Polytope of Type {4,48}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,48}*1152a
if this polytope has a name.
Group : SmallGroup(1152,32083)
Rank : 3
Schlafli Type : {4,48}
Number of vertices, edges, etc : 12, 288, 144
Order of s0s1s2 : 16
Order of s0s1s2s1 : 6
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 : {4,24}*576a
   4-fold quotients : {4,12}*288
   8-fold quotients : {4,6}*144
   9-fold quotients : {4,16}*128a
   16-fold quotients : {4,6}*72
   18-fold quotients : {4,8}*64a, {2,16}*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*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      72 facets:
         72 of {4}*8
      6 vertex figures:
         6 of {48}*96
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      48 facets:
         48 of {4}*8
      4 vertex figures:
         4 of {48}*96
   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
      8 vertex figures:
         2 of {48}*96
         6 of {16}*32

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

Twisty Puzzle