Polytope of Type {6,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*1152g
if this polytope has a name.
Group : SmallGroup(1152,157458)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 48, 288, 96
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
   8-fold quotients : {3,6}*144, {3,12}*144
   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=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 2.
      48 facets:
         48 of {6}*12
      32 vertex figures:
         16 of {12}*24
         16 of {6}*12
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      48 facets:
         48 of {6}*12
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2> of order 3.
      32 facets:
         32 of {6}*12
      16 vertex figures:
         16 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 3.
      32 facets:
         32 of {6}*12
      24 vertex figures:
         12 of {12}*24
         12 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 6.
      16 facets:
         16 of {6}*12
      16 vertex figures:
         4 of {12}*24
         4 of {4}*8
         4 of {2}*4
         4 of {6}*12
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 6.
      16 facets:
         16 of {6}*12
      12 vertex figures:
         6 of {12}*24
         6 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 := (  1,421)(  2,422)(  3,419)(  4,420)(  5,417)(  6,418)(  7,424)(  8,423)(  9,445)( 10,446)( 11,443)( 12,444)( 13,441)( 14,442)( 15,448)( 16,447)( 17,437)( 18,438)( 19,435)( 20,436)( 21,433)( 22,434)( 23,440)( 24,439)( 25,429)( 26,430)( 27,427)( 28,428)( 29,425)( 30,426)( 31,432)( 32,431)( 33,389)( 34,390)( 35,387)( 36,388)( 37,385)( 38,386)( 39,392)( 40,391)( 41,413)( 42,414)( 43,411)( 44,412)( 45,409)( 46,410)( 47,416)( 48,415)( 49,405)( 50,406)( 51,403)( 52,404)( 53,401)( 54,402)( 55,408)( 56,407)( 57,397)( 58,398)( 59,395)( 60,396)( 61,393)( 62,394)( 63,400)( 64,399)( 65,453)( 66,454)( 67,451)( 68,452)( 69,449)( 70,450)( 71,456)( 72,455)( 73,477)( 74,478)( 75,475)( 76,476)( 77,473)( 78,474)( 79,480)( 80,479)( 81,469)( 82,470)( 83,467)( 84,468)( 85,465)( 86,466)( 87,472)( 88,471)( 89,461)( 90,462)( 91,459)( 92,460)( 93,457)( 94,458)( 95,464)( 96,463)( 97,325)( 98,326)( 99,323)(100,324)(101,321)(102,322)(103,328)(104,327)(105,349)(106,350)(107,347)(108,348)(109,345)(110,346)(111,352)(112,351)(113,341)(114,342)(115,339)(116,340)(117,337)(118,338)(119,344)(120,343)(121,333)(122,334)(123,331)(124,332)(125,329)(126,330)(127,336)(128,335)(129,293)(130,294)(131,291)(132,292)(133,289)(134,290)(135,296)(136,295)(137,317)(138,318)(139,315)(140,316)(141,313)(142,314)(143,320)(144,319)(145,309)(146,310)(147,307)(148,308)(149,305)(150,306)(151,312)(152,311)(153,301)(154,302)(155,299)(156,300)(157,297)(158,298)(159,304)(160,303)(161,357)(162,358)(163,355)(164,356)(165,353)(166,354)(167,360)(168,359)(169,381)(170,382)(171,379)(172,380)(173,377)(174,378)(175,384)(176,383)(177,373)(178,374)(179,371)(180,372)(181,369)(182,370)(183,376)(184,375)(185,365)(186,366)(187,363)(188,364)(189,361)(190,362)(191,368)(192,367)(193,517)(194,518)(195,515)(196,516)(197,513)(198,514)(199,520)(200,519)(201,541)(202,542)(203,539)(204,540)(205,537)(206,538)(207,544)(208,543)(209,533)(210,534)(211,531)(212,532)(213,529)(214,530)(215,536)(216,535)(217,525)(218,526)(219,523)(220,524)(221,521)(222,522)(223,528)(224,527)(225,485)(226,486)(227,483)(228,484)(229,481)(230,482)(231,488)(232,487)(233,509)(234,510)(235,507)(236,508)(237,505)(238,506)(239,512)(240,511)(241,501)(242,502)(243,499)(244,500)(245,497)(246,498)(247,504)(248,503)(249,493)(250,494)(251,491)(252,492)(253,489)(254,490)(255,496)(256,495)(257,549)(258,550)(259,547)(260,548)(261,545)(262,546)(263,552)(264,551)(265,573)(266,574)(267,571)(268,572)(269,569)(270,570)(271,576)(272,575)(273,565)(274,566)(275,563)(276,564)(277,561)(278,562)(279,568)(280,567)(281,557)(282,558)(283,555)(284,556)(285,553)(286,554)(287,560)(288,559);;
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*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*s1*s2 ];;
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)!(  1,421)(  2,422)(  3,419)(  4,420)(  5,417)(  6,418)(  7,424)(  8,423)(  9,445)( 10,446)( 11,443)( 12,444)( 13,441)( 14,442)( 15,448)( 16,447)( 17,437)( 18,438)( 19,435)( 20,436)( 21,433)( 22,434)( 23,440)( 24,439)( 25,429)( 26,430)( 27,427)( 28,428)( 29,425)( 30,426)( 31,432)( 32,431)( 33,389)( 34,390)( 35,387)( 36,388)( 37,385)( 38,386)( 39,392)( 40,391)( 41,413)( 42,414)( 43,411)( 44,412)( 45,409)( 46,410)( 47,416)( 48,415)( 49,405)( 50,406)( 51,403)( 52,404)( 53,401)( 54,402)( 55,408)( 56,407)( 57,397)( 58,398)( 59,395)( 60,396)( 61,393)( 62,394)( 63,400)( 64,399)( 65,453)( 66,454)( 67,451)( 68,452)( 69,449)( 70,450)( 71,456)( 72,455)( 73,477)( 74,478)( 75,475)( 76,476)( 77,473)( 78,474)( 79,480)( 80,479)( 81,469)( 82,470)( 83,467)( 84,468)( 85,465)( 86,466)( 87,472)( 88,471)( 89,461)( 90,462)( 91,459)( 92,460)( 93,457)( 94,458)( 95,464)( 96,463)( 97,325)( 98,326)( 99,323)(100,324)(101,321)(102,322)(103,328)(104,327)(105,349)(106,350)(107,347)(108,348)(109,345)(110,346)(111,352)(112,351)(113,341)(114,342)(115,339)(116,340)(117,337)(118,338)(119,344)(120,343)(121,333)(122,334)(123,331)(124,332)(125,329)(126,330)(127,336)(128,335)(129,293)(130,294)(131,291)(132,292)(133,289)(134,290)(135,296)(136,295)(137,317)(138,318)(139,315)(140,316)(141,313)(142,314)(143,320)(144,319)(145,309)(146,310)(147,307)(148,308)(149,305)(150,306)(151,312)(152,311)(153,301)(154,302)(155,299)(156,300)(157,297)(158,298)(159,304)(160,303)(161,357)(162,358)(163,355)(164,356)(165,353)(166,354)(167,360)(168,359)(169,381)(170,382)(171,379)(172,380)(173,377)(174,378)(175,384)(176,383)(177,373)(178,374)(179,371)(180,372)(181,369)(182,370)(183,376)(184,375)(185,365)(186,366)(187,363)(188,364)(189,361)(190,362)(191,368)(192,367)(193,517)(194,518)(195,515)(196,516)(197,513)(198,514)(199,520)(200,519)(201,541)(202,542)(203,539)(204,540)(205,537)(206,538)(207,544)(208,543)(209,533)(210,534)(211,531)(212,532)(213,529)(214,530)(215,536)(216,535)(217,525)(218,526)(219,523)(220,524)(221,521)(222,522)(223,528)(224,527)(225,485)(226,486)(227,483)(228,484)(229,481)(230,482)(231,488)(232,487)(233,509)(234,510)(235,507)(236,508)(237,505)(238,506)(239,512)(240,511)(241,501)(242,502)(243,499)(244,500)(245,497)(246,498)(247,504)(248,503)(249,493)(250,494)(251,491)(252,492)(253,489)(254,490)(255,496)(256,495)(257,549)(258,550)(259,547)(260,548)(261,545)(262,546)(263,552)(264,551)(265,573)(266,574)(267,571)(268,572)(269,569)(270,570)(271,576)(272,575)(273,565)(274,566)(275,563)(276,564)(277,561)(278,562)(279,568)(280,567)(281,557)(282,558)(283,555)(284,556)(285,553)(286,554)(287,560)(288,559);
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*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*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*s1*s2 >;
References : None.
to this polytope

Twisty Puzzle