Polytope of Type {81,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {81,4}*1296
if this polytope has a name.
Group : SmallGroup(1296,630)
Rank : 3
Schlafli Type : {81,4}
Number of vertices, edges, etc : 162, 324, 8
Order of s0s1s2 : 162
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {81,4}*648
3-fold quotients : {27,4}*432
4-fold quotients : {81,2}*324
6-fold quotients : {27,4}*216
9-fold quotients : {9,4}*144
12-fold quotients : {27,2}*108
18-fold quotients : {9,4}*72
27-fold quotients : {3,4}*48
36-fold quotients : {9,2}*36
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 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)( 43,104)
( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)( 51, 96)
( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)
( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)( 67, 80)
( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(109,321)(110,322)(111,324)
(112,323)(113,317)(114,318)(115,320)(116,319)(117,313)(118,314)(119,316)
(120,315)(121,309)(122,310)(123,312)(124,311)(125,305)(126,306)(127,308)
(128,307)(129,301)(130,302)(131,304)(132,303)(133,297)(134,298)(135,300)
(136,299)(137,293)(138,294)(139,296)(140,295)(141,289)(142,290)(143,292)
(144,291)(145,285)(146,286)(147,288)(148,287)(149,281)(150,282)(151,284)
(152,283)(153,277)(154,278)(155,280)(156,279)(157,273)(158,274)(159,276)
(160,275)(161,269)(162,270)(163,272)(164,271)(165,265)(166,266)(167,268)
(168,267)(169,261)(170,262)(171,264)(172,263)(173,257)(174,258)(175,260)
(176,259)(177,253)(178,254)(179,256)(180,255)(181,249)(182,250)(183,252)
(184,251)(185,245)(186,246)(187,248)(188,247)(189,241)(190,242)(191,244)
(192,243)(193,237)(194,238)(195,240)(196,239)(197,233)(198,234)(199,236)
(200,235)(201,229)(202,230)(203,232)(204,231)(205,225)(206,226)(207,228)
(208,227)(209,221)(210,222)(211,224)(212,223)(213,217)(214,218)(215,220)
(216,219)(327,328)(329,333)(330,334)(331,336)(332,335)(337,357)(338,358)
(339,360)(340,359)(341,353)(342,354)(343,356)(344,355)(345,349)(346,350)
(347,352)(348,351)(361,429)(362,430)(363,432)(364,431)(365,425)(366,426)
(367,428)(368,427)(369,421)(370,422)(371,424)(372,423)(373,417)(374,418)
(375,420)(376,419)(377,413)(378,414)(379,416)(380,415)(381,409)(382,410)
(383,412)(384,411)(385,405)(386,406)(387,408)(388,407)(389,401)(390,402)
(391,404)(392,403)(393,397)(394,398)(395,400)(396,399)(433,645)(434,646)
(435,648)(436,647)(437,641)(438,642)(439,644)(440,643)(441,637)(442,638)
(443,640)(444,639)(445,633)(446,634)(447,636)(448,635)(449,629)(450,630)
(451,632)(452,631)(453,625)(454,626)(455,628)(456,627)(457,621)(458,622)
(459,624)(460,623)(461,617)(462,618)(463,620)(464,619)(465,613)(466,614)
(467,616)(468,615)(469,609)(470,610)(471,612)(472,611)(473,605)(474,606)
(475,608)(476,607)(477,601)(478,602)(479,604)(480,603)(481,597)(482,598)
(483,600)(484,599)(485,593)(486,594)(487,596)(488,595)(489,589)(490,590)
(491,592)(492,591)(493,585)(494,586)(495,588)(496,587)(497,581)(498,582)
(499,584)(500,583)(501,577)(502,578)(503,580)(504,579)(505,573)(506,574)
(507,576)(508,575)(509,569)(510,570)(511,572)(512,571)(513,565)(514,566)
(515,568)(516,567)(517,561)(518,562)(519,564)(520,563)(521,557)(522,558)
(523,560)(524,559)(525,553)(526,554)(527,556)(528,555)(529,549)(530,550)
(531,552)(532,551)(533,545)(534,546)(535,548)(536,547)(537,541)(538,542)
(539,544)(540,543);;
s1 := ( 1,109)( 2,112)( 3,111)( 4,110)( 5,117)( 6,120)( 7,119)( 8,118)
( 9,113)( 10,116)( 11,115)( 12,114)( 13,141)( 14,144)( 15,143)( 16,142)
( 17,137)( 18,140)( 19,139)( 20,138)( 21,133)( 22,136)( 23,135)( 24,134)
( 25,129)( 26,132)( 27,131)( 28,130)( 29,125)( 30,128)( 31,127)( 32,126)
( 33,121)( 34,124)( 35,123)( 36,122)( 37,213)( 38,216)( 39,215)( 40,214)
( 41,209)( 42,212)( 43,211)( 44,210)( 45,205)( 46,208)( 47,207)( 48,206)
( 49,201)( 50,204)( 51,203)( 52,202)( 53,197)( 54,200)( 55,199)( 56,198)
( 57,193)( 58,196)( 59,195)( 60,194)( 61,189)( 62,192)( 63,191)( 64,190)
( 65,185)( 66,188)( 67,187)( 68,186)( 69,181)( 70,184)( 71,183)( 72,182)
( 73,177)( 74,180)( 75,179)( 76,178)( 77,173)( 78,176)( 79,175)( 80,174)
( 81,169)( 82,172)( 83,171)( 84,170)( 85,165)( 86,168)( 87,167)( 88,166)
( 89,161)( 90,164)( 91,163)( 92,162)( 93,157)( 94,160)( 95,159)( 96,158)
( 97,153)( 98,156)( 99,155)(100,154)(101,149)(102,152)(103,151)(104,150)
(105,145)(106,148)(107,147)(108,146)(217,321)(218,324)(219,323)(220,322)
(221,317)(222,320)(223,319)(224,318)(225,313)(226,316)(227,315)(228,314)
(229,309)(230,312)(231,311)(232,310)(233,305)(234,308)(235,307)(236,306)
(237,301)(238,304)(239,303)(240,302)(241,297)(242,300)(243,299)(244,298)
(245,293)(246,296)(247,295)(248,294)(249,289)(250,292)(251,291)(252,290)
(253,285)(254,288)(255,287)(256,286)(257,281)(258,284)(259,283)(260,282)
(261,277)(262,280)(263,279)(264,278)(265,273)(266,276)(267,275)(268,274)
(270,272)(325,433)(326,436)(327,435)(328,434)(329,441)(330,444)(331,443)
(332,442)(333,437)(334,440)(335,439)(336,438)(337,465)(338,468)(339,467)
(340,466)(341,461)(342,464)(343,463)(344,462)(345,457)(346,460)(347,459)
(348,458)(349,453)(350,456)(351,455)(352,454)(353,449)(354,452)(355,451)
(356,450)(357,445)(358,448)(359,447)(360,446)(361,537)(362,540)(363,539)
(364,538)(365,533)(366,536)(367,535)(368,534)(369,529)(370,532)(371,531)
(372,530)(373,525)(374,528)(375,527)(376,526)(377,521)(378,524)(379,523)
(380,522)(381,517)(382,520)(383,519)(384,518)(385,513)(386,516)(387,515)
(388,514)(389,509)(390,512)(391,511)(392,510)(393,505)(394,508)(395,507)
(396,506)(397,501)(398,504)(399,503)(400,502)(401,497)(402,500)(403,499)
(404,498)(405,493)(406,496)(407,495)(408,494)(409,489)(410,492)(411,491)
(412,490)(413,485)(414,488)(415,487)(416,486)(417,481)(418,484)(419,483)
(420,482)(421,477)(422,480)(423,479)(424,478)(425,473)(426,476)(427,475)
(428,474)(429,469)(430,472)(431,471)(432,470)(541,645)(542,648)(543,647)
(544,646)(545,641)(546,644)(547,643)(548,642)(549,637)(550,640)(551,639)
(552,638)(553,633)(554,636)(555,635)(556,634)(557,629)(558,632)(559,631)
(560,630)(561,625)(562,628)(563,627)(564,626)(565,621)(566,624)(567,623)
(568,622)(569,617)(570,620)(571,619)(572,618)(573,613)(574,616)(575,615)
(576,614)(577,609)(578,612)(579,611)(580,610)(581,605)(582,608)(583,607)
(584,606)(585,601)(586,604)(587,603)(588,602)(589,597)(590,600)(591,599)
(592,598)(594,596);;
s2 := ( 1,326)( 2,325)( 3,328)( 4,327)( 5,330)( 6,329)( 7,332)( 8,331)
( 9,334)( 10,333)( 11,336)( 12,335)( 13,338)( 14,337)( 15,340)( 16,339)
( 17,342)( 18,341)( 19,344)( 20,343)( 21,346)( 22,345)( 23,348)( 24,347)
( 25,350)( 26,349)( 27,352)( 28,351)( 29,354)( 30,353)( 31,356)( 32,355)
( 33,358)( 34,357)( 35,360)( 36,359)( 37,362)( 38,361)( 39,364)( 40,363)
( 41,366)( 42,365)( 43,368)( 44,367)( 45,370)( 46,369)( 47,372)( 48,371)
( 49,374)( 50,373)( 51,376)( 52,375)( 53,378)( 54,377)( 55,380)( 56,379)
( 57,382)( 58,381)( 59,384)( 60,383)( 61,386)( 62,385)( 63,388)( 64,387)
( 65,390)( 66,389)( 67,392)( 68,391)( 69,394)( 70,393)( 71,396)( 72,395)
( 73,398)( 74,397)( 75,400)( 76,399)( 77,402)( 78,401)( 79,404)( 80,403)
( 81,406)( 82,405)( 83,408)( 84,407)( 85,410)( 86,409)( 87,412)( 88,411)
( 89,414)( 90,413)( 91,416)( 92,415)( 93,418)( 94,417)( 95,420)( 96,419)
( 97,422)( 98,421)( 99,424)(100,423)(101,426)(102,425)(103,428)(104,427)
(105,430)(106,429)(107,432)(108,431)(109,434)(110,433)(111,436)(112,435)
(113,438)(114,437)(115,440)(116,439)(117,442)(118,441)(119,444)(120,443)
(121,446)(122,445)(123,448)(124,447)(125,450)(126,449)(127,452)(128,451)
(129,454)(130,453)(131,456)(132,455)(133,458)(134,457)(135,460)(136,459)
(137,462)(138,461)(139,464)(140,463)(141,466)(142,465)(143,468)(144,467)
(145,470)(146,469)(147,472)(148,471)(149,474)(150,473)(151,476)(152,475)
(153,478)(154,477)(155,480)(156,479)(157,482)(158,481)(159,484)(160,483)
(161,486)(162,485)(163,488)(164,487)(165,490)(166,489)(167,492)(168,491)
(169,494)(170,493)(171,496)(172,495)(173,498)(174,497)(175,500)(176,499)
(177,502)(178,501)(179,504)(180,503)(181,506)(182,505)(183,508)(184,507)
(185,510)(186,509)(187,512)(188,511)(189,514)(190,513)(191,516)(192,515)
(193,518)(194,517)(195,520)(196,519)(197,522)(198,521)(199,524)(200,523)
(201,526)(202,525)(203,528)(204,527)(205,530)(206,529)(207,532)(208,531)
(209,534)(210,533)(211,536)(212,535)(213,538)(214,537)(215,540)(216,539)
(217,542)(218,541)(219,544)(220,543)(221,546)(222,545)(223,548)(224,547)
(225,550)(226,549)(227,552)(228,551)(229,554)(230,553)(231,556)(232,555)
(233,558)(234,557)(235,560)(236,559)(237,562)(238,561)(239,564)(240,563)
(241,566)(242,565)(243,568)(244,567)(245,570)(246,569)(247,572)(248,571)
(249,574)(250,573)(251,576)(252,575)(253,578)(254,577)(255,580)(256,579)
(257,582)(258,581)(259,584)(260,583)(261,586)(262,585)(263,588)(264,587)
(265,590)(266,589)(267,592)(268,591)(269,594)(270,593)(271,596)(272,595)
(273,598)(274,597)(275,600)(276,599)(277,602)(278,601)(279,604)(280,603)
(281,606)(282,605)(283,608)(284,607)(285,610)(286,609)(287,612)(288,611)
(289,614)(290,613)(291,616)(292,615)(293,618)(294,617)(295,620)(296,619)
(297,622)(298,621)(299,624)(300,623)(301,626)(302,625)(303,628)(304,627)
(305,630)(306,629)(307,632)(308,631)(309,634)(310,633)(311,636)(312,635)
(313,638)(314,637)(315,640)(316,639)(317,642)(318,641)(319,644)(320,643)
(321,646)(322,645)(323,648)(324,647);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(648)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 33)( 14, 34)
( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)
( 23, 28)( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)
( 43,104)( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)
( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)
( 59, 88)( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)
( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(109,321)(110,322)
(111,324)(112,323)(113,317)(114,318)(115,320)(116,319)(117,313)(118,314)
(119,316)(120,315)(121,309)(122,310)(123,312)(124,311)(125,305)(126,306)
(127,308)(128,307)(129,301)(130,302)(131,304)(132,303)(133,297)(134,298)
(135,300)(136,299)(137,293)(138,294)(139,296)(140,295)(141,289)(142,290)
(143,292)(144,291)(145,285)(146,286)(147,288)(148,287)(149,281)(150,282)
(151,284)(152,283)(153,277)(154,278)(155,280)(156,279)(157,273)(158,274)
(159,276)(160,275)(161,269)(162,270)(163,272)(164,271)(165,265)(166,266)
(167,268)(168,267)(169,261)(170,262)(171,264)(172,263)(173,257)(174,258)
(175,260)(176,259)(177,253)(178,254)(179,256)(180,255)(181,249)(182,250)
(183,252)(184,251)(185,245)(186,246)(187,248)(188,247)(189,241)(190,242)
(191,244)(192,243)(193,237)(194,238)(195,240)(196,239)(197,233)(198,234)
(199,236)(200,235)(201,229)(202,230)(203,232)(204,231)(205,225)(206,226)
(207,228)(208,227)(209,221)(210,222)(211,224)(212,223)(213,217)(214,218)
(215,220)(216,219)(327,328)(329,333)(330,334)(331,336)(332,335)(337,357)
(338,358)(339,360)(340,359)(341,353)(342,354)(343,356)(344,355)(345,349)
(346,350)(347,352)(348,351)(361,429)(362,430)(363,432)(364,431)(365,425)
(366,426)(367,428)(368,427)(369,421)(370,422)(371,424)(372,423)(373,417)
(374,418)(375,420)(376,419)(377,413)(378,414)(379,416)(380,415)(381,409)
(382,410)(383,412)(384,411)(385,405)(386,406)(387,408)(388,407)(389,401)
(390,402)(391,404)(392,403)(393,397)(394,398)(395,400)(396,399)(433,645)
(434,646)(435,648)(436,647)(437,641)(438,642)(439,644)(440,643)(441,637)
(442,638)(443,640)(444,639)(445,633)(446,634)(447,636)(448,635)(449,629)
(450,630)(451,632)(452,631)(453,625)(454,626)(455,628)(456,627)(457,621)
(458,622)(459,624)(460,623)(461,617)(462,618)(463,620)(464,619)(465,613)
(466,614)(467,616)(468,615)(469,609)(470,610)(471,612)(472,611)(473,605)
(474,606)(475,608)(476,607)(477,601)(478,602)(479,604)(480,603)(481,597)
(482,598)(483,600)(484,599)(485,593)(486,594)(487,596)(488,595)(489,589)
(490,590)(491,592)(492,591)(493,585)(494,586)(495,588)(496,587)(497,581)
(498,582)(499,584)(500,583)(501,577)(502,578)(503,580)(504,579)(505,573)
(506,574)(507,576)(508,575)(509,569)(510,570)(511,572)(512,571)(513,565)
(514,566)(515,568)(516,567)(517,561)(518,562)(519,564)(520,563)(521,557)
(522,558)(523,560)(524,559)(525,553)(526,554)(527,556)(528,555)(529,549)
(530,550)(531,552)(532,551)(533,545)(534,546)(535,548)(536,547)(537,541)
(538,542)(539,544)(540,543);
s1 := Sym(648)!( 1,109)( 2,112)( 3,111)( 4,110)( 5,117)( 6,120)( 7,119)
( 8,118)( 9,113)( 10,116)( 11,115)( 12,114)( 13,141)( 14,144)( 15,143)
( 16,142)( 17,137)( 18,140)( 19,139)( 20,138)( 21,133)( 22,136)( 23,135)
( 24,134)( 25,129)( 26,132)( 27,131)( 28,130)( 29,125)( 30,128)( 31,127)
( 32,126)( 33,121)( 34,124)( 35,123)( 36,122)( 37,213)( 38,216)( 39,215)
( 40,214)( 41,209)( 42,212)( 43,211)( 44,210)( 45,205)( 46,208)( 47,207)
( 48,206)( 49,201)( 50,204)( 51,203)( 52,202)( 53,197)( 54,200)( 55,199)
( 56,198)( 57,193)( 58,196)( 59,195)( 60,194)( 61,189)( 62,192)( 63,191)
( 64,190)( 65,185)( 66,188)( 67,187)( 68,186)( 69,181)( 70,184)( 71,183)
( 72,182)( 73,177)( 74,180)( 75,179)( 76,178)( 77,173)( 78,176)( 79,175)
( 80,174)( 81,169)( 82,172)( 83,171)( 84,170)( 85,165)( 86,168)( 87,167)
( 88,166)( 89,161)( 90,164)( 91,163)( 92,162)( 93,157)( 94,160)( 95,159)
( 96,158)( 97,153)( 98,156)( 99,155)(100,154)(101,149)(102,152)(103,151)
(104,150)(105,145)(106,148)(107,147)(108,146)(217,321)(218,324)(219,323)
(220,322)(221,317)(222,320)(223,319)(224,318)(225,313)(226,316)(227,315)
(228,314)(229,309)(230,312)(231,311)(232,310)(233,305)(234,308)(235,307)
(236,306)(237,301)(238,304)(239,303)(240,302)(241,297)(242,300)(243,299)
(244,298)(245,293)(246,296)(247,295)(248,294)(249,289)(250,292)(251,291)
(252,290)(253,285)(254,288)(255,287)(256,286)(257,281)(258,284)(259,283)
(260,282)(261,277)(262,280)(263,279)(264,278)(265,273)(266,276)(267,275)
(268,274)(270,272)(325,433)(326,436)(327,435)(328,434)(329,441)(330,444)
(331,443)(332,442)(333,437)(334,440)(335,439)(336,438)(337,465)(338,468)
(339,467)(340,466)(341,461)(342,464)(343,463)(344,462)(345,457)(346,460)
(347,459)(348,458)(349,453)(350,456)(351,455)(352,454)(353,449)(354,452)
(355,451)(356,450)(357,445)(358,448)(359,447)(360,446)(361,537)(362,540)
(363,539)(364,538)(365,533)(366,536)(367,535)(368,534)(369,529)(370,532)
(371,531)(372,530)(373,525)(374,528)(375,527)(376,526)(377,521)(378,524)
(379,523)(380,522)(381,517)(382,520)(383,519)(384,518)(385,513)(386,516)
(387,515)(388,514)(389,509)(390,512)(391,511)(392,510)(393,505)(394,508)
(395,507)(396,506)(397,501)(398,504)(399,503)(400,502)(401,497)(402,500)
(403,499)(404,498)(405,493)(406,496)(407,495)(408,494)(409,489)(410,492)
(411,491)(412,490)(413,485)(414,488)(415,487)(416,486)(417,481)(418,484)
(419,483)(420,482)(421,477)(422,480)(423,479)(424,478)(425,473)(426,476)
(427,475)(428,474)(429,469)(430,472)(431,471)(432,470)(541,645)(542,648)
(543,647)(544,646)(545,641)(546,644)(547,643)(548,642)(549,637)(550,640)
(551,639)(552,638)(553,633)(554,636)(555,635)(556,634)(557,629)(558,632)
(559,631)(560,630)(561,625)(562,628)(563,627)(564,626)(565,621)(566,624)
(567,623)(568,622)(569,617)(570,620)(571,619)(572,618)(573,613)(574,616)
(575,615)(576,614)(577,609)(578,612)(579,611)(580,610)(581,605)(582,608)
(583,607)(584,606)(585,601)(586,604)(587,603)(588,602)(589,597)(590,600)
(591,599)(592,598)(594,596);
s2 := Sym(648)!( 1,326)( 2,325)( 3,328)( 4,327)( 5,330)( 6,329)( 7,332)
( 8,331)( 9,334)( 10,333)( 11,336)( 12,335)( 13,338)( 14,337)( 15,340)
( 16,339)( 17,342)( 18,341)( 19,344)( 20,343)( 21,346)( 22,345)( 23,348)
( 24,347)( 25,350)( 26,349)( 27,352)( 28,351)( 29,354)( 30,353)( 31,356)
( 32,355)( 33,358)( 34,357)( 35,360)( 36,359)( 37,362)( 38,361)( 39,364)
( 40,363)( 41,366)( 42,365)( 43,368)( 44,367)( 45,370)( 46,369)( 47,372)
( 48,371)( 49,374)( 50,373)( 51,376)( 52,375)( 53,378)( 54,377)( 55,380)
( 56,379)( 57,382)( 58,381)( 59,384)( 60,383)( 61,386)( 62,385)( 63,388)
( 64,387)( 65,390)( 66,389)( 67,392)( 68,391)( 69,394)( 70,393)( 71,396)
( 72,395)( 73,398)( 74,397)( 75,400)( 76,399)( 77,402)( 78,401)( 79,404)
( 80,403)( 81,406)( 82,405)( 83,408)( 84,407)( 85,410)( 86,409)( 87,412)
( 88,411)( 89,414)( 90,413)( 91,416)( 92,415)( 93,418)( 94,417)( 95,420)
( 96,419)( 97,422)( 98,421)( 99,424)(100,423)(101,426)(102,425)(103,428)
(104,427)(105,430)(106,429)(107,432)(108,431)(109,434)(110,433)(111,436)
(112,435)(113,438)(114,437)(115,440)(116,439)(117,442)(118,441)(119,444)
(120,443)(121,446)(122,445)(123,448)(124,447)(125,450)(126,449)(127,452)
(128,451)(129,454)(130,453)(131,456)(132,455)(133,458)(134,457)(135,460)
(136,459)(137,462)(138,461)(139,464)(140,463)(141,466)(142,465)(143,468)
(144,467)(145,470)(146,469)(147,472)(148,471)(149,474)(150,473)(151,476)
(152,475)(153,478)(154,477)(155,480)(156,479)(157,482)(158,481)(159,484)
(160,483)(161,486)(162,485)(163,488)(164,487)(165,490)(166,489)(167,492)
(168,491)(169,494)(170,493)(171,496)(172,495)(173,498)(174,497)(175,500)
(176,499)(177,502)(178,501)(179,504)(180,503)(181,506)(182,505)(183,508)
(184,507)(185,510)(186,509)(187,512)(188,511)(189,514)(190,513)(191,516)
(192,515)(193,518)(194,517)(195,520)(196,519)(197,522)(198,521)(199,524)
(200,523)(201,526)(202,525)(203,528)(204,527)(205,530)(206,529)(207,532)
(208,531)(209,534)(210,533)(211,536)(212,535)(213,538)(214,537)(215,540)
(216,539)(217,542)(218,541)(219,544)(220,543)(221,546)(222,545)(223,548)
(224,547)(225,550)(226,549)(227,552)(228,551)(229,554)(230,553)(231,556)
(232,555)(233,558)(234,557)(235,560)(236,559)(237,562)(238,561)(239,564)
(240,563)(241,566)(242,565)(243,568)(244,567)(245,570)(246,569)(247,572)
(248,571)(249,574)(250,573)(251,576)(252,575)(253,578)(254,577)(255,580)
(256,579)(257,582)(258,581)(259,584)(260,583)(261,586)(262,585)(263,588)
(264,587)(265,590)(266,589)(267,592)(268,591)(269,594)(270,593)(271,596)
(272,595)(273,598)(274,597)(275,600)(276,599)(277,602)(278,601)(279,604)
(280,603)(281,606)(282,605)(283,608)(284,607)(285,610)(286,609)(287,612)
(288,611)(289,614)(290,613)(291,616)(292,615)(293,618)(294,617)(295,620)
(296,619)(297,622)(298,621)(299,624)(300,623)(301,626)(302,625)(303,628)
(304,627)(305,630)(306,629)(307,632)(308,631)(309,634)(310,633)(311,636)
(312,635)(313,638)(314,637)(315,640)(316,639)(317,642)(318,641)(319,644)
(320,643)(321,646)(322,645)(323,648)(324,647);
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope