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}*1296e
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 : 18
Order of s0s1s2s1 : 4
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}*648a
   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 := (  1,406)(  2,407)(  3,408)(  4,412)(  5,413)(  6,414)(  7,409)(  8,410)(  9,411)( 10,424)( 11,425)( 12,426)( 13,430)( 14,431)( 15,432)( 16,427)( 17,428)( 18,429)( 19,415)( 20,416)( 21,417)( 22,421)( 23,422)( 24,423)( 25,418)( 26,419)( 27,420)( 28,379)( 29,380)( 30,381)( 31,385)( 32,386)( 33,387)( 34,382)( 35,383)( 36,384)( 37,397)( 38,398)( 39,399)( 40,403)( 41,404)( 42,405)( 43,400)( 44,401)( 45,402)( 46,388)( 47,389)( 48,390)( 49,394)( 50,395)( 51,396)( 52,391)( 53,392)( 54,393)( 55,352)( 56,353)( 57,354)( 58,358)( 59,359)( 60,360)( 61,355)( 62,356)( 63,357)( 64,370)( 65,371)( 66,372)( 67,376)( 68,377)( 69,378)( 70,373)( 71,374)( 72,375)( 73,361)( 74,362)( 75,363)( 76,367)( 77,368)( 78,369)( 79,364)( 80,365)( 81,366)( 82,325)( 83,326)( 84,327)( 85,331)( 86,332)( 87,333)( 88,328)( 89,329)( 90,330)( 91,343)( 92,344)( 93,345)( 94,349)( 95,350)( 96,351)( 97,346)( 98,347)( 99,348)(100,334)(101,335)(102,336)(103,340)(104,341)(105,342)(106,337)(107,338)(108,339)(109,514)(110,515)(111,516)(112,520)(113,521)(114,522)(115,517)(116,518)(117,519)(118,532)(119,533)(120,534)(121,538)(122,539)(123,540)(124,535)(125,536)(126,537)(127,523)(128,524)(129,525)(130,529)(131,530)(132,531)(133,526)(134,527)(135,528)(136,487)(137,488)(138,489)(139,493)(140,494)(141,495)(142,490)(143,491)(144,492)(145,505)(146,506)(147,507)(148,511)(149,512)(150,513)(151,508)(152,509)(153,510)(154,496)(155,497)(156,498)(157,502)(158,503)(159,504)(160,499)(161,500)(162,501)(163,460)(164,461)(165,462)(166,466)(167,467)(168,468)(169,463)(170,464)(171,465)(172,478)(173,479)(174,480)(175,484)(176,485)(177,486)(178,481)(179,482)(180,483)(181,469)(182,470)(183,471)(184,475)(185,476)(186,477)(187,472)(188,473)(189,474)(190,433)(191,434)(192,435)(193,439)(194,440)(195,441)(196,436)(197,437)(198,438)(199,451)(200,452)(201,453)(202,457)(203,458)(204,459)(205,454)(206,455)(207,456)(208,442)(209,443)(210,444)(211,448)(212,449)(213,450)(214,445)(215,446)(216,447)(217,622)(218,623)(219,624)(220,628)(221,629)(222,630)(223,625)(224,626)(225,627)(226,640)(227,641)(228,642)(229,646)(230,647)(231,648)(232,643)(233,644)(234,645)(235,631)(236,632)(237,633)(238,637)(239,638)(240,639)(241,634)(242,635)(243,636)(244,595)(245,596)(246,597)(247,601)(248,602)(249,603)(250,598)(251,599)(252,600)(253,613)(254,614)(255,615)(256,619)(257,620)(258,621)(259,616)(260,617)(261,618)(262,604)(263,605)(264,606)(265,610)(266,611)(267,612)(268,607)(269,608)(270,609)(271,568)(272,569)(273,570)(274,574)(275,575)(276,576)(277,571)(278,572)(279,573)(280,586)(281,587)(282,588)(283,592)(284,593)(285,594)(286,589)(287,590)(288,591)(289,577)(290,578)(291,579)(292,583)(293,584)(294,585)(295,580)(296,581)(297,582)(298,541)(299,542)(300,543)(301,547)(302,548)(303,549)(304,544)(305,545)(306,546)(307,559)(308,560)(309,561)(310,565)(311,566)(312,567)(313,562)(314,563)(315,564)(316,550)(317,551)(318,552)(319,556)(320,557)(321,558)(322,553)(323,554)(324,555);;
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*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*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)!(  1,406)(  2,407)(  3,408)(  4,412)(  5,413)(  6,414)(  7,409)(  8,410)(  9,411)( 10,424)( 11,425)( 12,426)( 13,430)( 14,431)( 15,432)( 16,427)( 17,428)( 18,429)( 19,415)( 20,416)( 21,417)( 22,421)( 23,422)( 24,423)( 25,418)( 26,419)( 27,420)( 28,379)( 29,380)( 30,381)( 31,385)( 32,386)( 33,387)( 34,382)( 35,383)( 36,384)( 37,397)( 38,398)( 39,399)( 40,403)( 41,404)( 42,405)( 43,400)( 44,401)( 45,402)( 46,388)( 47,389)( 48,390)( 49,394)( 50,395)( 51,396)( 52,391)( 53,392)( 54,393)( 55,352)( 56,353)( 57,354)( 58,358)( 59,359)( 60,360)( 61,355)( 62,356)( 63,357)( 64,370)( 65,371)( 66,372)( 67,376)( 68,377)( 69,378)( 70,373)( 71,374)( 72,375)( 73,361)( 74,362)( 75,363)( 76,367)( 77,368)( 78,369)( 79,364)( 80,365)( 81,366)( 82,325)( 83,326)( 84,327)( 85,331)( 86,332)( 87,333)( 88,328)( 89,329)( 90,330)( 91,343)( 92,344)( 93,345)( 94,349)( 95,350)( 96,351)( 97,346)( 98,347)( 99,348)(100,334)(101,335)(102,336)(103,340)(104,341)(105,342)(106,337)(107,338)(108,339)(109,514)(110,515)(111,516)(112,520)(113,521)(114,522)(115,517)(116,518)(117,519)(118,532)(119,533)(120,534)(121,538)(122,539)(123,540)(124,535)(125,536)(126,537)(127,523)(128,524)(129,525)(130,529)(131,530)(132,531)(133,526)(134,527)(135,528)(136,487)(137,488)(138,489)(139,493)(140,494)(141,495)(142,490)(143,491)(144,492)(145,505)(146,506)(147,507)(148,511)(149,512)(150,513)(151,508)(152,509)(153,510)(154,496)(155,497)(156,498)(157,502)(158,503)(159,504)(160,499)(161,500)(162,501)(163,460)(164,461)(165,462)(166,466)(167,467)(168,468)(169,463)(170,464)(171,465)(172,478)(173,479)(174,480)(175,484)(176,485)(177,486)(178,481)(179,482)(180,483)(181,469)(182,470)(183,471)(184,475)(185,476)(186,477)(187,472)(188,473)(189,474)(190,433)(191,434)(192,435)(193,439)(194,440)(195,441)(196,436)(197,437)(198,438)(199,451)(200,452)(201,453)(202,457)(203,458)(204,459)(205,454)(206,455)(207,456)(208,442)(209,443)(210,444)(211,448)(212,449)(213,450)(214,445)(215,446)(216,447)(217,622)(218,623)(219,624)(220,628)(221,629)(222,630)(223,625)(224,626)(225,627)(226,640)(227,641)(228,642)(229,646)(230,647)(231,648)(232,643)(233,644)(234,645)(235,631)(236,632)(237,633)(238,637)(239,638)(240,639)(241,634)(242,635)(243,636)(244,595)(245,596)(246,597)(247,601)(248,602)(249,603)(250,598)(251,599)(252,600)(253,613)(254,614)(255,615)(256,619)(257,620)(258,621)(259,616)(260,617)(261,618)(262,604)(263,605)(264,606)(265,610)(266,611)(267,612)(268,607)(269,608)(270,609)(271,568)(272,569)(273,570)(274,574)(275,575)(276,576)(277,571)(278,572)(279,573)(280,586)(281,587)(282,588)(283,592)(284,593)(285,594)(286,589)(287,590)(288,591)(289,577)(290,578)(291,579)(292,583)(293,584)(294,585)(295,580)(296,581)(297,582)(298,541)(299,542)(300,543)(301,547)(302,548)(303,549)(304,544)(305,545)(306,546)(307,559)(308,560)(309,561)(310,565)(311,566)(312,567)(313,562)(314,563)(315,564)(316,550)(317,551)(318,552)(319,556)(320,557)(321,558)(322,553)(323,554)(324,555);
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*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle