)(310,397)(311,407)(312,406)(313,405)(314,404)(315,403)(316,402)(317,401)(318,400)(319,399)(320,387)(321,386)(322,396)(323,395)(324,394)(325,393)(326,392)(327,391)(328,390)(329,389)(330,388)(331,453)(332,452)(333,462)(334,461)(335,460)(336,459)(337,458)(338,457)(339,456)(340,455)(341,454)(342,442)(343,441)(344,451)(345,450)(346,449)(347,448)(348,447)(349,446)(350,445)(351,444)(352,443)(353,431)(354,430)(355,440)(356,439)(357,438)(358,437)(359,436)(360,435)(361,434)(362,433)(363,432)(364,420)(365,419)(366,429)(367,428)(368,427)(369,426)(370,425)(371,424)(372,423)(373,422)(374,421)(375,409)(376,408)(377,418)(378,417)(379,416)(380,415)(381,414)(382,413)(383,412)(384,411)(385,410); s2 := Sym(462)!( 1,309)( 2,310)( 3,311)( 4,312)( 5,313)( 6,314)( 7,315)( 8,316)( 9,317)( 10,318)( 11,319)( 12,320)( 13,321)( 14,322)( 15,323)( 16,324)( 17,325)( 18,326)( 19,327)( 20,328)( 21,329)( 22,330)( 23,331)( 24,332)( 25,333)( 26,334)( 27,335)( 28,336)( 29,337)( 30,338)( 31,339)( 32,340)( 33,341)( 34,342)( 35,343)( 36,344)( 37,345)( 38,346)( 39,347)( 40,348)( 41,349)( 42,350)( 43,351)( 44,352)( 45,353)( 46,354)( 47,355)( 48,356)( 49,357)( 50,358)( 51,359)( 52,360)( 53,361)( 54,362)( 55,363)( 56,364)( 57,365)( 58,366)( 59,367)( 60,368)( 61,369)( 62,370)( 63,371)( 64,372)( 65,373)( 66,374)( 67,375)( 68,376)( 69,377)( 70,378)( 71,379)( 72,380)( 73,381)( 74,382)( 75,383)( 76,384)( 77,385)( 78,232)( 79,233)( 80,234)( 81,235)( 82,236)( 83,237)( 84,238)( 85,239)( 86,240)( 87,241)( 88,242)( 89,243)( 90,244)( 91,245)( 92,246)( 93,247)( 94,248)( 95,249)( 96,250)( 97,251)( 98,252)( 99,253)(100,254)(101,255)(102,256)(103,257)(104,258)(105,259)(106,260)(107,261)(108,262)(109,263)(110,264)(111,265)(112,266)(113,267)(114,268)(115,269)(116,270)(117,271)(118,272)(119,273)(120,274)(121,275)(122,276)(123,277)(124,278)(125,279)(126,280)(127,281)(128,282)(129,283)(130,284)(131,285)(132,286)(133,287)(134,288)(135,289)(136,290)(137,291)(138,292)(139,293)(140,294)(141,295)(142,296)(143,297)(144,298)(145,299)(146,300)(147,301)(148,302)(149,303)(150,304)(151,305)(152,306)(153,307)(154,308)(155,386)(156,387)(157,388)(158,389)(159,390)(160,391)(161,392)(162,393)(163,394)(164,395)(165,396)(166,397)(167,398)(168,399)(169,400)(170,401)(171,402)(172,403)(173,404)(174,405)(175,406)(176,407)(177,408)(178,409)(179,410)(180,411)(181,412)(182,413)(183,414)(184,415)(185,416)(186,417)(187,418)(188,419)(189,420)(190,421)(191,422)(192,423)(193,424)(194,425)(195,426)(196,427)(197,428)(198,429)(199,430)(200,431)(201,432)(202,433)(203,434)(204,435)(205,436)(206,437)(207,438)(208,439)(209,440)(210,441)(211,442)(212,443)(213,444)(214,445)(215,446)(216,447)(217,448)(218,449)(219,450)(220,451)(221,452)(222,453)(223,454)(224,455)(225,456)(226,457)(227,458)(228,459)(229,460)(230,461)(231,462); poly := sub<Sym(462)|s0,s1,s2>;Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;References : None.