Polytope of Type {3,18}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,18}*1296b
if this polytope has a name.
Group : SmallGroup(1296,3492)
Rank : 3
Schlafli Type : {3,18}
Number of vertices, edges, etc : 36, 324, 216
Order of s0s1s2 : 12
Order of s0s1s2s1 : 18
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 : {3,9}*648
27-fold quotients : {3,6}*48
54-fold quotients : {3,3}*24
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)( 2,429)( 3,428)( 4,409)( 5,411)( 6,410)( 7,418)( 8,420)
( 9,419)( 10,430)( 11,432)( 12,431)( 13,412)( 14,414)( 15,413)( 16,421)
( 17,423)( 18,422)( 19,424)( 20,426)( 21,425)( 22,406)( 23,408)( 24,407)
( 25,415)( 26,417)( 27,416)( 28,373)( 29,375)( 30,374)( 31,355)( 32,357)
( 33,356)( 34,364)( 35,366)( 36,365)( 37,376)( 38,378)( 39,377)( 40,358)
( 41,360)( 42,359)( 43,367)( 44,369)( 45,368)( 46,370)( 47,372)( 48,371)
( 49,352)( 50,354)( 51,353)( 52,361)( 53,363)( 54,362)( 55,400)( 56,402)
( 57,401)( 58,382)( 59,384)( 60,383)( 61,391)( 62,393)( 63,392)( 64,403)
( 65,405)( 66,404)( 67,385)( 68,387)( 69,386)( 70,394)( 71,396)( 72,395)
( 73,397)( 74,399)( 75,398)( 76,379)( 77,381)( 78,380)( 79,388)( 80,390)
( 81,389)( 82,346)( 83,348)( 84,347)( 85,328)( 86,330)( 87,329)( 88,337)
( 89,339)( 90,338)( 91,349)( 92,351)( 93,350)( 94,331)( 95,333)( 96,332)
( 97,340)( 98,342)( 99,341)(100,343)(101,345)(102,344)(103,325)(104,327)
(105,326)(106,334)(107,336)(108,335)(109,643)(110,645)(111,644)(112,625)
(113,627)(114,626)(115,634)(116,636)(117,635)(118,646)(119,648)(120,647)
(121,628)(122,630)(123,629)(124,637)(125,639)(126,638)(127,640)(128,642)
(129,641)(130,622)(131,624)(132,623)(133,631)(134,633)(135,632)(136,589)
(137,591)(138,590)(139,571)(140,573)(141,572)(142,580)(143,582)(144,581)
(145,592)(146,594)(147,593)(148,574)(149,576)(150,575)(151,583)(152,585)
(153,584)(154,586)(155,588)(156,587)(157,568)(158,570)(159,569)(160,577)
(161,579)(162,578)(163,616)(164,618)(165,617)(166,598)(167,600)(168,599)
(169,607)(170,609)(171,608)(172,619)(173,621)(174,620)(175,601)(176,603)
(177,602)(178,610)(179,612)(180,611)(181,613)(182,615)(183,614)(184,595)
(185,597)(186,596)(187,604)(188,606)(189,605)(190,562)(191,564)(192,563)
(193,544)(194,546)(195,545)(196,553)(197,555)(198,554)(199,565)(200,567)
(201,566)(202,547)(203,549)(204,548)(205,556)(206,558)(207,557)(208,559)
(209,561)(210,560)(211,541)(212,543)(213,542)(214,550)(215,552)(216,551)
(217,535)(218,537)(219,536)(220,517)(221,519)(222,518)(223,526)(224,528)
(225,527)(226,538)(227,540)(228,539)(229,520)(230,522)(231,521)(232,529)
(233,531)(234,530)(235,532)(236,534)(237,533)(238,514)(239,516)(240,515)
(241,523)(242,525)(243,524)(244,481)(245,483)(246,482)(247,463)(248,465)
(249,464)(250,472)(251,474)(252,473)(253,484)(254,486)(255,485)(256,466)
(257,468)(258,467)(259,475)(260,477)(261,476)(262,478)(263,480)(264,479)
(265,460)(266,462)(267,461)(268,469)(269,471)(270,470)(271,508)(272,510)
(273,509)(274,490)(275,492)(276,491)(277,499)(278,501)(279,500)(280,511)
(281,513)(282,512)(283,493)(284,495)(285,494)(286,502)(287,504)(288,503)
(289,505)(290,507)(291,506)(292,487)(293,489)(294,488)(295,496)(296,498)
(297,497)(298,454)(299,456)(300,455)(301,436)(302,438)(303,437)(304,445)
(305,447)(306,446)(307,457)(308,459)(309,458)(310,439)(311,441)(312,440)
(313,448)(314,450)(315,449)(316,451)(317,453)(318,452)(319,433)(320,435)
(321,434)(322,442)(323,444)(324,443);;
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*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*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)!( 1,109)( 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)( 2,429)( 3,428)( 4,409)( 5,411)( 6,410)( 7,418)
( 8,420)( 9,419)( 10,430)( 11,432)( 12,431)( 13,412)( 14,414)( 15,413)
( 16,421)( 17,423)( 18,422)( 19,424)( 20,426)( 21,425)( 22,406)( 23,408)
( 24,407)( 25,415)( 26,417)( 27,416)( 28,373)( 29,375)( 30,374)( 31,355)
( 32,357)( 33,356)( 34,364)( 35,366)( 36,365)( 37,376)( 38,378)( 39,377)
( 40,358)( 41,360)( 42,359)( 43,367)( 44,369)( 45,368)( 46,370)( 47,372)
( 48,371)( 49,352)( 50,354)( 51,353)( 52,361)( 53,363)( 54,362)( 55,400)
( 56,402)( 57,401)( 58,382)( 59,384)( 60,383)( 61,391)( 62,393)( 63,392)
( 64,403)( 65,405)( 66,404)( 67,385)( 68,387)( 69,386)( 70,394)( 71,396)
( 72,395)( 73,397)( 74,399)( 75,398)( 76,379)( 77,381)( 78,380)( 79,388)
( 80,390)( 81,389)( 82,346)( 83,348)( 84,347)( 85,328)( 86,330)( 87,329)
( 88,337)( 89,339)( 90,338)( 91,349)( 92,351)( 93,350)( 94,331)( 95,333)
( 96,332)( 97,340)( 98,342)( 99,341)(100,343)(101,345)(102,344)(103,325)
(104,327)(105,326)(106,334)(107,336)(108,335)(109,643)(110,645)(111,644)
(112,625)(113,627)(114,626)(115,634)(116,636)(117,635)(118,646)(119,648)
(120,647)(121,628)(122,630)(123,629)(124,637)(125,639)(126,638)(127,640)
(128,642)(129,641)(130,622)(131,624)(132,623)(133,631)(134,633)(135,632)
(136,589)(137,591)(138,590)(139,571)(140,573)(141,572)(142,580)(143,582)
(144,581)(145,592)(146,594)(147,593)(148,574)(149,576)(150,575)(151,583)
(152,585)(153,584)(154,586)(155,588)(156,587)(157,568)(158,570)(159,569)
(160,577)(161,579)(162,578)(163,616)(164,618)(165,617)(166,598)(167,600)
(168,599)(169,607)(170,609)(171,608)(172,619)(173,621)(174,620)(175,601)
(176,603)(177,602)(178,610)(179,612)(180,611)(181,613)(182,615)(183,614)
(184,595)(185,597)(186,596)(187,604)(188,606)(189,605)(190,562)(191,564)
(192,563)(193,544)(194,546)(195,545)(196,553)(197,555)(198,554)(199,565)
(200,567)(201,566)(202,547)(203,549)(204,548)(205,556)(206,558)(207,557)
(208,559)(209,561)(210,560)(211,541)(212,543)(213,542)(214,550)(215,552)
(216,551)(217,535)(218,537)(219,536)(220,517)(221,519)(222,518)(223,526)
(224,528)(225,527)(226,538)(227,540)(228,539)(229,520)(230,522)(231,521)
(232,529)(233,531)(234,530)(235,532)(236,534)(237,533)(238,514)(239,516)
(240,515)(241,523)(242,525)(243,524)(244,481)(245,483)(246,482)(247,463)
(248,465)(249,464)(250,472)(251,474)(252,473)(253,484)(254,486)(255,485)
(256,466)(257,468)(258,467)(259,475)(260,477)(261,476)(262,478)(263,480)
(264,479)(265,460)(266,462)(267,461)(268,469)(269,471)(270,470)(271,508)
(272,510)(273,509)(274,490)(275,492)(276,491)(277,499)(278,501)(279,500)
(280,511)(281,513)(282,512)(283,493)(284,495)(285,494)(286,502)(287,504)
(288,503)(289,505)(290,507)(291,506)(292,487)(293,489)(294,488)(295,496)
(296,498)(297,497)(298,454)(299,456)(300,455)(301,436)(302,438)(303,437)
(304,445)(305,447)(306,446)(307,457)(308,459)(309,458)(310,439)(311,441)
(312,440)(313,448)(314,450)(315,449)(316,451)(317,453)(318,452)(319,433)
(320,435)(321,434)(322,442)(323,444)(324,443);
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*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References : None.
to this polytope