Polytope of Type {12,6}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle