Polytope of Type {8,82}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,82}*1312
Also Known As : {8,82|2}. if this polytope has another name.
Group : SmallGroup(1312,155)
Rank : 3
Schlafli Type : {8,82}
Number of vertices, edges, etc : 8, 328, 82
Order of s₀s₁s₂ : 328
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,82}*656
   4-fold quotients : {2,82}*328
   8-fold quotients : {2,41}*164
   41-fold quotients : {8,2}*32
   82-fold quotients : {4,2}*16
   164-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 83,124)( 84,125)( 85,126)( 86,127)( 87,128)( 88,129)( 89,130)( 90,131)
( 91,132)( 92,133)( 93,134)( 94,135)( 95,136)( 96,137)( 97,138)( 98,139)
( 99,140)(100,141)(101,142)(102,143)(103,144)(104,145)(105,146)(106,147)
(107,148)(108,149)(109,150)(110,151)(111,152)(112,153)(113,154)(114,155)
(115,156)(116,157)(117,158)(118,159)(119,160)(120,161)(121,162)(122,163)
(123,164)(247,288)(248,289)(249,290)(250,291)(251,292)(252,293)(253,294)
(254,295)(255,296)(256,297)(257,298)(258,299)(259,300)(260,301)(261,302)
(262,303)(263,304)(264,305)(265,306)(266,307)(267,308)(268,309)(269,310)
(270,311)(271,312)(272,313)(273,314)(274,315)(275,316)(276,317)(277,318)
(278,319)(279,320)(280,321)(281,322)(282,323)(283,324)(284,325)(285,326)
(286,327)(287,328)(329,411)(330,412)(331,413)(332,414)(333,415)(334,416)
(335,417)(336,418)(337,419)(338,420)(339,421)(340,422)(341,423)(342,424)
(343,425)(344,426)(345,427)(346,428)(347,429)(348,430)(349,431)(350,432)
(351,433)(352,434)(353,435)(354,436)(355,437)(356,438)(357,439)(358,440)
(359,441)(360,442)(361,443)(362,444)(363,445)(364,446)(365,447)(366,448)
(367,449)(368,450)(369,451)(370,452)(371,453)(372,454)(373,455)(374,456)
(375,457)(376,458)(377,459)(378,460)(379,461)(380,462)(381,463)(382,464)
(383,465)(384,466)(385,467)(386,468)(387,469)(388,470)(389,471)(390,472)
(391,473)(392,474)(393,475)(394,476)(395,477)(396,478)(397,479)(398,480)
(399,481)(400,482)(401,483)(402,484)(403,485)(404,486)(405,487)(406,488)
(407,489)(408,490)(409,491)(410,492)(493,575)(494,576)(495,577)(496,578)
(497,579)(498,580)(499,581)(500,582)(501,583)(502,584)(503,585)(504,586)
(505,587)(506,588)(507,589)(508,590)(509,591)(510,592)(511,593)(512,594)
(513,595)(514,596)(515,597)(516,598)(517,599)(518,600)(519,601)(520,602)
(521,603)(522,604)(523,605)(524,606)(525,607)(526,608)(527,609)(528,610)
(529,611)(530,612)(531,613)(532,614)(533,615)(534,616)(535,617)(536,618)
(537,619)(538,620)(539,621)(540,622)(541,623)(542,624)(543,625)(544,626)
(545,627)(546,628)(547,629)(548,630)(549,631)(550,632)(551,633)(552,634)
(553,635)(554,636)(555,637)(556,638)(557,639)(558,640)(559,641)(560,642)
(561,643)(562,644)(563,645)(564,646)(565,647)(566,648)(567,649)(568,650)
(569,651)(570,652)(571,653)(572,654)(573,655)(574,656);;
s1 := (  1,493)(  2,533)(  3,532)(  4,531)(  5,530)(  6,529)(  7,528)(  8,527)
(  9,526)( 10,525)( 11,524)( 12,523)( 13,522)( 14,521)( 15,520)( 16,519)
( 17,518)( 18,517)( 19,516)( 20,515)( 21,514)( 22,513)( 23,512)( 24,511)
( 25,510)( 26,509)( 27,508)( 28,507)( 29,506)( 30,505)( 31,504)( 32,503)
( 33,502)( 34,501)( 35,500)( 36,499)( 37,498)( 38,497)( 39,496)( 40,495)
( 41,494)( 42,534)( 43,574)( 44,573)( 45,572)( 46,571)( 47,570)( 48,569)
( 49,568)( 50,567)( 51,566)( 52,565)( 53,564)( 54,563)( 55,562)( 56,561)
( 57,560)( 58,559)( 59,558)( 60,557)( 61,556)( 62,555)( 63,554)( 64,553)
( 65,552)( 66,551)( 67,550)( 68,549)( 69,548)( 70,547)( 71,546)( 72,545)
( 73,544)( 74,543)( 75,542)( 76,541)( 77,540)( 78,539)( 79,538)( 80,537)
( 81,536)( 82,535)( 83,616)( 84,656)( 85,655)( 86,654)( 87,653)( 88,652)
( 89,651)( 90,650)( 91,649)( 92,648)( 93,647)( 94,646)( 95,645)( 96,644)
( 97,643)( 98,642)( 99,641)(100,640)(101,639)(102,638)(103,637)(104,636)
(105,635)(106,634)(107,633)(108,632)(109,631)(110,630)(111,629)(112,628)
(113,627)(114,626)(115,625)(116,624)(117,623)(118,622)(119,621)(120,620)
(121,619)(122,618)(123,617)(124,575)(125,615)(126,614)(127,613)(128,612)
(129,611)(130,610)(131,609)(132,608)(133,607)(134,606)(135,605)(136,604)
(137,603)(138,602)(139,601)(140,600)(141,599)(142,598)(143,597)(144,596)
(145,595)(146,594)(147,593)(148,592)(149,591)(150,590)(151,589)(152,588)
(153,587)(154,586)(155,585)(156,584)(157,583)(158,582)(159,581)(160,580)
(161,579)(162,578)(163,577)(164,576)(165,329)(166,369)(167,368)(168,367)
(169,366)(170,365)(171,364)(172,363)(173,362)(174,361)(175,360)(176,359)
(177,358)(178,357)(179,356)(180,355)(181,354)(182,353)(183,352)(184,351)
(185,350)(186,349)(187,348)(188,347)(189,346)(190,345)(191,344)(192,343)
(193,342)(194,341)(195,340)(196,339)(197,338)(198,337)(199,336)(200,335)
(201,334)(202,333)(203,332)(204,331)(205,330)(206,370)(207,410)(208,409)
(209,408)(210,407)(211,406)(212,405)(213,404)(214,403)(215,402)(216,401)
(217,400)(218,399)(219,398)(220,397)(221,396)(222,395)(223,394)(224,393)
(225,392)(226,391)(227,390)(228,389)(229,388)(230,387)(231,386)(232,385)
(233,384)(234,383)(235,382)(236,381)(237,380)(238,379)(239,378)(240,377)
(241,376)(242,375)(243,374)(244,373)(245,372)(246,371)(247,452)(248,492)
(249,491)(250,490)(251,489)(252,488)(253,487)(254,486)(255,485)(256,484)
(257,483)(258,482)(259,481)(260,480)(261,479)(262,478)(263,477)(264,476)
(265,475)(266,474)(267,473)(268,472)(269,471)(270,470)(271,469)(272,468)
(273,467)(274,466)(275,465)(276,464)(277,463)(278,462)(279,461)(280,460)
(281,459)(282,458)(283,457)(284,456)(285,455)(286,454)(287,453)(288,411)
(289,451)(290,450)(291,449)(292,448)(293,447)(294,446)(295,445)(296,444)
(297,443)(298,442)(299,441)(300,440)(301,439)(302,438)(303,437)(304,436)
(305,435)(306,434)(307,433)(308,432)(309,431)(310,430)(311,429)(312,428)
(313,427)(314,426)(315,425)(316,424)(317,423)(318,422)(319,421)(320,420)
(321,419)(322,418)(323,417)(324,416)(325,415)(326,414)(327,413)(328,412);;
s2 := (  1,166)(  2,165)(  3,205)(  4,204)(  5,203)(  6,202)(  7,201)(  8,200)
(  9,199)( 10,198)( 11,197)( 12,196)( 13,195)( 14,194)( 15,193)( 16,192)
( 17,191)( 18,190)( 19,189)( 20,188)( 21,187)( 22,186)( 23,185)( 24,184)
( 25,183)( 26,182)( 27,181)( 28,180)( 29,179)( 30,178)( 31,177)( 32,176)
( 33,175)( 34,174)( 35,173)( 36,172)( 37,171)( 38,170)( 39,169)( 40,168)
( 41,167)( 42,207)( 43,206)( 44,246)( 45,245)( 46,244)( 47,243)( 48,242)
( 49,241)( 50,240)( 51,239)( 52,238)( 53,237)( 54,236)( 55,235)( 56,234)
( 57,233)( 58,232)( 59,231)( 60,230)( 61,229)( 62,228)( 63,227)( 64,226)
( 65,225)( 66,224)( 67,223)( 68,222)( 69,221)( 70,220)( 71,219)( 72,218)
( 73,217)( 74,216)( 75,215)( 76,214)( 77,213)( 78,212)( 79,211)( 80,210)
( 81,209)( 82,208)( 83,248)( 84,247)( 85,287)( 86,286)( 87,285)( 88,284)
( 89,283)( 90,282)( 91,281)( 92,280)( 93,279)( 94,278)( 95,277)( 96,276)
( 97,275)( 98,274)( 99,273)(100,272)(101,271)(102,270)(103,269)(104,268)
(105,267)(106,266)(107,265)(108,264)(109,263)(110,262)(111,261)(112,260)
(113,259)(114,258)(115,257)(116,256)(117,255)(118,254)(119,253)(120,252)
(121,251)(122,250)(123,249)(124,289)(125,288)(126,328)(127,327)(128,326)
(129,325)(130,324)(131,323)(132,322)(133,321)(134,320)(135,319)(136,318)
(137,317)(138,316)(139,315)(140,314)(141,313)(142,312)(143,311)(144,310)
(145,309)(146,308)(147,307)(148,306)(149,305)(150,304)(151,303)(152,302)
(153,301)(154,300)(155,299)(156,298)(157,297)(158,296)(159,295)(160,294)
(161,293)(162,292)(163,291)(164,290)(329,494)(330,493)(331,533)(332,532)
(333,531)(334,530)(335,529)(336,528)(337,527)(338,526)(339,525)(340,524)
(341,523)(342,522)(343,521)(344,520)(345,519)(346,518)(347,517)(348,516)
(349,515)(350,514)(351,513)(352,512)(353,511)(354,510)(355,509)(356,508)
(357,507)(358,506)(359,505)(360,504)(361,503)(362,502)(363,501)(364,500)
(365,499)(366,498)(367,497)(368,496)(369,495)(370,535)(371,534)(372,574)
(373,573)(374,572)(375,571)(376,570)(377,569)(378,568)(379,567)(380,566)
(381,565)(382,564)(383,563)(384,562)(385,561)(386,560)(387,559)(388,558)
(389,557)(390,556)(391,555)(392,554)(393,553)(394,552)(395,551)(396,550)
(397,549)(398,548)(399,547)(400,546)(401,545)(402,544)(403,543)(404,542)
(405,541)(406,540)(407,539)(408,538)(409,537)(410,536)(411,576)(412,575)
(413,615)(414,614)(415,613)(416,612)(417,611)(418,610)(419,609)(420,608)
(421,607)(422,606)(423,605)(424,604)(425,603)(426,602)(427,601)(428,600)
(429,599)(430,598)(431,597)(432,596)(433,595)(434,594)(435,593)(436,592)
(437,591)(438,590)(439,589)(440,588)(441,587)(442,586)(443,585)(444,584)
(445,583)(446,582)(447,581)(448,580)(449,579)(450,578)(451,577)(452,617)
(453,616)(454,656)(455,655)(456,654)(457,653)(458,652)(459,651)(460,650)
(461,649)(462,648)(463,647)(464,646)(465,645)(466,644)(467,643)(468,642)
(469,641)(470,640)(471,639)(472,638)(473,637)(474,636)(475,635)(476,634)
(477,633)(478,632)(479,631)(480,630)(481,629)(482,628)(483,627)(484,626)
(485,625)(486,624)(487,623)(488,622)(489,621)(490,620)(491,619)(492,618);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(656)!( 83,124)( 84,125)( 85,126)( 86,127)( 87,128)( 88,129)( 89,130)
( 90,131)( 91,132)( 92,133)( 93,134)( 94,135)( 95,136)( 96,137)( 97,138)
( 98,139)( 99,140)(100,141)(101,142)(102,143)(103,144)(104,145)(105,146)
(106,147)(107,148)(108,149)(109,150)(110,151)(111,152)(112,153)(113,154)
(114,155)(115,156)(116,157)(117,158)(118,159)(119,160)(120,161)(121,162)
(122,163)(123,164)(247,288)(248,289)(249,290)(250,291)(251,292)(252,293)
(253,294)(254,295)(255,296)(256,297)(257,298)(258,299)(259,300)(260,301)
(261,302)(262,303)(263,304)(264,305)(265,306)(266,307)(267,308)(268,309)
(269,310)(270,311)(271,312)(272,313)(273,314)(274,315)(275,316)(276,317)
(277,318)(278,319)(279,320)(280,321)(281,322)(282,323)(283,324)(284,325)
(285,326)(286,327)(287,328)(329,411)(330,412)(331,413)(332,414)(333,415)
(334,416)(335,417)(336,418)(337,419)(338,420)(339,421)(340,422)(341,423)
(342,424)(343,425)(344,426)(345,427)(346,428)(347,429)(348,430)(349,431)
(350,432)(351,433)(352,434)(353,435)(354,436)(355,437)(356,438)(357,439)
(358,440)(359,441)(360,442)(361,443)(362,444)(363,445)(364,446)(365,447)
(366,448)(367,449)(368,450)(369,451)(370,452)(371,453)(372,454)(373,455)
(374,456)(375,457)(376,458)(377,459)(378,460)(379,461)(380,462)(381,463)
(382,464)(383,465)(384,466)(385,467)(386,468)(387,469)(388,470)(389,471)
(390,472)(391,473)(392,474)(393,475)(394,476)(395,477)(396,478)(397,479)
(398,480)(399,481)(400,482)(401,483)(402,484)(403,485)(404,486)(405,487)
(406,488)(407,489)(408,490)(409,491)(410,492)(493,575)(494,576)(495,577)
(496,578)(497,579)(498,580)(499,581)(500,582)(501,583)(502,584)(503,585)
(504,586)(505,587)(506,588)(507,589)(508,590)(509,591)(510,592)(511,593)
(512,594)(513,595)(514,596)(515,597)(516,598)(517,599)(518,600)(519,601)
(520,602)(521,603)(522,604)(523,605)(524,606)(525,607)(526,608)(527,609)
(528,610)(529,611)(530,612)(531,613)(532,614)(533,615)(534,616)(535,617)
(536,618)(537,619)(538,620)(539,621)(540,622)(541,623)(542,624)(543,625)
(544,626)(545,627)(546,628)(547,629)(548,630)(549,631)(550,632)(551,633)
(552,634)(553,635)(554,636)(555,637)(556,638)(557,639)(558,640)(559,641)
(560,642)(561,643)(562,644)(563,645)(564,646)(565,647)(566,648)(567,649)
(568,650)(569,651)(570,652)(571,653)(572,654)(573,655)(574,656);
s1 := Sym(656)!(  1,493)(  2,533)(  3,532)(  4,531)(  5,530)(  6,529)(  7,528)
(  8,527)(  9,526)( 10,525)( 11,524)( 12,523)( 13,522)( 14,521)( 15,520)
( 16,519)( 17,518)( 18,517)( 19,516)( 20,515)( 21,514)( 22,513)( 23,512)
( 24,511)( 25,510)( 26,509)( 27,508)( 28,507)( 29,506)( 30,505)( 31,504)
( 32,503)( 33,502)( 34,501)( 35,500)( 36,499)( 37,498)( 38,497)( 39,496)
( 40,495)( 41,494)( 42,534)( 43,574)( 44,573)( 45,572)( 46,571)( 47,570)
( 48,569)( 49,568)( 50,567)( 51,566)( 52,565)( 53,564)( 54,563)( 55,562)
( 56,561)( 57,560)( 58,559)( 59,558)( 60,557)( 61,556)( 62,555)( 63,554)
( 64,553)( 65,552)( 66,551)( 67,550)( 68,549)( 69,548)( 70,547)( 71,546)
( 72,545)( 73,544)( 74,543)( 75,542)( 76,541)( 77,540)( 78,539)( 79,538)
( 80,537)( 81,536)( 82,535)( 83,616)( 84,656)( 85,655)( 86,654)( 87,653)
( 88,652)( 89,651)( 90,650)( 91,649)( 92,648)( 93,647)( 94,646)( 95,645)
( 96,644)( 97,643)( 98,642)( 99,641)(100,640)(101,639)(102,638)(103,637)
(104,636)(105,635)(106,634)(107,633)(108,632)(109,631)(110,630)(111,629)
(112,628)(113,627)(114,626)(115,625)(116,624)(117,623)(118,622)(119,621)
(120,620)(121,619)(122,618)(123,617)(124,575)(125,615)(126,614)(127,613)
(128,612)(129,611)(130,610)(131,609)(132,608)(133,607)(134,606)(135,605)
(136,604)(137,603)(138,602)(139,601)(140,600)(141,599)(142,598)(143,597)
(144,596)(145,595)(146,594)(147,593)(148,592)(149,591)(150,590)(151,589)
(152,588)(153,587)(154,586)(155,585)(156,584)(157,583)(158,582)(159,581)
(160,580)(161,579)(162,578)(163,577)(164,576)(165,329)(166,369)(167,368)
(168,367)(169,366)(170,365)(171,364)(172,363)(173,362)(174,361)(175,360)
(176,359)(177,358)(178,357)(179,356)(180,355)(181,354)(182,353)(183,352)
(184,351)(185,350)(186,349)(187,348)(188,347)(189,346)(190,345)(191,344)
(192,343)(193,342)(194,341)(195,340)(196,339)(197,338)(198,337)(199,336)
(200,335)(201,334)(202,333)(203,332)(204,331)(205,330)(206,370)(207,410)
(208,409)(209,408)(210,407)(211,406)(212,405)(213,404)(214,403)(215,402)
(216,401)(217,400)(218,399)(219,398)(220,397)(221,396)(222,395)(223,394)
(224,393)(225,392)(226,391)(227,390)(228,389)(229,388)(230,387)(231,386)
(232,385)(233,384)(234,383)(235,382)(236,381)(237,380)(238,379)(239,378)
(240,377)(241,376)(242,375)(243,374)(244,373)(245,372)(246,371)(247,452)
(248,492)(249,491)(250,490)(251,489)(252,488)(253,487)(254,486)(255,485)
(256,484)(257,483)(258,482)(259,481)(260,480)(261,479)(262,478)(263,477)
(264,476)(265,475)(266,474)(267,473)(268,472)(269,471)(270,470)(271,469)
(272,468)(273,467)(274,466)(275,465)(276,464)(277,463)(278,462)(279,461)
(280,460)(281,459)(282,458)(283,457)(284,456)(285,455)(286,454)(287,453)
(288,411)(289,451)(290,450)(291,449)(292,448)(293,447)(294,446)(295,445)
(296,444)(297,443)(298,442)(299,441)(300,440)(301,439)(302,438)(303,437)
(304,436)(305,435)(306,434)(307,433)(308,432)(309,431)(310,430)(311,429)
(312,428)(313,427)(314,426)(315,425)(316,424)(317,423)(318,422)(319,421)
(320,420)(321,419)(322,418)(323,417)(324,416)(325,415)(326,414)(327,413)
(328,412);
s2 := Sym(656)!(  1,166)(  2,165)(  3,205)(  4,204)(  5,203)(  6,202)(  7,201)
(  8,200)(  9,199)( 10,198)( 11,197)( 12,196)( 13,195)( 14,194)( 15,193)
( 16,192)( 17,191)( 18,190)( 19,189)( 20,188)( 21,187)( 22,186)( 23,185)
( 24,184)( 25,183)( 26,182)( 27,181)( 28,180)( 29,179)( 30,178)( 31,177)
( 32,176)( 33,175)( 34,174)( 35,173)( 36,172)( 37,171)( 38,170)( 39,169)
( 40,168)( 41,167)( 42,207)( 43,206)( 44,246)( 45,245)( 46,244)( 47,243)
( 48,242)( 49,241)( 50,240)( 51,239)( 52,238)( 53,237)( 54,236)( 55,235)
( 56,234)( 57,233)( 58,232)( 59,231)( 60,230)( 61,229)( 62,228)( 63,227)
( 64,226)( 65,225)( 66,224)( 67,223)( 68,222)( 69,221)( 70,220)( 71,219)
( 72,218)( 73,217)( 74,216)( 75,215)( 76,214)( 77,213)( 78,212)( 79,211)
( 80,210)( 81,209)( 82,208)( 83,248)( 84,247)( 85,287)( 86,286)( 87,285)
( 88,284)( 89,283)( 90,282)( 91,281)( 92,280)( 93,279)( 94,278)( 95,277)
( 96,276)( 97,275)( 98,274)( 99,273)(100,272)(101,271)(102,270)(103,269)
(104,268)(105,267)(106,266)(107,265)(108,264)(109,263)(110,262)(111,261)
(112,260)(113,259)(114,258)(115,257)(116,256)(117,255)(118,254)(119,253)
(120,252)(121,251)(122,250)(123,249)(124,289)(125,288)(126,328)(127,327)
(128,326)(129,325)(130,324)(131,323)(132,322)(133,321)(134,320)(135,319)
(136,318)(137,317)(138,316)(139,315)(140,314)(141,313)(142,312)(143,311)
(144,310)(145,309)(146,308)(147,307)(148,306)(149,305)(150,304)(151,303)
(152,302)(153,301)(154,300)(155,299)(156,298)(157,297)(158,296)(159,295)
(160,294)(161,293)(162,292)(163,291)(164,290)(329,494)(330,493)(331,533)
(332,532)(333,531)(334,530)(335,529)(336,528)(337,527)(338,526)(339,525)
(340,524)(341,523)(342,522)(343,521)(344,520)(345,519)(346,518)(347,517)
(348,516)(349,515)(350,514)(351,513)(352,512)(353,511)(354,510)(355,509)
(356,508)(357,507)(358,506)(359,505)(360,504)(361,503)(362,502)(363,501)
(364,500)(365,499)(366,498)(367,497)(368,496)(369,495)(370,535)(371,534)
(372,574)(373,573)(374,572)(375,571)(376,570)(377,569)(378,568)(379,567)
(380,566)(381,565)(382,564)(383,563)(384,562)(385,561)(386,560)(387,559)
(388,558)(389,557)(390,556)(391,555)(392,554)(393,553)(394,552)(395,551)
(396,550)(397,549)(398,548)(399,547)(400,546)(401,545)(402,544)(403,543)
(404,542)(405,541)(406,540)(407,539)(408,538)(409,537)(410,536)(411,576)
(412,575)(413,615)(414,614)(415,613)(416,612)(417,611)(418,610)(419,609)
(420,608)(421,607)(422,606)(423,605)(424,604)(425,603)(426,602)(427,601)
(428,600)(429,599)(430,598)(431,597)(432,596)(433,595)(434,594)(435,593)
(436,592)(437,591)(438,590)(439,589)(440,588)(441,587)(442,586)(443,585)
(444,584)(445,583)(446,582)(447,581)(448,580)(449,579)(450,578)(451,577)
(452,617)(453,616)(454,656)(455,655)(456,654)(457,653)(458,652)(459,651)
(460,650)(461,649)(462,648)(463,647)(464,646)(465,645)(466,644)(467,643)
(468,642)(469,641)(470,640)(471,639)(472,638)(473,637)(474,636)(475,635)
(476,634)(477,633)(478,632)(479,631)(480,630)(481,629)(482,628)(483,627)
(484,626)(485,625)(486,624)(487,623)(488,622)(489,621)(490,620)(491,619)
(492,618);
poly := sub<Sym(656)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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