Polytope of Type {8,18}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,18}*1152e
if this polytope has a name.
Group : SmallGroup(1152,154283)
Rank : 3
Schlafli Type : {8,18}
Number of vertices, edges, etc : 32, 288, 72
Order of s0s1s2 : 18
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {8,18}*576a
   3-fold quotients : {8,6}*384d
   4-fold quotients : {4,18}*288
   6-fold quotients : {8,6}*192a
   8-fold quotients : {4,9}*144, {4,18}*144b, {4,18}*144c
   12-fold quotients : {4,6}*96
   16-fold quotients : {4,9}*72, {2,18}*72
   24-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {2,9}*36
   48-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {2,3}*12
   144-fold quotients : {2,2}*8
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*s0*s1*s0*s1> of order 2.
      48 facets:
         24 of {4}*8
         24 of {8}*16
      16 vertex figures:
         16 of {18}*36
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      36 facets:
         36 of {8}*16
      16 vertex figures:
         16 of {18}*36
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      36 facets:
         36 of {8}*16
      16 vertex figures:
         16 of {18}*36
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      24 facets:
         12 of {4}*8
         12 of {8}*16
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      24 facets:
         12 of {4}*8
         12 of {8}*16
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s1*s0*s1> of order 4.
      36 facets:
         24 of {2}*4
         12 of {8}*16
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2> of order 4.
      24 facets:
         12 of {4}*8
         12 of {8}*16
      8 vertex figures:
         8 of {18}*36

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

Twisty Puzzle