Polytope of Type {8,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8}*1152a
if this polytope has a name.
Group : SmallGroup(1152,12919)
Rank : 3
Schlafli Type : {8,8}
Number of vertices, edges, etc : 72, 288, 72
Order of s0s1s2 : 24
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,8}*576a, {8,4}*576a
   4-fold quotients : {4,4}*288
   8-fold quotients : {4,4}*144
   9-fold quotients : {8,8}*128b
   16-fold quotients : {4,4}*72
   18-fold quotients : {4,8}*64a, {8,4}*64a
   36-fold quotients : {4,4}*32, {2,8}*32, {8,2}*32
   72-fold quotients : {2,4}*16, {4,2}*16
   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*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 2.
      36 facets:
         36 of {8}*16
      36 vertex figures:
         36 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 3.
      24 facets:
         24 of {8}*16
      24 vertex figures:
         24 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      24 facets:
         24 of {8}*16
      24 vertex figures:
         24 of {8}*16
   P/N, where N=<s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 6.
      12 facets:
         12 of {8}*16
      12 vertex figures:
         12 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 6.
      12 facets:
         12 of {8}*16
      12 vertex figures:
         12 of {8}*16

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

Twisty Puzzle