Polytope of Type {3,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157458)
Rank : 3
Schlafli Type : {3,12}
Number of vertices, edges, etc : 48, 288, 192
Order of s0s1s2 : 24
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 : {3,12}*576
   4-fold quotients : {3,12}*288
   8-fold quotients : {3,6}*144, {3,12}*144
   12-fold quotients : {3,12}*96
   24-fold quotients : {3,4}*48, {3,6}*48
   32-fold quotients : {3,6}*36
   48-fold quotients : {3,3}*24, {3,4}*24
   96-fold quotients : {3,2}*12
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*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
      96 facets:
         96 of {3}*6
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 2.
      96 facets:
         96 of {3}*6
      32 vertex figures:
         16 of {12}*24
         16 of {6}*12
   P/N, where N=<s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      96 facets:
         96 of {3}*6
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 3.
      64 facets:
         64 of {3}*6
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 3.
      64 facets:
         64 of {3}*6
      24 vertex figures:
         12 of {12}*24
         12 of {4}*8
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2> of order 4.
      48 facets:
         48 of {3}*6
      20 vertex figures:
         16 of {6}*12
         4 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s2*s1*s0*s2*s1> of order 4.
      48 facets:
         48 of {3}*6
      20 vertex figures:
         8 of {12}*24
         8 of {3}*6
         4 of {6}*12
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 6.
      32 facets:
         32 of {3}*6
      16 vertex figures:
         4 of {12}*24
         4 of {4}*8
         4 of {6}*12
         4 of {2}*4
   P/N, where N=<s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2, s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 6.
      32 facets:
         32 of {3}*6
      12 vertex figures:
         6 of {12}*24
         6 of {4}*8
   P/N, where N=<s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2> of order 6.
      32 facets:
         32 of {3}*6
      12 vertex figures:
         6 of {12}*24
         6 of {4}*8
   P/N, where N=<s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 12.
      16 facets:
         16 of {3}*6
      10 vertex figures:
         4 of {6}*12
         4 of {2}*4
         1 of {12}*24
         1 of {4}*8

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

Twisty Puzzle