Polytope of Type {9,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,12}*1296f
if this polytope has a name.
Group : SmallGroup(1296,3492)
Rank : 3
Schlafli Type : {9,12}
Number of vertices, edges, etc : 54, 324, 72
Order of s0s1s2 : 6
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 : {9,12}*648b
   27-fold quotients : {3,4}*48
   54-fold quotients : {3,4}*24
   108-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*s0*s2*s1> of order 3.
      24 facets:
         24 of {9}*18
      30 vertex figures:
         12 of {12}*24
         18 of {4}*8

Permutation Representation (GAP) : 
s0 := (  2,  3)(  4, 19)(  5, 21)(  6, 20)(  7, 10)(  8, 12)(  9, 11)( 13, 25)( 14, 27)( 15, 26)( 17, 18)( 23, 24)( 28, 55)( 29, 57)( 30, 56)( 31, 73)( 32, 75)( 33, 74)( 34, 64)( 35, 66)( 36, 65)( 37, 61)( 38, 63)( 39, 62)( 40, 79)( 41, 81)( 42, 80)( 43, 70)( 44, 72)( 45, 71)( 46, 58)( 47, 60)( 48, 59)( 49, 76)( 50, 78)( 51, 77)( 52, 67)( 53, 69)( 54, 68)( 83, 84)( 85,100)( 86,102)( 87,101)( 88, 91)( 89, 93)( 90, 92)( 94,106)( 95,108)( 96,107)( 98, 99)(104,105)(109,217)(110,219)(111,218)(112,235)(113,237)(114,236)(115,226)(116,228)(117,227)(118,223)(119,225)(120,224)(121,241)(122,243)(123,242)(124,232)(125,234)(126,233)(127,220)(128,222)(129,221)(130,238)(131,240)(132,239)(133,229)(134,231)(135,230)(136,271)(137,273)(138,272)(139,289)(140,291)(141,290)(142,280)(143,282)(144,281)(145,277)(146,279)(147,278)(148,295)(149,297)(150,296)(151,286)(152,288)(153,287)(154,274)(155,276)(156,275)(157,292)(158,294)(159,293)(160,283)(161,285)(162,284)(163,244)(164,246)(165,245)(166,262)(167,264)(168,263)(169,253)(170,255)(171,254)(172,250)(173,252)(174,251)(175,268)(176,270)(177,269)(178,259)(179,261)(180,260)(181,247)(182,249)(183,248)(184,265)(185,267)(186,266)(187,256)(188,258)(189,257)(190,298)(191,300)(192,299)(193,316)(194,318)(195,317)(196,307)(197,309)(198,308)(199,304)(200,306)(201,305)(202,322)(203,324)(204,323)(205,313)(206,315)(207,314)(208,301)(209,303)(210,302)(211,319)(212,321)(213,320)(214,310)(215,312)(216,311)(326,327)(328,343)(329,345)(330,344)(331,334)(332,336)(333,335)(337,349)(338,351)(339,350)(341,342)(347,348)(352,379)(353,381)(354,380)(355,397)(356,399)(357,398)(358,388)(359,390)(360,389)(361,385)(362,387)(363,386)(364,403)(365,405)(366,404)(367,394)(368,396)(369,395)(370,382)(371,384)(372,383)(373,400)(374,402)(375,401)(376,391)(377,393)(378,392)(407,408)(409,424)(410,426)(411,425)(412,415)(413,417)(414,416)(418,430)(419,432)(420,431)(422,423)(428,429)(433,541)(434,543)(435,542)(436,559)(437,561)(438,560)(439,550)(440,552)(441,551)(442,547)(443,549)(444,548)(445,565)(446,567)(447,566)(448,556)(449,558)(450,557)(451,544)(452,546)(453,545)(454,562)(455,564)(456,563)(457,553)(458,555)(459,554)(460,595)(461,597)(462,596)(463,613)(464,615)(465,614)(466,604)(467,606)(468,605)(469,601)(470,603)(471,602)(472,619)(473,621)(474,620)(475,610)(476,612)(477,611)(478,598)(479,600)(480,599)(481,616)(482,618)(483,617)(484,607)(485,609)(486,608)(487,568)(488,570)(489,569)(490,586)(491,588)(492,587)(493,577)(494,579)(495,578)(496,574)(497,576)(498,575)(499,592)(500,594)(501,593)(502,583)(503,585)(504,584)(505,571)(506,573)(507,572)(508,589)(509,591)(510,590)(511,580)(512,582)(513,581)(514,622)(515,624)(516,623)(517,640)(518,642)(519,641)(520,631)(521,633)(522,632)(523,628)(524,630)(525,629)(526,646)(527,648)(528,647)(529,637)(530,639)(531,638)(532,625)(533,627)(534,626)(535,643)(536,645)(537,644)(538,634)(539,636)(540,635);;
s1 := (  1,112)(  2,130)(  3,121)(  4,109)(  5,127)(  6,118)(  7,115)(  8,133)(  9,124)( 10,114)( 11,132)( 12,123)( 13,111)( 14,129)( 15,120)( 16,117)( 17,135)( 18,126)( 19,113)( 20,131)( 21,122)( 22,110)( 23,128)( 24,119)( 25,116)( 26,134)( 27,125)( 28,139)( 29,157)( 30,148)( 31,136)( 32,154)( 33,145)( 34,142)( 35,160)( 36,151)( 37,141)( 38,159)( 39,150)( 40,138)( 41,156)( 42,147)( 43,144)( 44,162)( 45,153)( 46,140)( 47,158)( 48,149)( 49,137)( 50,155)( 51,146)( 52,143)( 53,161)( 54,152)( 55,193)( 56,211)( 57,202)( 58,190)( 59,208)( 60,199)( 61,196)( 62,214)( 63,205)( 64,195)( 65,213)( 66,204)( 67,192)( 68,210)( 69,201)( 70,198)( 71,216)( 72,207)( 73,194)( 74,212)( 75,203)( 76,191)( 77,209)( 78,200)( 79,197)( 80,215)( 81,206)( 82,166)( 83,184)( 84,175)( 85,163)( 86,181)( 87,172)( 88,169)( 89,187)( 90,178)( 91,168)( 92,186)( 93,177)( 94,165)( 95,183)( 96,174)( 97,171)( 98,189)( 99,180)(100,167)(101,185)(102,176)(103,164)(104,182)(105,173)(106,170)(107,188)(108,179)(217,220)(218,238)(219,229)(221,235)(222,226)(224,241)(225,232)(227,240)(228,231)(230,237)(233,243)(236,239)(244,247)(245,265)(246,256)(248,262)(249,253)(251,268)(252,259)(254,267)(255,258)(257,264)(260,270)(263,266)(271,301)(272,319)(273,310)(274,298)(275,316)(276,307)(277,304)(278,322)(279,313)(280,303)(281,321)(282,312)(283,300)(284,318)(285,309)(286,306)(287,324)(288,315)(289,302)(290,320)(291,311)(292,299)(293,317)(294,308)(295,305)(296,323)(297,314)(325,436)(326,454)(327,445)(328,433)(329,451)(330,442)(331,439)(332,457)(333,448)(334,438)(335,456)(336,447)(337,435)(338,453)(339,444)(340,441)(341,459)(342,450)(343,437)(344,455)(345,446)(346,434)(347,452)(348,443)(349,440)(350,458)(351,449)(352,463)(353,481)(354,472)(355,460)(356,478)(357,469)(358,466)(359,484)(360,475)(361,465)(362,483)(363,474)(364,462)(365,480)(366,471)(367,468)(368,486)(369,477)(370,464)(371,482)(372,473)(373,461)(374,479)(375,470)(376,467)(377,485)(378,476)(379,517)(380,535)(381,526)(382,514)(383,532)(384,523)(385,520)(386,538)(387,529)(388,519)(389,537)(390,528)(391,516)(392,534)(393,525)(394,522)(395,540)(396,531)(397,518)(398,536)(399,527)(400,515)(401,533)(402,524)(403,521)(404,539)(405,530)(406,490)(407,508)(408,499)(409,487)(410,505)(411,496)(412,493)(413,511)(414,502)(415,492)(416,510)(417,501)(418,489)(419,507)(420,498)(421,495)(422,513)(423,504)(424,491)(425,509)(426,500)(427,488)(428,506)(429,497)(430,494)(431,512)(432,503)(541,544)(542,562)(543,553)(545,559)(546,550)(548,565)(549,556)(551,564)(552,555)(554,561)(557,567)(560,563)(568,571)(569,589)(570,580)(572,586)(573,577)(575,592)(576,583)(578,591)(579,582)(581,588)(584,594)(587,590)(595,625)(596,643)(597,634)(598,622)(599,640)(600,631)(601,628)(602,646)(603,637)(604,627)(605,645)(606,636)(607,624)(608,642)(609,633)(610,630)(611,648)(612,639)(613,626)(614,644)(615,635)(616,623)(617,641)(618,632)(619,629)(620,647)(621,638);;
s2 := (  1,421)(  2,422)(  3,423)(  4,418)(  5,419)(  6,420)(  7,415)(  8,416)(  9,417)( 10,412)( 11,413)( 12,414)( 13,409)( 14,410)( 15,411)( 16,406)( 17,407)( 18,408)( 19,430)( 20,431)( 21,432)( 22,427)( 23,428)( 24,429)( 25,424)( 26,425)( 27,426)( 28,394)( 29,395)( 30,396)( 31,391)( 32,392)( 33,393)( 34,388)( 35,389)( 36,390)( 37,385)( 38,386)( 39,387)( 40,382)( 41,383)( 42,384)( 43,379)( 44,380)( 45,381)( 46,403)( 47,404)( 48,405)( 49,400)( 50,401)( 51,402)( 52,397)( 53,398)( 54,399)( 55,367)( 56,368)( 57,369)( 58,364)( 59,365)( 60,366)( 61,361)( 62,362)( 63,363)( 64,358)( 65,359)( 66,360)( 67,355)( 68,356)( 69,357)( 70,352)( 71,353)( 72,354)( 73,376)( 74,377)( 75,378)( 76,373)( 77,374)( 78,375)( 79,370)( 80,371)( 81,372)( 82,340)( 83,341)( 84,342)( 85,337)( 86,338)( 87,339)( 88,334)( 89,335)( 90,336)( 91,331)( 92,332)( 93,333)( 94,328)( 95,329)( 96,330)( 97,325)( 98,326)( 99,327)(100,349)(101,350)(102,351)(103,346)(104,347)(105,348)(106,343)(107,344)(108,345)(109,529)(110,530)(111,531)(112,526)(113,527)(114,528)(115,523)(116,524)(117,525)(118,520)(119,521)(120,522)(121,517)(122,518)(123,519)(124,514)(125,515)(126,516)(127,538)(128,539)(129,540)(130,535)(131,536)(132,537)(133,532)(134,533)(135,534)(136,502)(137,503)(138,504)(139,499)(140,500)(141,501)(142,496)(143,497)(144,498)(145,493)(146,494)(147,495)(148,490)(149,491)(150,492)(151,487)(152,488)(153,489)(154,511)(155,512)(156,513)(157,508)(158,509)(159,510)(160,505)(161,506)(162,507)(163,475)(164,476)(165,477)(166,472)(167,473)(168,474)(169,469)(170,470)(171,471)(172,466)(173,467)(174,468)(175,463)(176,464)(177,465)(178,460)(179,461)(180,462)(181,484)(182,485)(183,486)(184,481)(185,482)(186,483)(187,478)(188,479)(189,480)(190,448)(191,449)(192,450)(193,445)(194,446)(195,447)(196,442)(197,443)(198,444)(199,439)(200,440)(201,441)(202,436)(203,437)(204,438)(205,433)(206,434)(207,435)(208,457)(209,458)(210,459)(211,454)(212,455)(213,456)(214,451)(215,452)(216,453)(217,637)(218,638)(219,639)(220,634)(221,635)(222,636)(223,631)(224,632)(225,633)(226,628)(227,629)(228,630)(229,625)(230,626)(231,627)(232,622)(233,623)(234,624)(235,646)(236,647)(237,648)(238,643)(239,644)(240,645)(241,640)(242,641)(243,642)(244,610)(245,611)(246,612)(247,607)(248,608)(249,609)(250,604)(251,605)(252,606)(253,601)(254,602)(255,603)(256,598)(257,599)(258,600)(259,595)(260,596)(261,597)(262,619)(263,620)(264,621)(265,616)(266,617)(267,618)(268,613)(269,614)(270,615)(271,583)(272,584)(273,585)(274,580)(275,581)(276,582)(277,577)(278,578)(279,579)(280,574)(281,575)(282,576)(283,571)(284,572)(285,573)(286,568)(287,569)(288,570)(289,592)(290,593)(291,594)(292,589)(293,590)(294,591)(295,586)(296,587)(297,588)(298,556)(299,557)(300,558)(301,553)(302,554)(303,555)(304,550)(305,551)(306,552)(307,547)(308,548)(309,549)(310,544)(311,545)(312,546)(313,541)(314,542)(315,543)(316,565)(317,566)(318,567)(319,562)(320,563)(321,564)(322,559)(323,560)(324,561);;
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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*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*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(648)!(  2,  3)(  4, 19)(  5, 21)(  6, 20)(  7, 10)(  8, 12)(  9, 11)( 13, 25)( 14, 27)( 15, 26)( 17, 18)( 23, 24)( 28, 55)( 29, 57)( 30, 56)( 31, 73)( 32, 75)( 33, 74)( 34, 64)( 35, 66)( 36, 65)( 37, 61)( 38, 63)( 39, 62)( 40, 79)( 41, 81)( 42, 80)( 43, 70)( 44, 72)( 45, 71)( 46, 58)( 47, 60)( 48, 59)( 49, 76)( 50, 78)( 51, 77)( 52, 67)( 53, 69)( 54, 68)( 83, 84)( 85,100)( 86,102)( 87,101)( 88, 91)( 89, 93)( 90, 92)( 94,106)( 95,108)( 96,107)( 98, 99)(104,105)(109,217)(110,219)(111,218)(112,235)(113,237)(114,236)(115,226)(116,228)(117,227)(118,223)(119,225)(120,224)(121,241)(122,243)(123,242)(124,232)(125,234)(126,233)(127,220)(128,222)(129,221)(130,238)(131,240)(132,239)(133,229)(134,231)(135,230)(136,271)(137,273)(138,272)(139,289)(140,291)(141,290)(142,280)(143,282)(144,281)(145,277)(146,279)(147,278)(148,295)(149,297)(150,296)(151,286)(152,288)(153,287)(154,274)(155,276)(156,275)(157,292)(158,294)(159,293)(160,283)(161,285)(162,284)(163,244)(164,246)(165,245)(166,262)(167,264)(168,263)(169,253)(170,255)(171,254)(172,250)(173,252)(174,251)(175,268)(176,270)(177,269)(178,259)(179,261)(180,260)(181,247)(182,249)(183,248)(184,265)(185,267)(186,266)(187,256)(188,258)(189,257)(190,298)(191,300)(192,299)(193,316)(194,318)(195,317)(196,307)(197,309)(198,308)(199,304)(200,306)(201,305)(202,322)(203,324)(204,323)(205,313)(206,315)(207,314)(208,301)(209,303)(210,302)(211,319)(212,321)(213,320)(214,310)(215,312)(216,311)(326,327)(328,343)(329,345)(330,344)(331,334)(332,336)(333,335)(337,349)(338,351)(339,350)(341,342)(347,348)(352,379)(353,381)(354,380)(355,397)(356,399)(357,398)(358,388)(359,390)(360,389)(361,385)(362,387)(363,386)(364,403)(365,405)(366,404)(367,394)(368,396)(369,395)(370,382)(371,384)(372,383)(373,400)(374,402)(375,401)(376,391)(377,393)(378,392)(407,408)(409,424)(410,426)(411,425)(412,415)(413,417)(414,416)(418,430)(419,432)(420,431)(422,423)(428,429)(433,541)(434,543)(435,542)(436,559)(437,561)(438,560)(439,550)(440,552)(441,551)(442,547)(443,549)(444,548)(445,565)(446,567)(447,566)(448,556)(449,558)(450,557)(451,544)(452,546)(453,545)(454,562)(455,564)(456,563)(457,553)(458,555)(459,554)(460,595)(461,597)(462,596)(463,613)(464,615)(465,614)(466,604)(467,606)(468,605)(469,601)(470,603)(471,602)(472,619)(473,621)(474,620)(475,610)(476,612)(477,611)(478,598)(479,600)(480,599)(481,616)(482,618)(483,617)(484,607)(485,609)(486,608)(487,568)(488,570)(489,569)(490,586)(491,588)(492,587)(493,577)(494,579)(495,578)(496,574)(497,576)(498,575)(499,592)(500,594)(501,593)(502,583)(503,585)(504,584)(505,571)(506,573)(507,572)(508,589)(509,591)(510,590)(511,580)(512,582)(513,581)(514,622)(515,624)(516,623)(517,640)(518,642)(519,641)(520,631)(521,633)(522,632)(523,628)(524,630)(525,629)(526,646)(527,648)(528,647)(529,637)(530,639)(531,638)(532,625)(533,627)(534,626)(535,643)(536,645)(537,644)(538,634)(539,636)(540,635);
s1 := Sym(648)!(  1,112)(  2,130)(  3,121)(  4,109)(  5,127)(  6,118)(  7,115)(  8,133)(  9,124)( 10,114)( 11,132)( 12,123)( 13,111)( 14,129)( 15,120)( 16,117)( 17,135)( 18,126)( 19,113)( 20,131)( 21,122)( 22,110)( 23,128)( 24,119)( 25,116)( 26,134)( 27,125)( 28,139)( 29,157)( 30,148)( 31,136)( 32,154)( 33,145)( 34,142)( 35,160)( 36,151)( 37,141)( 38,159)( 39,150)( 40,138)( 41,156)( 42,147)( 43,144)( 44,162)( 45,153)( 46,140)( 47,158)( 48,149)( 49,137)( 50,155)( 51,146)( 52,143)( 53,161)( 54,152)( 55,193)( 56,211)( 57,202)( 58,190)( 59,208)( 60,199)( 61,196)( 62,214)( 63,205)( 64,195)( 65,213)( 66,204)( 67,192)( 68,210)( 69,201)( 70,198)( 71,216)( 72,207)( 73,194)( 74,212)( 75,203)( 76,191)( 77,209)( 78,200)( 79,197)( 80,215)( 81,206)( 82,166)( 83,184)( 84,175)( 85,163)( 86,181)( 87,172)( 88,169)( 89,187)( 90,178)( 91,168)( 92,186)( 93,177)( 94,165)( 95,183)( 96,174)( 97,171)( 98,189)( 99,180)(100,167)(101,185)(102,176)(103,164)(104,182)(105,173)(106,170)(107,188)(108,179)(217,220)(218,238)(219,229)(221,235)(222,226)(224,241)(225,232)(227,240)(228,231)(230,237)(233,243)(236,239)(244,247)(245,265)(246,256)(248,262)(249,253)(251,268)(252,259)(254,267)(255,258)(257,264)(260,270)(263,266)(271,301)(272,319)(273,310)(274,298)(275,316)(276,307)(277,304)(278,322)(279,313)(280,303)(281,321)(282,312)(283,300)(284,318)(285,309)(286,306)(287,324)(288,315)(289,302)(290,320)(291,311)(292,299)(293,317)(294,308)(295,305)(296,323)(297,314)(325,436)(326,454)(327,445)(328,433)(329,451)(330,442)(331,439)(332,457)(333,448)(334,438)(335,456)(336,447)(337,435)(338,453)(339,444)(340,441)(341,459)(342,450)(343,437)(344,455)(345,446)(346,434)(347,452)(348,443)(349,440)(350,458)(351,449)(352,463)(353,481)(354,472)(355,460)(356,478)(357,469)(358,466)(359,484)(360,475)(361,465)(362,483)(363,474)(364,462)(365,480)(366,471)(367,468)(368,486)(369,477)(370,464)(371,482)(372,473)(373,461)(374,479)(375,470)(376,467)(377,485)(378,476)(379,517)(380,535)(381,526)(382,514)(383,532)(384,523)(385,520)(386,538)(387,529)(388,519)(389,537)(390,528)(391,516)(392,534)(393,525)(394,522)(395,540)(396,531)(397,518)(398,536)(399,527)(400,515)(401,533)(402,524)(403,521)(404,539)(405,530)(406,490)(407,508)(408,499)(409,487)(410,505)(411,496)(412,493)(413,511)(414,502)(415,492)(416,510)(417,501)(418,489)(419,507)(420,498)(421,495)(422,513)(423,504)(424,491)(425,509)(426,500)(427,488)(428,506)(429,497)(430,494)(431,512)(432,503)(541,544)(542,562)(543,553)(545,559)(546,550)(548,565)(549,556)(551,564)(552,555)(554,561)(557,567)(560,563)(568,571)(569,589)(570,580)(572,586)(573,577)(575,592)(576,583)(578,591)(579,582)(581,588)(584,594)(587,590)(595,625)(596,643)(597,634)(598,622)(599,640)(600,631)(601,628)(602,646)(603,637)(604,627)(605,645)(606,636)(607,624)(608,642)(609,633)(610,630)(611,648)(612,639)(613,626)(614,644)(615,635)(616,623)(617,641)(618,632)(619,629)(620,647)(621,638);
s2 := Sym(648)!(  1,421)(  2,422)(  3,423)(  4,418)(  5,419)(  6,420)(  7,415)(  8,416)(  9,417)( 10,412)( 11,413)( 12,414)( 13,409)( 14,410)( 15,411)( 16,406)( 17,407)( 18,408)( 19,430)( 20,431)( 21,432)( 22,427)( 23,428)( 24,429)( 25,424)( 26,425)( 27,426)( 28,394)( 29,395)( 30,396)( 31,391)( 32,392)( 33,393)( 34,388)( 35,389)( 36,390)( 37,385)( 38,386)( 39,387)( 40,382)( 41,383)( 42,384)( 43,379)( 44,380)( 45,381)( 46,403)( 47,404)( 48,405)( 49,400)( 50,401)( 51,402)( 52,397)( 53,398)( 54,399)( 55,367)( 56,368)( 57,369)( 58,364)( 59,365)( 60,366)( 61,361)( 62,362)( 63,363)( 64,358)( 65,359)( 66,360)( 67,355)( 68,356)( 69,357)( 70,352)( 71,353)( 72,354)( 73,376)( 74,377)( 75,378)( 76,373)( 77,374)( 78,375)( 79,370)( 80,371)( 81,372)( 82,340)( 83,341)( 84,342)( 85,337)( 86,338)( 87,339)( 88,334)( 89,335)( 90,336)( 91,331)( 92,332)( 93,333)( 94,328)( 95,329)( 96,330)( 97,325)( 98,326)( 99,327)(100,349)(101,350)(102,351)(103,346)(104,347)(105,348)(106,343)(107,344)(108,345)(109,529)(110,530)(111,531)(112,526)(113,527)(114,528)(115,523)(116,524)(117,525)(118,520)(119,521)(120,522)(121,517)(122,518)(123,519)(124,514)(125,515)(126,516)(127,538)(128,539)(129,540)(130,535)(131,536)(132,537)(133,532)(134,533)(135,534)(136,502)(137,503)(138,504)(139,499)(140,500)(141,501)(142,496)(143,497)(144,498)(145,493)(146,494)(147,495)(148,490)(149,491)(150,492)(151,487)(152,488)(153,489)(154,511)(155,512)(156,513)(157,508)(158,509)(159,510)(160,505)(161,506)(162,507)(163,475)(164,476)(165,477)(166,472)(167,473)(168,474)(169,469)(170,470)(171,471)(172,466)(173,467)(174,468)(175,463)(176,464)(177,465)(178,460)(179,461)(180,462)(181,484)(182,485)(183,486)(184,481)(185,482)(186,483)(187,478)(188,479)(189,480)(190,448)(191,449)(192,450)(193,445)(194,446)(195,447)(196,442)(197,443)(198,444)(199,439)(200,440)(201,441)(202,436)(203,437)(204,438)(205,433)(206,434)(207,435)(208,457)(209,458)(210,459)(211,454)(212,455)(213,456)(214,451)(215,452)(216,453)(217,637)(218,638)(219,639)(220,634)(221,635)(222,636)(223,631)(224,632)(225,633)(226,628)(227,629)(228,630)(229,625)(230,626)(231,627)(232,622)(233,623)(234,624)(235,646)(236,647)(237,648)(238,643)(239,644)(240,645)(241,640)(242,641)(243,642)(244,610)(245,611)(246,612)(247,607)(248,608)(249,609)(250,604)(251,605)(252,606)(253,601)(254,602)(255,603)(256,598)(257,599)(258,600)(259,595)(260,596)(261,597)(262,619)(263,620)(264,621)(265,616)(266,617)(267,618)(268,613)(269,614)(270,615)(271,583)(272,584)(273,585)(274,580)(275,581)(276,582)(277,577)(278,578)(279,579)(280,574)(281,575)(282,576)(283,571)(284,572)(285,573)(286,568)(287,569)(288,570)(289,592)(290,593)(291,594)(292,589)(293,590)(294,591)(295,586)(296,587)(297,588)(298,556)(299,557)(300,558)(301,553)(302,554)(303,555)(304,550)(305,551)(306,552)(307,547)(308,548)(309,549)(310,544)(311,545)(312,546)(313,541)(314,542)(315,543)(316,565)(317,566)(318,567)(319,562)(320,563)(321,564)(322,559)(323,560)(324,561);
poly := sub<Sym(648)|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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*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*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle