Polytope of Type {24,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,24}*1152j
if this polytope has a name.
Group : SmallGroup(1152,14484)
Rank : 3
Schlafli Type : {24,24}
Number of vertices, edges, etc : 24, 288, 24
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   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 : {24,12}*576a, {12,24}*576f
   3-fold quotients : {8,24}*384c
   4-fold quotients : {12,12}*288b
   6-fold quotients : {4,24}*192b, {8,12}*192b
   8-fold quotients : {6,12}*144b, {12,6}*144c
   9-fold quotients : {8,8}*128d
   12-fold quotients : {4,12}*96a
   16-fold quotients : {6,6}*72b
   18-fold quotients : {4,8}*64b, {8,4}*64b
   24-fold quotients : {2,12}*48, {4,6}*48a
   32-fold quotients : {6,3}*36
   36-fold quotients : {4,4}*32
   48-fold quotients : {2,6}*24
   72-fold quotients : {2,4}*16, {4,2}*16
   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):
   None.

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

Twisty Puzzle