Polytope of Type {36,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {36,4}*1152b
if this polytope has a name.
Group : SmallGroup(1152,153957)
Rank : 3
Schlafli Type : {36,4}
Number of vertices, edges, etc : 144, 288, 16
Order of s0s1s2 : 36
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {18,4}*576a
   3-fold quotients : {12,4}*384b
   4-fold quotients : {36,4}*288b
   6-fold quotients : {6,4}*192a
   8-fold quotients : {18,4}*144b
   12-fold quotients : {12,4}*96b
   16-fold quotients : {9,4}*72
   24-fold quotients : {6,4}*48c
   48-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0> of order 2.
      8 facets:
         8 of {36}*72
      84 vertex figures:
         60 of {4}*8
         24 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      8 facets:
         8 of {36}*72
      72 vertex figures:
         72 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 2.
      8 facets:
         8 of {36}*72
      72 vertex figures:
         72 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*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*s2*s1*s0*s1*s0*s1*s0*s2*s1> of order 4.
      4 facets:
         4 of {36}*72
      36 vertex figures:
         36 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      4 facets:
         4 of {36}*72
      48 vertex figures:
         24 of {4}*8
         24 of {2}*4
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0> of order 4.
      4 facets:
         4 of {36}*72
      54 vertex figures:
         36 of {2}*4
         18 of {4}*8

Permutation Representation (GAP) : 
s0 := (  3,  4)(  7,  8)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49,129)( 50,130)( 51,132)( 52,131)( 53,133)( 54,134)( 55,136)( 56,135)( 57,141)( 58,142)( 59,144)( 60,143)( 61,137)( 62,138)( 63,140)( 64,139)( 65,113)( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,125)( 74,126)( 75,128)( 76,127)( 77,121)( 78,122)( 79,124)( 80,123)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,109)( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(193,273)(194,274)(195,276)(196,275)(197,277)(198,278)(199,280)(200,279)(201,285)(202,286)(203,288)(204,287)(205,281)(206,282)(207,284)(208,283)(209,257)(210,258)(211,260)(212,259)(213,261)(214,262)(215,264)(216,263)(217,269)(218,270)(219,272)(220,271)(221,265)(222,266)(223,268)(224,267)(225,241)(226,242)(227,244)(228,243)(229,245)(230,246)(231,248)(232,247)(233,253)(234,254)(235,256)(236,255)(237,249)(238,250)(239,252)(240,251)(289,433)(290,434)(291,436)(292,435)(293,437)(294,438)(295,440)(296,439)(297,445)(298,446)(299,448)(300,447)(301,441)(302,442)(303,444)(304,443)(305,465)(306,466)(307,468)(308,467)(309,469)(310,470)(311,472)(312,471)(313,477)(314,478)(315,480)(316,479)(317,473)(318,474)(319,476)(320,475)(321,449)(322,450)(323,452)(324,451)(325,453)(326,454)(327,456)(328,455)(329,461)(330,462)(331,464)(332,463)(333,457)(334,458)(335,460)(336,459)(337,561)(338,562)(339,564)(340,563)(341,565)(342,566)(343,568)(344,567)(345,573)(346,574)(347,576)(348,575)(349,569)(350,570)(351,572)(352,571)(353,545)(354,546)(355,548)(356,547)(357,549)(358,550)(359,552)(360,551)(361,557)(362,558)(363,560)(364,559)(365,553)(366,554)(367,556)(368,555)(369,529)(370,530)(371,532)(372,531)(373,533)(374,534)(375,536)(376,535)(377,541)(378,542)(379,544)(380,543)(381,537)(382,538)(383,540)(384,539)(385,513)(386,514)(387,516)(388,515)(389,517)(390,518)(391,520)(392,519)(393,525)(394,526)(395,528)(396,527)(397,521)(398,522)(399,524)(400,523)(401,497)(402,498)(403,500)(404,499)(405,501)(406,502)(407,504)(408,503)(409,509)(410,510)(411,512)(412,511)(413,505)(414,506)(415,508)(416,507)(417,481)(418,482)(419,484)(420,483)(421,485)(422,486)(423,488)(424,487)(425,493)(426,494)(427,496)(428,495)(429,489)(430,490)(431,492)(432,491);;
s1 := (  1,337)(  2,340)(  3,339)(  4,338)(  5,352)(  6,349)(  7,350)(  8,351)(  9,347)( 10,346)( 11,345)( 12,348)( 13,342)( 14,343)( 15,344)( 16,341)( 17,369)( 18,372)( 19,371)( 20,370)( 21,384)( 22,381)( 23,382)( 24,383)( 25,379)( 26,378)( 27,377)( 28,380)( 29,374)( 30,375)( 31,376)( 32,373)( 33,353)( 34,356)( 35,355)( 36,354)( 37,368)( 38,365)( 39,366)( 40,367)( 41,363)( 42,362)( 43,361)( 44,364)( 45,358)( 46,359)( 47,360)( 48,357)( 49,289)( 50,292)( 51,291)( 52,290)( 53,304)( 54,301)( 55,302)( 56,303)( 57,299)( 58,298)( 59,297)( 60,300)( 61,294)( 62,295)( 63,296)( 64,293)( 65,321)( 66,324)( 67,323)( 68,322)( 69,336)( 70,333)( 71,334)( 72,335)( 73,331)( 74,330)( 75,329)( 76,332)( 77,326)( 78,327)( 79,328)( 80,325)( 81,305)( 82,308)( 83,307)( 84,306)( 85,320)( 86,317)( 87,318)( 88,319)( 89,315)( 90,314)( 91,313)( 92,316)( 93,310)( 94,311)( 95,312)( 96,309)( 97,417)( 98,420)( 99,419)(100,418)(101,432)(102,429)(103,430)(104,431)(105,427)(106,426)(107,425)(108,428)(109,422)(110,423)(111,424)(112,421)(113,401)(114,404)(115,403)(116,402)(117,416)(118,413)(119,414)(120,415)(121,411)(122,410)(123,409)(124,412)(125,406)(126,407)(127,408)(128,405)(129,385)(130,388)(131,387)(132,386)(133,400)(134,397)(135,398)(136,399)(137,395)(138,394)(139,393)(140,396)(141,390)(142,391)(143,392)(144,389)(145,481)(146,484)(147,483)(148,482)(149,496)(150,493)(151,494)(152,495)(153,491)(154,490)(155,489)(156,492)(157,486)(158,487)(159,488)(160,485)(161,513)(162,516)(163,515)(164,514)(165,528)(166,525)(167,526)(168,527)(169,523)(170,522)(171,521)(172,524)(173,518)(174,519)(175,520)(176,517)(177,497)(178,500)(179,499)(180,498)(181,512)(182,509)(183,510)(184,511)(185,507)(186,506)(187,505)(188,508)(189,502)(190,503)(191,504)(192,501)(193,433)(194,436)(195,435)(196,434)(197,448)(198,445)(199,446)(200,447)(201,443)(202,442)(203,441)(204,444)(205,438)(206,439)(207,440)(208,437)(209,465)(210,468)(211,467)(212,466)(213,480)(214,477)(215,478)(216,479)(217,475)(218,474)(219,473)(220,476)(221,470)(222,471)(223,472)(224,469)(225,449)(226,452)(227,451)(228,450)(229,464)(230,461)(231,462)(232,463)(233,459)(234,458)(235,457)(236,460)(237,454)(238,455)(239,456)(240,453)(241,561)(242,564)(243,563)(244,562)(245,576)(246,573)(247,574)(248,575)(249,571)(250,570)(251,569)(252,572)(253,566)(254,567)(255,568)(256,565)(257,545)(258,548)(259,547)(260,546)(261,560)(262,557)(263,558)(264,559)(265,555)(266,554)(267,553)(268,556)(269,550)(270,551)(271,552)(272,549)(273,529)(274,532)(275,531)(276,530)(277,544)(278,541)(279,542)(280,543)(281,539)(282,538)(283,537)(284,540)(285,534)(286,535)(287,536)(288,533);;
s2 := (  1,  5)(  2,  6)(  3,  7)(  4,  8)(  9, 13)( 10, 14)( 11, 15)( 12, 16)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 29)( 26, 30)( 27, 31)( 28, 32)( 33, 37)( 34, 38)( 35, 39)( 36, 40)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 61)( 58, 62)( 59, 63)( 60, 64)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 77)( 74, 78)( 75, 79)( 76, 80)( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 93)( 90, 94)( 91, 95)( 92, 96)( 97,101)( 98,102)( 99,103)(100,104)(105,109)(106,110)(107,111)(108,112)(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160)(161,165)(162,166)(163,167)(164,168)(169,173)(170,174)(171,175)(172,176)(177,181)(178,182)(179,183)(180,184)(185,189)(186,190)(187,191)(188,192)(193,197)(194,198)(195,199)(196,200)(201,205)(202,206)(203,207)(204,208)(209,213)(210,214)(211,215)(212,216)(217,221)(218,222)(219,223)(220,224)(225,229)(226,230)(227,231)(228,232)(233,237)(234,238)(235,239)(236,240)(241,245)(242,246)(243,247)(244,248)(249,253)(250,254)(251,255)(252,256)(257,261)(258,262)(259,263)(260,264)(265,269)(266,270)(267,271)(268,272)(273,277)(274,278)(275,279)(276,280)(281,285)(282,286)(283,287)(284,288)(289,293)(290,294)(291,295)(292,296)(297,301)(298,302)(299,303)(300,304)(305,309)(306,310)(307,311)(308,312)(313,317)(314,318)(315,319)(316,320)(321,325)(322,326)(323,327)(324,328)(329,333)(330,334)(331,335)(332,336)(337,341)(338,342)(339,343)(340,344)(345,349)(346,350)(347,351)(348,352)(353,357)(354,358)(355,359)(356,360)(361,365)(362,366)(363,367)(364,368)(369,373)(370,374)(371,375)(372,376)(377,381)(378,382)(379,383)(380,384)(385,389)(386,390)(387,391)(388,392)(393,397)(394,398)(395,399)(396,400)(401,405)(402,406)(403,407)(404,408)(409,413)(410,414)(411,415)(412,416)(417,421)(418,422)(419,423)(420,424)(425,429)(426,430)(427,431)(428,432)(433,437)(434,438)(435,439)(436,440)(441,445)(442,446)(443,447)(444,448)(449,453)(450,454)(451,455)(452,456)(457,461)(458,462)(459,463)(460,464)(465,469)(466,470)(467,471)(468,472)(473,477)(474,478)(475,479)(476,480)(481,485)(482,486)(483,487)(484,488)(489,493)(490,494)(491,495)(492,496)(497,501)(498,502)(499,503)(500,504)(505,509)(506,510)(507,511)(508,512)(513,517)(514,518)(515,519)(516,520)(521,525)(522,526)(523,527)(524,528)(529,533)(530,534)(531,535)(532,536)(537,541)(538,542)(539,543)(540,544)(545,549)(546,550)(547,551)(548,552)(553,557)(554,558)(555,559)(556,560)(561,565)(562,566)(563,567)(564,568)(569,573)(570,574)(571,575)(572,576);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(576)!(  3,  4)(  7,  8)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 37)( 22, 38)( 23, 40)( 24, 39)( 25, 45)( 26, 46)( 27, 48)( 28, 47)( 29, 41)( 30, 42)( 31, 44)( 32, 43)( 49,129)( 50,130)( 51,132)( 52,131)( 53,133)( 54,134)( 55,136)( 56,135)( 57,141)( 58,142)( 59,144)( 60,143)( 61,137)( 62,138)( 63,140)( 64,139)( 65,113)( 66,114)( 67,116)( 68,115)( 69,117)( 70,118)( 71,120)( 72,119)( 73,125)( 74,126)( 75,128)( 76,127)( 77,121)( 78,122)( 79,124)( 80,123)( 81, 97)( 82, 98)( 83,100)( 84, 99)( 85,101)( 86,102)( 87,104)( 88,103)( 89,109)( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107)(147,148)(151,152)(153,157)(154,158)(155,160)(156,159)(161,177)(162,178)(163,180)(164,179)(165,181)(166,182)(167,184)(168,183)(169,189)(170,190)(171,192)(172,191)(173,185)(174,186)(175,188)(176,187)(193,273)(194,274)(195,276)(196,275)(197,277)(198,278)(199,280)(200,279)(201,285)(202,286)(203,288)(204,287)(205,281)(206,282)(207,284)(208,283)(209,257)(210,258)(211,260)(212,259)(213,261)(214,262)(215,264)(216,263)(217,269)(218,270)(219,272)(220,271)(221,265)(222,266)(223,268)(224,267)(225,241)(226,242)(227,244)(228,243)(229,245)(230,246)(231,248)(232,247)(233,253)(234,254)(235,256)(236,255)(237,249)(238,250)(239,252)(240,251)(289,433)(290,434)(291,436)(292,435)(293,437)(294,438)(295,440)(296,439)(297,445)(298,446)(299,448)(300,447)(301,441)(302,442)(303,444)(304,443)(305,465)(306,466)(307,468)(308,467)(309,469)(310,470)(311,472)(312,471)(313,477)(314,478)(315,480)(316,479)(317,473)(318,474)(319,476)(320,475)(321,449)(322,450)(323,452)(324,451)(325,453)(326,454)(327,456)(328,455)(329,461)(330,462)(331,464)(332,463)(333,457)(334,458)(335,460)(336,459)(337,561)(338,562)(339,564)(340,563)(341,565)(342,566)(343,568)(344,567)(345,573)(346,574)(347,576)(348,575)(349,569)(350,570)(351,572)(352,571)(353,545)(354,546)(355,548)(356,547)(357,549)(358,550)(359,552)(360,551)(361,557)(362,558)(363,560)(364,559)(365,553)(366,554)(367,556)(368,555)(369,529)(370,530)(371,532)(372,531)(373,533)(374,534)(375,536)(376,535)(377,541)(378,542)(379,544)(380,543)(381,537)(382,538)(383,540)(384,539)(385,513)(386,514)(387,516)(388,515)(389,517)(390,518)(391,520)(392,519)(393,525)(394,526)(395,528)(396,527)(397,521)(398,522)(399,524)(400,523)(401,497)(402,498)(403,500)(404,499)(405,501)(406,502)(407,504)(408,503)(409,509)(410,510)(411,512)(412,511)(413,505)(414,506)(415,508)(416,507)(417,481)(418,482)(419,484)(420,483)(421,485)(422,486)(423,488)(424,487)(425,493)(426,494)(427,496)(428,495)(429,489)(430,490)(431,492)(432,491);
s1 := Sym(576)!(  1,337)(  2,340)(  3,339)(  4,338)(  5,352)(  6,349)(  7,350)(  8,351)(  9,347)( 10,346)( 11,345)( 12,348)( 13,342)( 14,343)( 15,344)( 16,341)( 17,369)( 18,372)( 19,371)( 20,370)( 21,384)( 22,381)( 23,382)( 24,383)( 25,379)( 26,378)( 27,377)( 28,380)( 29,374)( 30,375)( 31,376)( 32,373)( 33,353)( 34,356)( 35,355)( 36,354)( 37,368)( 38,365)( 39,366)( 40,367)( 41,363)( 42,362)( 43,361)( 44,364)( 45,358)( 46,359)( 47,360)( 48,357)( 49,289)( 50,292)( 51,291)( 52,290)( 53,304)( 54,301)( 55,302)( 56,303)( 57,299)( 58,298)( 59,297)( 60,300)( 61,294)( 62,295)( 63,296)( 64,293)( 65,321)( 66,324)( 67,323)( 68,322)( 69,336)( 70,333)( 71,334)( 72,335)( 73,331)( 74,330)( 75,329)( 76,332)( 77,326)( 78,327)( 79,328)( 80,325)( 81,305)( 82,308)( 83,307)( 84,306)( 85,320)( 86,317)( 87,318)( 88,319)( 89,315)( 90,314)( 91,313)( 92,316)( 93,310)( 94,311)( 95,312)( 96,309)( 97,417)( 98,420)( 99,419)(100,418)(101,432)(102,429)(103,430)(104,431)(105,427)(106,426)(107,425)(108,428)(109,422)(110,423)(111,424)(112,421)(113,401)(114,404)(115,403)(116,402)(117,416)(118,413)(119,414)(120,415)(121,411)(122,410)(123,409)(124,412)(125,406)(126,407)(127,408)(128,405)(129,385)(130,388)(131,387)(132,386)(133,400)(134,397)(135,398)(136,399)(137,395)(138,394)(139,393)(140,396)(141,390)(142,391)(143,392)(144,389)(145,481)(146,484)(147,483)(148,482)(149,496)(150,493)(151,494)(152,495)(153,491)(154,490)(155,489)(156,492)(157,486)(158,487)(159,488)(160,485)(161,513)(162,516)(163,515)(164,514)(165,528)(166,525)(167,526)(168,527)(169,523)(170,522)(171,521)(172,524)(173,518)(174,519)(175,520)(176,517)(177,497)(178,500)(179,499)(180,498)(181,512)(182,509)(183,510)(184,511)(185,507)(186,506)(187,505)(188,508)(189,502)(190,503)(191,504)(192,501)(193,433)(194,436)(195,435)(196,434)(197,448)(198,445)(199,446)(200,447)(201,443)(202,442)(203,441)(204,444)(205,438)(206,439)(207,440)(208,437)(209,465)(210,468)(211,467)(212,466)(213,480)(214,477)(215,478)(216,479)(217,475)(218,474)(219,473)(220,476)(221,470)(222,471)(223,472)(224,469)(225,449)(226,452)(227,451)(228,450)(229,464)(230,461)(231,462)(232,463)(233,459)(234,458)(235,457)(236,460)(237,454)(238,455)(239,456)(240,453)(241,561)(242,564)(243,563)(244,562)(245,576)(246,573)(247,574)(248,575)(249,571)(250,570)(251,569)(252,572)(253,566)(254,567)(255,568)(256,565)(257,545)(258,548)(259,547)(260,546)(261,560)(262,557)(263,558)(264,559)(265,555)(266,554)(267,553)(268,556)(269,550)(270,551)(271,552)(272,549)(273,529)(274,532)(275,531)(276,530)(277,544)(278,541)(279,542)(280,543)(281,539)(282,538)(283,537)(284,540)(285,534)(286,535)(287,536)(288,533);
s2 := Sym(576)!(  1,  5)(  2,  6)(  3,  7)(  4,  8)(  9, 13)( 10, 14)( 11, 15)( 12, 16)( 17, 21)( 18, 22)( 19, 23)( 20, 24)( 25, 29)( 26, 30)( 27, 31)( 28, 32)( 33, 37)( 34, 38)( 35, 39)( 36, 40)( 41, 45)( 42, 46)( 43, 47)( 44, 48)( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 57, 61)( 58, 62)( 59, 63)( 60, 64)( 65, 69)( 66, 70)( 67, 71)( 68, 72)( 73, 77)( 74, 78)( 75, 79)( 76, 80)( 81, 85)( 82, 86)( 83, 87)( 84, 88)( 89, 93)( 90, 94)( 91, 95)( 92, 96)( 97,101)( 98,102)( 99,103)(100,104)(105,109)(106,110)(107,111)(108,112)(113,117)(114,118)(115,119)(116,120)(121,125)(122,126)(123,127)(124,128)(129,133)(130,134)(131,135)(132,136)(137,141)(138,142)(139,143)(140,144)(145,149)(146,150)(147,151)(148,152)(153,157)(154,158)(155,159)(156,160)(161,165)(162,166)(163,167)(164,168)(169,173)(170,174)(171,175)(172,176)(177,181)(178,182)(179,183)(180,184)(185,189)(186,190)(187,191)(188,192)(193,197)(194,198)(195,199)(196,200)(201,205)(202,206)(203,207)(204,208)(209,213)(210,214)(211,215)(212,216)(217,221)(218,222)(219,223)(220,224)(225,229)(226,230)(227,231)(228,232)(233,237)(234,238)(235,239)(236,240)(241,245)(242,246)(243,247)(244,248)(249,253)(250,254)(251,255)(252,256)(257,261)(258,262)(259,263)(260,264)(265,269)(266,270)(267,271)(268,272)(273,277)(274,278)(275,279)(276,280)(281,285)(282,286)(283,287)(284,288)(289,293)(290,294)(291,295)(292,296)(297,301)(298,302)(299,303)(300,304)(305,309)(306,310)(307,311)(308,312)(313,317)(314,318)(315,319)(316,320)(321,325)(322,326)(323,327)(324,328)(329,333)(330,334)(331,335)(332,336)(337,341)(338,342)(339,343)(340,344)(345,349)(346,350)(347,351)(348,352)(353,357)(354,358)(355,359)(356,360)(361,365)(362,366)(363,367)(364,368)(369,373)(370,374)(371,375)(372,376)(377,381)(378,382)(379,383)(380,384)(385,389)(386,390)(387,391)(388,392)(393,397)(394,398)(395,399)(396,400)(401,405)(402,406)(403,407)(404,408)(409,413)(410,414)(411,415)(412,416)(417,421)(418,422)(419,423)(420,424)(425,429)(426,430)(427,431)(428,432)(433,437)(434,438)(435,439)(436,440)(441,445)(442,446)(443,447)(444,448)(449,453)(450,454)(451,455)(452,456)(457,461)(458,462)(459,463)(460,464)(465,469)(466,470)(467,471)(468,472)(473,477)(474,478)(475,479)(476,480)(481,485)(482,486)(483,487)(484,488)(489,493)(490,494)(491,495)(492,496)(497,501)(498,502)(499,503)(500,504)(505,509)(506,510)(507,511)(508,512)(513,517)(514,518)(515,519)(516,520)(521,525)(522,526)(523,527)(524,528)(529,533)(530,534)(531,535)(532,536)(537,541)(538,542)(539,543)(540,544)(545,549)(546,550)(547,551)(548,552)(553,557)(554,558)(555,559)(556,560)(561,565)(562,566)(563,567)(564,568)(569,573)(570,574)(571,575)(572,576);
poly := sub<Sym(576)|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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*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 >;
References : None.
to this polytope

Twisty Puzzle