Polytope of Type {8,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,24}*1152d
if this polytope has a name.
Group : SmallGroup(1152,14487)
Rank : 3
Schlafli Type : {8,24}
Number of vertices, edges, etc : 24, 288, 72
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
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 : {4,24}*576b, {8,12}*576b
   4-fold quotients : {4,12}*288
   8-fold quotients : {4,6}*144
   9-fold quotients : {8,8}*128d
   16-fold quotients : {4,6}*72
   18-fold quotients : {4,8}*64b, {8,4}*64b
   36-fold quotients : {4,4}*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*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 3.
      24 facets:
         24 of {8}*16
      8 vertex figures:
         8 of {24}*48
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 3.
      24 facets:
         24 of {8}*16
      16 vertex figures:
         4 of {24}*48
         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)( 37,208)( 38,210)( 39,209)( 40,212)( 41,211)( 42,213)( 43,216)( 44,215)( 45,214)( 46,199)( 47,201)( 48,200)( 49,203)( 50,202)( 51,204)( 52,207)( 53,206)( 54,205)( 55,190)( 56,192)( 57,191)( 58,194)( 59,193)( 60,195)( 61,198)( 62,197)( 63,196)( 64,181)( 65,183)( 66,182)( 67,185)( 68,184)( 69,186)( 70,189)( 71,188)( 72,187)( 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)(109,271)(110,273)(111,272)(112,275)(113,274)(114,276)(115,279)(116,278)(117,277)(118,280)(119,282)(120,281)(121,284)(122,283)(123,285)(124,288)(125,287)(126,286)(127,253)(128,255)(129,254)(130,257)(131,256)(132,258)(133,261)(134,260)(135,259)(136,262)(137,264)(138,263)(139,266)(140,265)(141,267)(142,270)(143,269)(144,268)(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)(325,496)(326,498)(327,497)(328,500)(329,499)(330,501)(331,504)(332,503)(333,502)(334,487)(335,489)(336,488)(337,491)(338,490)(339,492)(340,495)(341,494)(342,493)(343,478)(344,480)(345,479)(346,482)(347,481)(348,483)(349,486)(350,485)(351,484)(352,469)(353,471)(354,470)(355,473)(356,472)(357,474)(358,477)(359,476)(360,475)(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)(397,559)(398,561)(399,560)(400,563)(401,562)(402,564)(403,567)(404,566)(405,565)(406,568)(407,570)(408,569)(409,572)(410,571)(411,573)(412,576)(413,575)(414,574)(415,541)(416,543)(417,542)(418,545)(419,544)(420,546)(421,549)(422,548)(423,547)(424,550)(425,552)(426,551)(427,554)(428,553)(429,555)(430,558)(431,557)(432,556);;
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, 64)( 38, 69)( 39, 71)( 40, 67)( 41, 72)( 42, 65)( 43, 70)( 44, 66)( 45, 68)( 46, 55)( 47, 60)( 48, 62)( 49, 58)( 50, 63)( 51, 56)( 52, 61)( 53, 57)( 54, 59)( 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)(109,118)(110,123)(111,125)(112,121)(113,126)(114,119)(115,124)(116,120)(117,122)(127,136)(128,141)(129,143)(130,139)(131,144)(132,137)(133,142)(134,138)(135,140)(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)(325,424)(326,429)(327,431)(328,427)(329,432)(330,425)(331,430)(332,426)(333,428)(334,415)(335,420)(336,422)(337,418)(338,423)(339,416)(340,421)(341,417)(342,419)(343,406)(344,411)(345,413)(346,409)(347,414)(348,407)(349,412)(350,408)(351,410)(352,397)(353,402)(354,404)(355,400)(356,405)(357,398)(358,403)(359,399)(360,401)(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 := (  1,296)(  2,295)(  3,297)(  4,293)(  5,292)(  6,294)(  7,290)(  8,289)(  9,291)( 10,305)( 11,304)( 12,306)( 13,302)( 14,301)( 15,303)( 16,299)( 17,298)( 18,300)( 19,314)( 20,313)( 21,315)( 22,311)( 23,310)( 24,312)( 25,308)( 26,307)( 27,309)( 28,323)( 29,322)( 30,324)( 31,320)( 32,319)( 33,321)( 34,317)( 35,316)( 36,318)( 37,341)( 38,340)( 39,342)( 40,338)( 41,337)( 42,339)( 43,335)( 44,334)( 45,336)( 46,332)( 47,331)( 48,333)( 49,329)( 50,328)( 51,330)( 52,326)( 53,325)( 54,327)( 55,359)( 56,358)( 57,360)( 58,356)( 59,355)( 60,357)( 61,353)( 62,352)( 63,354)( 64,350)( 65,349)( 66,351)( 67,347)( 68,346)( 69,348)( 70,344)( 71,343)( 72,345)( 73,386)( 74,385)( 75,387)( 76,383)( 77,382)( 78,384)( 79,380)( 80,379)( 81,381)( 82,395)( 83,394)( 84,396)( 85,392)( 86,391)( 87,393)( 88,389)( 89,388)( 90,390)( 91,368)( 92,367)( 93,369)( 94,365)( 95,364)( 96,366)( 97,362)( 98,361)( 99,363)(100,377)(101,376)(102,378)(103,374)(104,373)(105,375)(106,371)(107,370)(108,372)(109,431)(110,430)(111,432)(112,428)(113,427)(114,429)(115,425)(116,424)(117,426)(118,422)(119,421)(120,423)(121,419)(122,418)(123,420)(124,416)(125,415)(126,417)(127,413)(128,412)(129,414)(130,410)(131,409)(132,411)(133,407)(134,406)(135,408)(136,404)(137,403)(138,405)(139,401)(140,400)(141,402)(142,398)(143,397)(144,399)(145,440)(146,439)(147,441)(148,437)(149,436)(150,438)(151,434)(152,433)(153,435)(154,449)(155,448)(156,450)(157,446)(158,445)(159,447)(160,443)(161,442)(162,444)(163,458)(164,457)(165,459)(166,455)(167,454)(168,456)(169,452)(170,451)(171,453)(172,467)(173,466)(174,468)(175,464)(176,463)(177,465)(178,461)(179,460)(180,462)(181,485)(182,484)(183,486)(184,482)(185,481)(186,483)(187,479)(188,478)(189,480)(190,476)(191,475)(192,477)(193,473)(194,472)(195,474)(196,470)(197,469)(198,471)(199,503)(200,502)(201,504)(202,500)(203,499)(204,501)(205,497)(206,496)(207,498)(208,494)(209,493)(210,495)(211,491)(212,490)(213,492)(214,488)(215,487)(216,489)(217,530)(218,529)(219,531)(220,527)(221,526)(222,528)(223,524)(224,523)(225,525)(226,539)(227,538)(228,540)(229,536)(230,535)(231,537)(232,533)(233,532)(234,534)(235,512)(236,511)(237,513)(238,509)(239,508)(240,510)(241,506)(242,505)(243,507)(244,521)(245,520)(246,522)(247,518)(248,517)(249,519)(250,515)(251,514)(252,516)(253,575)(254,574)(255,576)(256,572)(257,571)(258,573)(259,569)(260,568)(261,570)(262,566)(263,565)(264,567)(265,563)(266,562)(267,564)(268,560)(269,559)(270,561)(271,557)(272,556)(273,558)(274,554)(275,553)(276,555)(277,551)(278,550)(279,552)(280,548)(281,547)(282,549)(283,545)(284,544)(285,546)(286,542)(287,541)(288,543);;
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*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*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)( 37,208)( 38,210)( 39,209)( 40,212)( 41,211)( 42,213)( 43,216)( 44,215)( 45,214)( 46,199)( 47,201)( 48,200)( 49,203)( 50,202)( 51,204)( 52,207)( 53,206)( 54,205)( 55,190)( 56,192)( 57,191)( 58,194)( 59,193)( 60,195)( 61,198)( 62,197)( 63,196)( 64,181)( 65,183)( 66,182)( 67,185)( 68,184)( 69,186)( 70,189)( 71,188)( 72,187)( 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)(109,271)(110,273)(111,272)(112,275)(113,274)(114,276)(115,279)(116,278)(117,277)(118,280)(119,282)(120,281)(121,284)(122,283)(123,285)(124,288)(125,287)(126,286)(127,253)(128,255)(129,254)(130,257)(131,256)(132,258)(133,261)(134,260)(135,259)(136,262)(137,264)(138,263)(139,266)(140,265)(141,267)(142,270)(143,269)(144,268)(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)(325,496)(326,498)(327,497)(328,500)(329,499)(330,501)(331,504)(332,503)(333,502)(334,487)(335,489)(336,488)(337,491)(338,490)(339,492)(340,495)(341,494)(342,493)(343,478)(344,480)(345,479)(346,482)(347,481)(348,483)(349,486)(350,485)(351,484)(352,469)(353,471)(354,470)(355,473)(356,472)(357,474)(358,477)(359,476)(360,475)(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)(397,559)(398,561)(399,560)(400,563)(401,562)(402,564)(403,567)(404,566)(405,565)(406,568)(407,570)(408,569)(409,572)(410,571)(411,573)(412,576)(413,575)(414,574)(415,541)(416,543)(417,542)(418,545)(419,544)(420,546)(421,549)(422,548)(423,547)(424,550)(425,552)(426,551)(427,554)(428,553)(429,555)(430,558)(431,557)(432,556);
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, 64)( 38, 69)( 39, 71)( 40, 67)( 41, 72)( 42, 65)( 43, 70)( 44, 66)( 45, 68)( 46, 55)( 47, 60)( 48, 62)( 49, 58)( 50, 63)( 51, 56)( 52, 61)( 53, 57)( 54, 59)( 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)(109,118)(110,123)(111,125)(112,121)(113,126)(114,119)(115,124)(116,120)(117,122)(127,136)(128,141)(129,143)(130,139)(131,144)(132,137)(133,142)(134,138)(135,140)(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)(325,424)(326,429)(327,431)(328,427)(329,432)(330,425)(331,430)(332,426)(333,428)(334,415)(335,420)(336,422)(337,418)(338,423)(339,416)(340,421)(341,417)(342,419)(343,406)(344,411)(345,413)(346,409)(347,414)(348,407)(349,412)(350,408)(351,410)(352,397)(353,402)(354,404)(355,400)(356,405)(357,398)(358,403)(359,399)(360,401)(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)!(  1,296)(  2,295)(  3,297)(  4,293)(  5,292)(  6,294)(  7,290)(  8,289)(  9,291)( 10,305)( 11,304)( 12,306)( 13,302)( 14,301)( 15,303)( 16,299)( 17,298)( 18,300)( 19,314)( 20,313)( 21,315)( 22,311)( 23,310)( 24,312)( 25,308)( 26,307)( 27,309)( 28,323)( 29,322)( 30,324)( 31,320)( 32,319)( 33,321)( 34,317)( 35,316)( 36,318)( 37,341)( 38,340)( 39,342)( 40,338)( 41,337)( 42,339)( 43,335)( 44,334)( 45,336)( 46,332)( 47,331)( 48,333)( 49,329)( 50,328)( 51,330)( 52,326)( 53,325)( 54,327)( 55,359)( 56,358)( 57,360)( 58,356)( 59,355)( 60,357)( 61,353)( 62,352)( 63,354)( 64,350)( 65,349)( 66,351)( 67,347)( 68,346)( 69,348)( 70,344)( 71,343)( 72,345)( 73,386)( 74,385)( 75,387)( 76,383)( 77,382)( 78,384)( 79,380)( 80,379)( 81,381)( 82,395)( 83,394)( 84,396)( 85,392)( 86,391)( 87,393)( 88,389)( 89,388)( 90,390)( 91,368)( 92,367)( 93,369)( 94,365)( 95,364)( 96,366)( 97,362)( 98,361)( 99,363)(100,377)(101,376)(102,378)(103,374)(104,373)(105,375)(106,371)(107,370)(108,372)(109,431)(110,430)(111,432)(112,428)(113,427)(114,429)(115,425)(116,424)(117,426)(118,422)(119,421)(120,423)(121,419)(122,418)(123,420)(124,416)(125,415)(126,417)(127,413)(128,412)(129,414)(130,410)(131,409)(132,411)(133,407)(134,406)(135,408)(136,404)(137,403)(138,405)(139,401)(140,400)(141,402)(142,398)(143,397)(144,399)(145,440)(146,439)(147,441)(148,437)(149,436)(150,438)(151,434)(152,433)(153,435)(154,449)(155,448)(156,450)(157,446)(158,445)(159,447)(160,443)(161,442)(162,444)(163,458)(164,457)(165,459)(166,455)(167,454)(168,456)(169,452)(170,451)(171,453)(172,467)(173,466)(174,468)(175,464)(176,463)(177,465)(178,461)(179,460)(180,462)(181,485)(182,484)(183,486)(184,482)(185,481)(186,483)(187,479)(188,478)(189,480)(190,476)(191,475)(192,477)(193,473)(194,472)(195,474)(196,470)(197,469)(198,471)(199,503)(200,502)(201,504)(202,500)(203,499)(204,501)(205,497)(206,496)(207,498)(208,494)(209,493)(210,495)(211,491)(212,490)(213,492)(214,488)(215,487)(216,489)(217,530)(218,529)(219,531)(220,527)(221,526)(222,528)(223,524)(224,523)(225,525)(226,539)(227,538)(228,540)(229,536)(230,535)(231,537)(232,533)(233,532)(234,534)(235,512)(236,511)(237,513)(238,509)(239,508)(240,510)(241,506)(242,505)(243,507)(244,521)(245,520)(246,522)(247,518)(248,517)(249,519)(250,515)(251,514)(252,516)(253,575)(254,574)(255,576)(256,572)(257,571)(258,573)(259,569)(260,568)(261,570)(262,566)(263,565)(264,567)(265,563)(266,562)(267,564)(268,560)(269,559)(270,561)(271,557)(272,556)(273,558)(274,554)(275,553)(276,555)(277,551)(278,550)(279,552)(280,548)(281,547)(282,549)(283,545)(284,544)(285,546)(286,542)(287,541)(288,543);
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*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle