Polytope of Type {9,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,6}*1296f
if this polytope has a name.
Group : SmallGroup(1296,3492)
Rank : 3
Schlafli Type : {9,6}
Number of vertices, edges, etc : 108, 324, 72
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 : {9,3}*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 := ( 1,112)( 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)( 2,423)( 3,422)( 4,430)( 5,432)( 6,431)( 7,412)( 8,414)
( 9,413)( 10,415)( 11,417)( 12,416)( 13,424)( 14,426)( 15,425)( 16,406)
( 17,408)( 18,407)( 19,418)( 20,420)( 21,419)( 22,427)( 23,429)( 24,428)
( 25,409)( 26,411)( 27,410)( 28,367)( 29,369)( 30,368)( 31,376)( 32,378)
( 33,377)( 34,358)( 35,360)( 36,359)( 37,361)( 38,363)( 39,362)( 40,370)
( 41,372)( 42,371)( 43,352)( 44,354)( 45,353)( 46,364)( 47,366)( 48,365)
( 49,373)( 50,375)( 51,374)( 52,355)( 53,357)( 54,356)( 55,394)( 56,396)
( 57,395)( 58,403)( 59,405)( 60,404)( 61,385)( 62,387)( 63,386)( 64,388)
( 65,390)( 66,389)( 67,397)( 68,399)( 69,398)( 70,379)( 71,381)( 72,380)
( 73,391)( 74,393)( 75,392)( 76,400)( 77,402)( 78,401)( 79,382)( 80,384)
( 81,383)( 82,340)( 83,342)( 84,341)( 85,349)( 86,351)( 87,350)( 88,331)
( 89,333)( 90,332)( 91,334)( 92,336)( 93,335)( 94,343)( 95,345)( 96,344)
( 97,325)( 98,327)( 99,326)(100,337)(101,339)(102,338)(103,346)(104,348)
(105,347)(106,328)(107,330)(108,329)(109,637)(110,639)(111,638)(112,646)
(113,648)(114,647)(115,628)(116,630)(117,629)(118,631)(119,633)(120,632)
(121,640)(122,642)(123,641)(124,622)(125,624)(126,623)(127,634)(128,636)
(129,635)(130,643)(131,645)(132,644)(133,625)(134,627)(135,626)(136,583)
(137,585)(138,584)(139,592)(140,594)(141,593)(142,574)(143,576)(144,575)
(145,577)(146,579)(147,578)(148,586)(149,588)(150,587)(151,568)(152,570)
(153,569)(154,580)(155,582)(156,581)(157,589)(158,591)(159,590)(160,571)
(161,573)(162,572)(163,610)(164,612)(165,611)(166,619)(167,621)(168,620)
(169,601)(170,603)(171,602)(172,604)(173,606)(174,605)(175,613)(176,615)
(177,614)(178,595)(179,597)(180,596)(181,607)(182,609)(183,608)(184,616)
(185,618)(186,617)(187,598)(188,600)(189,599)(190,556)(191,558)(192,557)
(193,565)(194,567)(195,566)(196,547)(197,549)(198,548)(199,550)(200,552)
(201,551)(202,559)(203,561)(204,560)(205,541)(206,543)(207,542)(208,553)
(209,555)(210,554)(211,562)(212,564)(213,563)(214,544)(215,546)(216,545)
(217,529)(218,531)(219,530)(220,538)(221,540)(222,539)(223,520)(224,522)
(225,521)(226,523)(227,525)(228,524)(229,532)(230,534)(231,533)(232,514)
(233,516)(234,515)(235,526)(236,528)(237,527)(238,535)(239,537)(240,536)
(241,517)(242,519)(243,518)(244,475)(245,477)(246,476)(247,484)(248,486)
(249,485)(250,466)(251,468)(252,467)(253,469)(254,471)(255,470)(256,478)
(257,480)(258,479)(259,460)(260,462)(261,461)(262,472)(263,474)(264,473)
(265,481)(266,483)(267,482)(268,463)(269,465)(270,464)(271,502)(272,504)
(273,503)(274,511)(275,513)(276,512)(277,493)(278,495)(279,494)(280,496)
(281,498)(282,497)(283,505)(284,507)(285,506)(286,487)(287,489)(288,488)
(289,499)(290,501)(291,500)(292,508)(293,510)(294,509)(295,490)(296,492)
(297,491)(298,448)(299,450)(300,449)(301,457)(302,459)(303,458)(304,439)
(305,441)(306,440)(307,442)(308,444)(309,443)(310,451)(311,453)(312,452)
(313,433)(314,435)(315,434)(316,445)(317,447)(318,446)(319,454)(320,456)
(321,455)(322,436)(323,438)(324,437);;
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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*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)!( 1,112)( 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)( 2,423)( 3,422)( 4,430)( 5,432)( 6,431)( 7,412)
( 8,414)( 9,413)( 10,415)( 11,417)( 12,416)( 13,424)( 14,426)( 15,425)
( 16,406)( 17,408)( 18,407)( 19,418)( 20,420)( 21,419)( 22,427)( 23,429)
( 24,428)( 25,409)( 26,411)( 27,410)( 28,367)( 29,369)( 30,368)( 31,376)
( 32,378)( 33,377)( 34,358)( 35,360)( 36,359)( 37,361)( 38,363)( 39,362)
( 40,370)( 41,372)( 42,371)( 43,352)( 44,354)( 45,353)( 46,364)( 47,366)
( 48,365)( 49,373)( 50,375)( 51,374)( 52,355)( 53,357)( 54,356)( 55,394)
( 56,396)( 57,395)( 58,403)( 59,405)( 60,404)( 61,385)( 62,387)( 63,386)
( 64,388)( 65,390)( 66,389)( 67,397)( 68,399)( 69,398)( 70,379)( 71,381)
( 72,380)( 73,391)( 74,393)( 75,392)( 76,400)( 77,402)( 78,401)( 79,382)
( 80,384)( 81,383)( 82,340)( 83,342)( 84,341)( 85,349)( 86,351)( 87,350)
( 88,331)( 89,333)( 90,332)( 91,334)( 92,336)( 93,335)( 94,343)( 95,345)
( 96,344)( 97,325)( 98,327)( 99,326)(100,337)(101,339)(102,338)(103,346)
(104,348)(105,347)(106,328)(107,330)(108,329)(109,637)(110,639)(111,638)
(112,646)(113,648)(114,647)(115,628)(116,630)(117,629)(118,631)(119,633)
(120,632)(121,640)(122,642)(123,641)(124,622)(125,624)(126,623)(127,634)
(128,636)(129,635)(130,643)(131,645)(132,644)(133,625)(134,627)(135,626)
(136,583)(137,585)(138,584)(139,592)(140,594)(141,593)(142,574)(143,576)
(144,575)(145,577)(146,579)(147,578)(148,586)(149,588)(150,587)(151,568)
(152,570)(153,569)(154,580)(155,582)(156,581)(157,589)(158,591)(159,590)
(160,571)(161,573)(162,572)(163,610)(164,612)(165,611)(166,619)(167,621)
(168,620)(169,601)(170,603)(171,602)(172,604)(173,606)(174,605)(175,613)
(176,615)(177,614)(178,595)(179,597)(180,596)(181,607)(182,609)(183,608)
(184,616)(185,618)(186,617)(187,598)(188,600)(189,599)(190,556)(191,558)
(192,557)(193,565)(194,567)(195,566)(196,547)(197,549)(198,548)(199,550)
(200,552)(201,551)(202,559)(203,561)(204,560)(205,541)(206,543)(207,542)
(208,553)(209,555)(210,554)(211,562)(212,564)(213,563)(214,544)(215,546)
(216,545)(217,529)(218,531)(219,530)(220,538)(221,540)(222,539)(223,520)
(224,522)(225,521)(226,523)(227,525)(228,524)(229,532)(230,534)(231,533)
(232,514)(233,516)(234,515)(235,526)(236,528)(237,527)(238,535)(239,537)
(240,536)(241,517)(242,519)(243,518)(244,475)(245,477)(246,476)(247,484)
(248,486)(249,485)(250,466)(251,468)(252,467)(253,469)(254,471)(255,470)
(256,478)(257,480)(258,479)(259,460)(260,462)(261,461)(262,472)(263,474)
(264,473)(265,481)(266,483)(267,482)(268,463)(269,465)(270,464)(271,502)
(272,504)(273,503)(274,511)(275,513)(276,512)(277,493)(278,495)(279,494)
(280,496)(281,498)(282,497)(283,505)(284,507)(285,506)(286,487)(287,489)
(288,488)(289,499)(290,501)(291,500)(292,508)(293,510)(294,509)(295,490)
(296,492)(297,491)(298,448)(299,450)(300,449)(301,457)(302,459)(303,458)
(304,439)(305,441)(306,440)(307,442)(308,444)(309,443)(310,451)(311,453)
(312,452)(313,433)(314,435)(315,434)(316,445)(317,447)(318,446)(319,454)
(320,456)(321,455)(322,436)(323,438)(324,437);
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*s2*s1*s0*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1 >;
References : None.
to this polytope