Polytope of Type {4,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*1152a
if this polytope has a name.
Group : SmallGroup(1152,12016)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 24, 288, 144
Order of s0s1s2 : 8
Order of s0s1s2s1 : 12
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 : {4,12}*576, {4,24}*576a, {4,24}*576b
   4-fold quotients : {4,12}*288
   8-fold quotients : {4,6}*144
   9-fold quotients : {4,8}*128a
   16-fold quotients : {4,6}*72
   18-fold quotients : {4,8}*64a, {4,8}*64b, {4,4}*64
   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*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 3.
      48 facets:
         48 of {4}*8
      16 vertex figures:
         4 of {24}*48
         12 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      48 facets:
         48 of {4}*8
      8 vertex figures:
         8 of {24}*48

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)( 37,181)( 38,183)( 39,182)( 40,185)( 41,184)( 42,186)( 43,189)( 44,188)( 45,187)( 46,190)( 47,192)( 48,191)( 49,194)( 50,193)( 51,195)( 52,198)( 53,197)( 54,196)( 55,199)( 56,201)( 57,200)( 58,203)( 59,202)( 60,204)( 61,207)( 62,206)( 63,205)( 64,208)( 65,210)( 66,209)( 67,212)( 68,211)( 69,213)( 70,216)( 71,215)( 72,214)( 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)(109,262)(110,264)(111,263)(112,266)(113,265)(114,267)(115,270)(116,269)(117,268)(118,253)(119,255)(120,254)(121,257)(122,256)(123,258)(124,261)(125,260)(126,259)(127,280)(128,282)(129,281)(130,284)(131,283)(132,285)(133,288)(134,287)(135,286)(136,271)(137,273)(138,272)(139,275)(140,274)(141,276)(142,279)(143,278)(144,277)(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)(325,469)(326,471)(327,470)(328,473)(329,472)(330,474)(331,477)(332,476)(333,475)(334,478)(335,480)(336,479)(337,482)(338,481)(339,483)(340,486)(341,485)(342,484)(343,487)(344,489)(345,488)(346,491)(347,490)(348,492)(349,495)(350,494)(351,493)(352,496)(353,498)(354,497)(355,500)(356,499)(357,501)(358,504)(359,503)(360,502)(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)(397,550)(398,552)(399,551)(400,554)(401,553)(402,555)(403,558)(404,557)(405,556)(406,541)(407,543)(408,542)(409,545)(410,544)(411,546)(412,549)(413,548)(414,547)(415,568)(416,570)(417,569)(418,572)(419,571)(420,573)(421,576)(422,575)(423,574)(424,559)(425,561)(426,560)(427,563)(428,562)(429,564)(430,567)(431,566)(432,565);;
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)( 38, 42)( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 56, 60)( 57, 62)( 59, 63)( 65, 69)( 66, 71)( 68, 72)( 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)(109,127)(110,132)(111,134)(112,130)(113,135)(114,128)(115,133)(116,129)(117,131)(118,136)(119,141)(120,143)(121,139)(122,144)(123,137)(124,142)(125,138)(126,140)(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)(325,397)(326,402)(327,404)(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)(335,411)(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)(343,415)(344,420)(345,422)(346,418)(347,423)(348,416)(349,421)(350,417)(351,419)(352,424)(353,429)(354,431)(355,427)(356,432)(357,425)(358,430)(359,426)(360,428)(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*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)( 37,181)( 38,183)( 39,182)( 40,185)( 41,184)( 42,186)( 43,189)( 44,188)( 45,187)( 46,190)( 47,192)( 48,191)( 49,194)( 50,193)( 51,195)( 52,198)( 53,197)( 54,196)( 55,199)( 56,201)( 57,200)( 58,203)( 59,202)( 60,204)( 61,207)( 62,206)( 63,205)( 64,208)( 65,210)( 66,209)( 67,212)( 68,211)( 69,213)( 70,216)( 71,215)( 72,214)( 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)(109,262)(110,264)(111,263)(112,266)(113,265)(114,267)(115,270)(116,269)(117,268)(118,253)(119,255)(120,254)(121,257)(122,256)(123,258)(124,261)(125,260)(126,259)(127,280)(128,282)(129,281)(130,284)(131,283)(132,285)(133,288)(134,287)(135,286)(136,271)(137,273)(138,272)(139,275)(140,274)(141,276)(142,279)(143,278)(144,277)(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)(325,469)(326,471)(327,470)(328,473)(329,472)(330,474)(331,477)(332,476)(333,475)(334,478)(335,480)(336,479)(337,482)(338,481)(339,483)(340,486)(341,485)(342,484)(343,487)(344,489)(345,488)(346,491)(347,490)(348,492)(349,495)(350,494)(351,493)(352,496)(353,498)(354,497)(355,500)(356,499)(357,501)(358,504)(359,503)(360,502)(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)(397,550)(398,552)(399,551)(400,554)(401,553)(402,555)(403,558)(404,557)(405,556)(406,541)(407,543)(408,542)(409,545)(410,544)(411,546)(412,549)(413,548)(414,547)(415,568)(416,570)(417,569)(418,572)(419,571)(420,573)(421,576)(422,575)(423,574)(424,559)(425,561)(426,560)(427,563)(428,562)(429,564)(430,567)(431,566)(432,565);
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)( 38, 42)( 39, 44)( 41, 45)( 47, 51)( 48, 53)( 50, 54)( 56, 60)( 57, 62)( 59, 63)( 65, 69)( 66, 71)( 68, 72)( 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)(109,127)(110,132)(111,134)(112,130)(113,135)(114,128)(115,133)(116,129)(117,131)(118,136)(119,141)(120,143)(121,139)(122,144)(123,137)(124,142)(125,138)(126,140)(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)(325,397)(326,402)(327,404)(328,400)(329,405)(330,398)(331,403)(332,399)(333,401)(334,406)(335,411)(336,413)(337,409)(338,414)(339,407)(340,412)(341,408)(342,410)(343,415)(344,420)(345,422)(346,418)(347,423)(348,416)(349,421)(350,417)(351,419)(352,424)(353,429)(354,431)(355,427)(356,432)(357,425)(358,430)(359,426)(360,428)(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*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle