Polytope of Type {8,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,12016)
Rank : 3
Schlafli Type : {8,4}
Number of vertices, edges, etc : 144, 288, 72
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4}*576, {8,4}*576a, {8,4}*576b
   4-fold quotients : {4,4}*288
   8-fold quotients : {4,4}*144
   9-fold quotients : {8,4}*128a
   16-fold quotients : {4,4}*72
   18-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
   36-fold quotients : {4,4}*32, {8,2}*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=<s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 2.
      36 facets:
         36 of {8}*16
      76 vertex figures:
         68 of {4}*8
         8 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 2.
      36 facets:
         36 of {8}*16
      72 vertex figures:
         72 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 3.
      24 facets:
         24 of {8}*16
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2> of order 3.
      24 facets:
         24 of {8}*16
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 4.
      18 facets:
         18 of {8}*16
      38 vertex figures:
         34 of {4}*8
         4 of {2}*4
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2, s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1> of order 6.
      12 facets:
         12 of {8}*16
      28 vertex figures:
         20 of {4}*8
         8 of {2}*4
   P/N, where N=<s1*s2*s1*s2, s0*s1*s0*s1*s2*s1*s0*s2*s1*s0> of order 6.
      12 facets:
         12 of {8}*16
      28 vertex figures:
         8 of {2}*4
         20 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 6.
      12 facets:
         12 of {8}*16
      24 vertex figures:
         24 of {4}*8

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

Twisty Puzzle