Polytope of Type {3,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12}*1296b
if this polytope has a name.
Group : SmallGroup(1296,3492)
Rank : 3
Schlafli Type : {3,12}
Number of vertices, edges, etc : 54, 324, 216
Order of s0s1s2 : 18
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}*648
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.
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 := ( 1,109)( 2,127)( 3,118)( 4,115)( 5,133)( 6,124)( 7,112)( 8,130)
( 9,121)( 10,111)( 11,129)( 12,120)( 13,117)( 14,135)( 15,126)( 16,114)
( 17,132)( 18,123)( 19,110)( 20,128)( 21,119)( 22,116)( 23,134)( 24,125)
( 25,113)( 26,131)( 27,122)( 28,136)( 29,154)( 30,145)( 31,142)( 32,160)
( 33,151)( 34,139)( 35,157)( 36,148)( 37,138)( 38,156)( 39,147)( 40,144)
( 41,162)( 42,153)( 43,141)( 44,159)( 45,150)( 46,137)( 47,155)( 48,146)
( 49,143)( 50,161)( 51,152)( 52,140)( 53,158)( 54,149)( 55,190)( 56,208)
( 57,199)( 58,196)( 59,214)( 60,205)( 61,193)( 62,211)( 63,202)( 64,192)
( 65,210)( 66,201)( 67,198)( 68,216)( 69,207)( 70,195)( 71,213)( 72,204)
( 73,191)( 74,209)( 75,200)( 76,197)( 77,215)( 78,206)( 79,194)( 80,212)
( 81,203)( 82,163)( 83,181)( 84,172)( 85,169)( 86,187)( 87,178)( 88,166)
( 89,184)( 90,175)( 91,165)( 92,183)( 93,174)( 94,171)( 95,189)( 96,180)
( 97,168)( 98,186)( 99,177)(100,164)(101,182)(102,173)(103,170)(104,188)
(105,179)(106,167)(107,185)(108,176)(218,235)(219,226)(220,223)(221,241)
(222,232)(224,238)(225,229)(227,237)(230,243)(231,234)(233,240)(239,242)
(245,262)(246,253)(247,250)(248,268)(249,259)(251,265)(252,256)(254,264)
(257,270)(258,261)(260,267)(266,269)(271,298)(272,316)(273,307)(274,304)
(275,322)(276,313)(277,301)(278,319)(279,310)(280,300)(281,318)(282,309)
(283,306)(284,324)(285,315)(286,303)(287,321)(288,312)(289,299)(290,317)
(291,308)(292,305)(293,323)(294,314)(295,302)(296,320)(297,311)(325,433)
(326,451)(327,442)(328,439)(329,457)(330,448)(331,436)(332,454)(333,445)
(334,435)(335,453)(336,444)(337,441)(338,459)(339,450)(340,438)(341,456)
(342,447)(343,434)(344,452)(345,443)(346,440)(347,458)(348,449)(349,437)
(350,455)(351,446)(352,460)(353,478)(354,469)(355,466)(356,484)(357,475)
(358,463)(359,481)(360,472)(361,462)(362,480)(363,471)(364,468)(365,486)
(366,477)(367,465)(368,483)(369,474)(370,461)(371,479)(372,470)(373,467)
(374,485)(375,476)(376,464)(377,482)(378,473)(379,514)(380,532)(381,523)
(382,520)(383,538)(384,529)(385,517)(386,535)(387,526)(388,516)(389,534)
(390,525)(391,522)(392,540)(393,531)(394,519)(395,537)(396,528)(397,515)
(398,533)(399,524)(400,521)(401,539)(402,530)(403,518)(404,536)(405,527)
(406,487)(407,505)(408,496)(409,493)(410,511)(411,502)(412,490)(413,508)
(414,499)(415,489)(416,507)(417,498)(418,495)(419,513)(420,504)(421,492)
(422,510)(423,501)(424,488)(425,506)(426,497)(427,494)(428,512)(429,503)
(430,491)(431,509)(432,500)(542,559)(543,550)(544,547)(545,565)(546,556)
(548,562)(549,553)(551,561)(554,567)(555,558)(557,564)(563,566)(569,586)
(570,577)(571,574)(572,592)(573,583)(575,589)(576,580)(578,588)(581,594)
(582,585)(584,591)(590,593)(595,622)(596,640)(597,631)(598,628)(599,646)
(600,637)(601,625)(602,643)(603,634)(604,624)(605,642)(606,633)(607,630)
(608,648)(609,639)(610,627)(611,645)(612,636)(613,623)(614,641)(615,632)
(616,629)(617,647)(618,638)(619,626)(620,644)(621,635);;
s2 := ( 1,427)( 2,428)( 3,429)( 4,424)( 5,425)( 6,426)( 7,430)( 8,431)
( 9,432)( 10,418)( 11,419)( 12,420)( 13,415)( 14,416)( 15,417)( 16,421)
( 17,422)( 18,423)( 19,409)( 20,410)( 21,411)( 22,406)( 23,407)( 24,408)
( 25,412)( 26,413)( 27,414)( 28,400)( 29,401)( 30,402)( 31,397)( 32,398)
( 33,399)( 34,403)( 35,404)( 36,405)( 37,391)( 38,392)( 39,393)( 40,388)
( 41,389)( 42,390)( 43,394)( 44,395)( 45,396)( 46,382)( 47,383)( 48,384)
( 49,379)( 50,380)( 51,381)( 52,385)( 53,386)( 54,387)( 55,373)( 56,374)
( 57,375)( 58,370)( 59,371)( 60,372)( 61,376)( 62,377)( 63,378)( 64,364)
( 65,365)( 66,366)( 67,361)( 68,362)( 69,363)( 70,367)( 71,368)( 72,369)
( 73,355)( 74,356)( 75,357)( 76,352)( 77,353)( 78,354)( 79,358)( 80,359)
( 81,360)( 82,346)( 83,347)( 84,348)( 85,343)( 86,344)( 87,345)( 88,349)
( 89,350)( 90,351)( 91,337)( 92,338)( 93,339)( 94,334)( 95,335)( 96,336)
( 97,340)( 98,341)( 99,342)(100,328)(101,329)(102,330)(103,325)(104,326)
(105,327)(106,331)(107,332)(108,333)(109,535)(110,536)(111,537)(112,532)
(113,533)(114,534)(115,538)(116,539)(117,540)(118,526)(119,527)(120,528)
(121,523)(122,524)(123,525)(124,529)(125,530)(126,531)(127,517)(128,518)
(129,519)(130,514)(131,515)(132,516)(133,520)(134,521)(135,522)(136,508)
(137,509)(138,510)(139,505)(140,506)(141,507)(142,511)(143,512)(144,513)
(145,499)(146,500)(147,501)(148,496)(149,497)(150,498)(151,502)(152,503)
(153,504)(154,490)(155,491)(156,492)(157,487)(158,488)(159,489)(160,493)
(161,494)(162,495)(163,481)(164,482)(165,483)(166,478)(167,479)(168,480)
(169,484)(170,485)(171,486)(172,472)(173,473)(174,474)(175,469)(176,470)
(177,471)(178,475)(179,476)(180,477)(181,463)(182,464)(183,465)(184,460)
(185,461)(186,462)(187,466)(188,467)(189,468)(190,454)(191,455)(192,456)
(193,451)(194,452)(195,453)(196,457)(197,458)(198,459)(199,445)(200,446)
(201,447)(202,442)(203,443)(204,444)(205,448)(206,449)(207,450)(208,436)
(209,437)(210,438)(211,433)(212,434)(213,435)(214,439)(215,440)(216,441)
(217,643)(218,644)(219,645)(220,640)(221,641)(222,642)(223,646)(224,647)
(225,648)(226,634)(227,635)(228,636)(229,631)(230,632)(231,633)(232,637)
(233,638)(234,639)(235,625)(236,626)(237,627)(238,622)(239,623)(240,624)
(241,628)(242,629)(243,630)(244,616)(245,617)(246,618)(247,613)(248,614)
(249,615)(250,619)(251,620)(252,621)(253,607)(254,608)(255,609)(256,604)
(257,605)(258,606)(259,610)(260,611)(261,612)(262,598)(263,599)(264,600)
(265,595)(266,596)(267,597)(268,601)(269,602)(270,603)(271,589)(272,590)
(273,591)(274,586)(275,587)(276,588)(277,592)(278,593)(279,594)(280,580)
(281,581)(282,582)(283,577)(284,578)(285,579)(286,583)(287,584)(288,585)
(289,571)(290,572)(291,573)(292,568)(293,569)(294,570)(295,574)(296,575)
(297,576)(298,562)(299,563)(300,564)(301,559)(302,560)(303,561)(304,565)
(305,566)(306,567)(307,553)(308,554)(309,555)(310,550)(311,551)(312,552)
(313,556)(314,557)(315,558)(316,544)(317,545)(318,546)(319,541)(320,542)
(321,543)(322,547)(323,548)(324,549);;
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,
s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1,
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(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)!( 1,109)( 2,127)( 3,118)( 4,115)( 5,133)( 6,124)( 7,112)
( 8,130)( 9,121)( 10,111)( 11,129)( 12,120)( 13,117)( 14,135)( 15,126)
( 16,114)( 17,132)( 18,123)( 19,110)( 20,128)( 21,119)( 22,116)( 23,134)
( 24,125)( 25,113)( 26,131)( 27,122)( 28,136)( 29,154)( 30,145)( 31,142)
( 32,160)( 33,151)( 34,139)( 35,157)( 36,148)( 37,138)( 38,156)( 39,147)
( 40,144)( 41,162)( 42,153)( 43,141)( 44,159)( 45,150)( 46,137)( 47,155)
( 48,146)( 49,143)( 50,161)( 51,152)( 52,140)( 53,158)( 54,149)( 55,190)
( 56,208)( 57,199)( 58,196)( 59,214)( 60,205)( 61,193)( 62,211)( 63,202)
( 64,192)( 65,210)( 66,201)( 67,198)( 68,216)( 69,207)( 70,195)( 71,213)
( 72,204)( 73,191)( 74,209)( 75,200)( 76,197)( 77,215)( 78,206)( 79,194)
( 80,212)( 81,203)( 82,163)( 83,181)( 84,172)( 85,169)( 86,187)( 87,178)
( 88,166)( 89,184)( 90,175)( 91,165)( 92,183)( 93,174)( 94,171)( 95,189)
( 96,180)( 97,168)( 98,186)( 99,177)(100,164)(101,182)(102,173)(103,170)
(104,188)(105,179)(106,167)(107,185)(108,176)(218,235)(219,226)(220,223)
(221,241)(222,232)(224,238)(225,229)(227,237)(230,243)(231,234)(233,240)
(239,242)(245,262)(246,253)(247,250)(248,268)(249,259)(251,265)(252,256)
(254,264)(257,270)(258,261)(260,267)(266,269)(271,298)(272,316)(273,307)
(274,304)(275,322)(276,313)(277,301)(278,319)(279,310)(280,300)(281,318)
(282,309)(283,306)(284,324)(285,315)(286,303)(287,321)(288,312)(289,299)
(290,317)(291,308)(292,305)(293,323)(294,314)(295,302)(296,320)(297,311)
(325,433)(326,451)(327,442)(328,439)(329,457)(330,448)(331,436)(332,454)
(333,445)(334,435)(335,453)(336,444)(337,441)(338,459)(339,450)(340,438)
(341,456)(342,447)(343,434)(344,452)(345,443)(346,440)(347,458)(348,449)
(349,437)(350,455)(351,446)(352,460)(353,478)(354,469)(355,466)(356,484)
(357,475)(358,463)(359,481)(360,472)(361,462)(362,480)(363,471)(364,468)
(365,486)(366,477)(367,465)(368,483)(369,474)(370,461)(371,479)(372,470)
(373,467)(374,485)(375,476)(376,464)(377,482)(378,473)(379,514)(380,532)
(381,523)(382,520)(383,538)(384,529)(385,517)(386,535)(387,526)(388,516)
(389,534)(390,525)(391,522)(392,540)(393,531)(394,519)(395,537)(396,528)
(397,515)(398,533)(399,524)(400,521)(401,539)(402,530)(403,518)(404,536)
(405,527)(406,487)(407,505)(408,496)(409,493)(410,511)(411,502)(412,490)
(413,508)(414,499)(415,489)(416,507)(417,498)(418,495)(419,513)(420,504)
(421,492)(422,510)(423,501)(424,488)(425,506)(426,497)(427,494)(428,512)
(429,503)(430,491)(431,509)(432,500)(542,559)(543,550)(544,547)(545,565)
(546,556)(548,562)(549,553)(551,561)(554,567)(555,558)(557,564)(563,566)
(569,586)(570,577)(571,574)(572,592)(573,583)(575,589)(576,580)(578,588)
(581,594)(582,585)(584,591)(590,593)(595,622)(596,640)(597,631)(598,628)
(599,646)(600,637)(601,625)(602,643)(603,634)(604,624)(605,642)(606,633)
(607,630)(608,648)(609,639)(610,627)(611,645)(612,636)(613,623)(614,641)
(615,632)(616,629)(617,647)(618,638)(619,626)(620,644)(621,635);
s2 := Sym(648)!( 1,427)( 2,428)( 3,429)( 4,424)( 5,425)( 6,426)( 7,430)
( 8,431)( 9,432)( 10,418)( 11,419)( 12,420)( 13,415)( 14,416)( 15,417)
( 16,421)( 17,422)( 18,423)( 19,409)( 20,410)( 21,411)( 22,406)( 23,407)
( 24,408)( 25,412)( 26,413)( 27,414)( 28,400)( 29,401)( 30,402)( 31,397)
( 32,398)( 33,399)( 34,403)( 35,404)( 36,405)( 37,391)( 38,392)( 39,393)
( 40,388)( 41,389)( 42,390)( 43,394)( 44,395)( 45,396)( 46,382)( 47,383)
( 48,384)( 49,379)( 50,380)( 51,381)( 52,385)( 53,386)( 54,387)( 55,373)
( 56,374)( 57,375)( 58,370)( 59,371)( 60,372)( 61,376)( 62,377)( 63,378)
( 64,364)( 65,365)( 66,366)( 67,361)( 68,362)( 69,363)( 70,367)( 71,368)
( 72,369)( 73,355)( 74,356)( 75,357)( 76,352)( 77,353)( 78,354)( 79,358)
( 80,359)( 81,360)( 82,346)( 83,347)( 84,348)( 85,343)( 86,344)( 87,345)
( 88,349)( 89,350)( 90,351)( 91,337)( 92,338)( 93,339)( 94,334)( 95,335)
( 96,336)( 97,340)( 98,341)( 99,342)(100,328)(101,329)(102,330)(103,325)
(104,326)(105,327)(106,331)(107,332)(108,333)(109,535)(110,536)(111,537)
(112,532)(113,533)(114,534)(115,538)(116,539)(117,540)(118,526)(119,527)
(120,528)(121,523)(122,524)(123,525)(124,529)(125,530)(126,531)(127,517)
(128,518)(129,519)(130,514)(131,515)(132,516)(133,520)(134,521)(135,522)
(136,508)(137,509)(138,510)(139,505)(140,506)(141,507)(142,511)(143,512)
(144,513)(145,499)(146,500)(147,501)(148,496)(149,497)(150,498)(151,502)
(152,503)(153,504)(154,490)(155,491)(156,492)(157,487)(158,488)(159,489)
(160,493)(161,494)(162,495)(163,481)(164,482)(165,483)(166,478)(167,479)
(168,480)(169,484)(170,485)(171,486)(172,472)(173,473)(174,474)(175,469)
(176,470)(177,471)(178,475)(179,476)(180,477)(181,463)(182,464)(183,465)
(184,460)(185,461)(186,462)(187,466)(188,467)(189,468)(190,454)(191,455)
(192,456)(193,451)(194,452)(195,453)(196,457)(197,458)(198,459)(199,445)
(200,446)(201,447)(202,442)(203,443)(204,444)(205,448)(206,449)(207,450)
(208,436)(209,437)(210,438)(211,433)(212,434)(213,435)(214,439)(215,440)
(216,441)(217,643)(218,644)(219,645)(220,640)(221,641)(222,642)(223,646)
(224,647)(225,648)(226,634)(227,635)(228,636)(229,631)(230,632)(231,633)
(232,637)(233,638)(234,639)(235,625)(236,626)(237,627)(238,622)(239,623)
(240,624)(241,628)(242,629)(243,630)(244,616)(245,617)(246,618)(247,613)
(248,614)(249,615)(250,619)(251,620)(252,621)(253,607)(254,608)(255,609)
(256,604)(257,605)(258,606)(259,610)(260,611)(261,612)(262,598)(263,599)
(264,600)(265,595)(266,596)(267,597)(268,601)(269,602)(270,603)(271,589)
(272,590)(273,591)(274,586)(275,587)(276,588)(277,592)(278,593)(279,594)
(280,580)(281,581)(282,582)(283,577)(284,578)(285,579)(286,583)(287,584)
(288,585)(289,571)(290,572)(291,573)(292,568)(293,569)(294,570)(295,574)
(296,575)(297,576)(298,562)(299,563)(300,564)(301,559)(302,560)(303,561)
(304,565)(305,566)(306,567)(307,553)(308,554)(309,555)(310,550)(311,551)
(312,552)(313,556)(314,557)(315,558)(316,544)(317,545)(318,546)(319,541)
(320,542)(321,543)(322,547)(323,548)(324,549);
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*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1,
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