Polytope of Type {24,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,8}*1152b
if this polytope has a name.
Group : SmallGroup(1152,12921)
Rank : 3
Schlafli Type : {24,8}
Number of vertices, edges, etc : 72, 288, 24
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {12,8}*576a, {24,4}*576b
   4-fold quotients : {6,8}*288, {12,4}*288
   8-fold quotients : {6,4}*144
   9-fold quotients : {8,8}*128a
   16-fold quotients : {6,4}*72
   18-fold quotients : {4,8}*64a, {8,4}*64b
   36-fold quotients : {4,4}*32, {2,8}*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*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 3.
      16 facets:
         12 of {8}*16
         4 of {24}*48
      24 vertex figures:
         24 of {8}*16
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 3.
      8 facets:
         8 of {24}*48
      24 vertex figures:
         24 of {8}*16

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

Twisty Puzzle