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}*576c
if this polytope has a name.
Group : SmallGroup(576,8319)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 48, 144, 24
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 :
   {12,6,2} of size 1152
Vertex Figure Of :
   {2,12,6} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,3}*288, {6,6}*288a
   3-fold quotients : {12,6}*192b
   4-fold quotients : {6,3}*144
   6-fold quotients : {12,3}*96, {6,6}*96
   8-fold quotients : {6,6}*72b
   12-fold quotients : {3,6}*48, {6,3}*48
   16-fold quotients : {6,3}*36
   24-fold quotients : {3,3}*24, {2,6}*24
   48-fold quotients : {2,3}*12
   72-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,12}*1152d, {12,12}*1152f, {12,6}*1152e
   3-fold covers : {12,18}*1728a, {12,6}*1728c, {12,6}*1728g
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      12 facets:
         6 of {4}*8
         6 of {12}*24
      16 vertex figures:
         16 of {6}*12

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

Twisty Puzzle