Polytope of Type {818}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {818}*1636
Also Known As : 818-gon, {818}. if this polytope has another name.
Group : SmallGroup(1636,4)
Rank : 2
Schlafli Type : {818}
Number of vertices, edges, etc : 818, 818
Order of s₀s₁ : 818
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
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 : {409}*818
   409-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,409)(  3,408)(  4,407)(  5,406)(  6,405)(  7,404)(  8,403)(  9,402)
( 10,401)( 11,400)( 12,399)( 13,398)( 14,397)( 15,396)( 16,395)( 17,394)
( 18,393)( 19,392)( 20,391)( 21,390)( 22,389)( 23,388)( 24,387)( 25,386)
( 26,385)( 27,384)( 28,383)( 29,382)( 30,381)( 31,380)( 32,379)( 33,378)
( 34,377)( 35,376)( 36,375)( 37,374)( 38,373)( 39,372)( 40,371)( 41,370)
( 42,369)( 43,368)( 44,367)( 45,366)( 46,365)( 47,364)( 48,363)( 49,362)
( 50,361)( 51,360)( 52,359)( 53,358)( 54,357)( 55,356)( 56,355)( 57,354)
( 58,353)( 59,352)( 60,351)( 61,350)( 62,349)( 63,348)( 64,347)( 65,346)
( 66,345)( 67,344)( 68,343)( 69,342)( 70,341)( 71,340)( 72,339)( 73,338)
( 74,337)( 75,336)( 76,335)( 77,334)( 78,333)( 79,332)( 80,331)( 81,330)
( 82,329)( 83,328)( 84,327)( 85,326)( 86,325)( 87,324)( 88,323)( 89,322)
( 90,321)( 91,320)( 92,319)( 93,318)( 94,317)( 95,316)( 96,315)( 97,314)
( 98,313)( 99,312)(100,311)(101,310)(102,309)(103,308)(104,307)(105,306)
(106,305)(107,304)(108,303)(109,302)(110,301)(111,300)(112,299)(113,298)
(114,297)(115,296)(116,295)(117,294)(118,293)(119,292)(120,291)(121,290)
(122,289)(123,288)(124,287)(125,286)(126,285)(127,284)(128,283)(129,282)
(130,281)(131,280)(132,279)(133,278)(134,277)(135,276)(136,275)(137,274)
(138,273)(139,272)(140,271)(141,270)(142,269)(143,268)(144,267)(145,266)
(146,265)(147,264)(148,263)(149,262)(150,261)(151,260)(152,259)(153,258)
(154,257)(155,256)(156,255)(157,254)(158,253)(159,252)(160,251)(161,250)
(162,249)(163,248)(164,247)(165,246)(166,245)(167,244)(168,243)(169,242)
(170,241)(171,240)(172,239)(173,238)(174,237)(175,236)(176,235)(177,234)
(178,233)(179,232)(180,231)(181,230)(182,229)(183,228)(184,227)(185,226)
(186,225)(187,224)(188,223)(189,222)(190,221)(191,220)(192,219)(193,218)
(194,217)(195,216)(196,215)(197,214)(198,213)(199,212)(200,211)(201,210)
(202,209)(203,208)(204,207)(205,206)(411,818)(412,817)(413,816)(414,815)
(415,814)(416,813)(417,812)(418,811)(419,810)(420,809)(421,808)(422,807)
(423,806)(424,805)(425,804)(426,803)(427,802)(428,801)(429,800)(430,799)
(431,798)(432,797)(433,796)(434,795)(435,794)(436,793)(437,792)(438,791)
(439,790)(440,789)(441,788)(442,787)(443,786)(444,785)(445,784)(446,783)
(447,782)(448,781)(449,780)(450,779)(451,778)(452,777)(453,776)(454,775)
(455,774)(456,773)(457,772)(458,771)(459,770)(460,769)(461,768)(462,767)
(463,766)(464,765)(465,764)(466,763)(467,762)(468,761)(469,760)(470,759)
(471,758)(472,757)(473,756)(474,755)(475,754)(476,753)(477,752)(478,751)
(479,750)(480,749)(481,748)(482,747)(483,746)(484,745)(485,744)(486,743)
(487,742)(488,741)(489,740)(490,739)(491,738)(492,737)(493,736)(494,735)
(495,734)(496,733)(497,732)(498,731)(499,730)(500,729)(501,728)(502,727)
(503,726)(504,725)(505,724)(506,723)(507,722)(508,721)(509,720)(510,719)
(511,718)(512,717)(513,716)(514,715)(515,714)(516,713)(517,712)(518,711)
(519,710)(520,709)(521,708)(522,707)(523,706)(524,705)(525,704)(526,703)
(527,702)(528,701)(529,700)(530,699)(531,698)(532,697)(533,696)(534,695)
(535,694)(536,693)(537,692)(538,691)(539,690)(540,689)(541,688)(542,687)
(543,686)(544,685)(545,684)(546,683)(547,682)(548,681)(549,680)(550,679)
(551,678)(552,677)(553,676)(554,675)(555,674)(556,673)(557,672)(558,671)
(559,670)(560,669)(561,668)(562,667)(563,666)(564,665)(565,664)(566,663)
(567,662)(568,661)(569,660)(570,659)(571,658)(572,657)(573,656)(574,655)
(575,654)(576,653)(577,652)(578,651)(579,650)(580,649)(581,648)(582,647)
(583,646)(584,645)(585,644)(586,643)(587,642)(588,641)(589,640)(590,639)
(591,638)(592,637)(593,636)(594,635)(595,634)(596,633)(597,632)(598,631)
(599,630)(600,629)(601,628)(602,627)(603,626)(604,625)(605,624)(606,623)
(607,622)(608,621)(609,620)(610,619)(611,618)(612,617)(613,616)(614,615);;
s1 := (  1,411)(  2,410)(  3,818)(  4,817)(  5,816)(  6,815)(  7,814)(  8,813)
(  9,812)( 10,811)( 11,810)( 12,809)( 13,808)( 14,807)( 15,806)( 16,805)
( 17,804)( 18,803)( 19,802)( 20,801)( 21,800)( 22,799)( 23,798)( 24,797)
( 25,796)( 26,795)( 27,794)( 28,793)( 29,792)( 30,791)( 31,790)( 32,789)
( 33,788)( 34,787)( 35,786)( 36,785)( 37,784)( 38,783)( 39,782)( 40,781)
( 41,780)( 42,779)( 43,778)( 44,777)( 45,776)( 46,775)( 47,774)( 48,773)
( 49,772)( 50,771)( 51,770)( 52,769)( 53,768)( 54,767)( 55,766)( 56,765)
( 57,764)( 58,763)( 59,762)( 60,761)( 61,760)( 62,759)( 63,758)( 64,757)
( 65,756)( 66,755)( 67,754)( 68,753)( 69,752)( 70,751)( 71,750)( 72,749)
( 73,748)( 74,747)( 75,746)( 76,745)( 77,744)( 78,743)( 79,742)( 80,741)
( 81,740)( 82,739)( 83,738)( 84,737)( 85,736)( 86,735)( 87,734)( 88,733)
( 89,732)( 90,731)( 91,730)( 92,729)( 93,728)( 94,727)( 95,726)( 96,725)
( 97,724)( 98,723)( 99,722)(100,721)(101,720)(102,719)(103,718)(104,717)
(105,716)(106,715)(107,714)(108,713)(109,712)(110,711)(111,710)(112,709)
(113,708)(114,707)(115,706)(116,705)(117,704)(118,703)(119,702)(120,701)
(121,700)(122,699)(123,698)(124,697)(125,696)(126,695)(127,694)(128,693)
(129,692)(130,691)(131,690)(132,689)(133,688)(134,687)(135,686)(136,685)
(137,684)(138,683)(139,682)(140,681)(141,680)(142,679)(143,678)(144,677)
(145,676)(146,675)(147,674)(148,673)(149,672)(150,671)(151,670)(152,669)
(153,668)(154,667)(155,666)(156,665)(157,664)(158,663)(159,662)(160,661)
(161,660)(162,659)(163,658)(164,657)(165,656)(166,655)(167,654)(168,653)
(169,652)(170,651)(171,650)(172,649)(173,648)(174,647)(175,646)(176,645)
(177,644)(178,643)(179,642)(180,641)(181,640)(182,639)(183,638)(184,637)
(185,636)(186,635)(187,634)(188,633)(189,632)(190,631)(191,630)(192,629)
(193,628)(194,627)(195,626)(196,625)(197,624)(198,623)(199,622)(200,621)
(201,620)(202,619)(203,618)(204,617)(205,616)(206,615)(207,614)(208,613)
(209,612)(210,611)(211,610)(212,609)(213,608)(214,607)(215,606)(216,605)
(217,604)(218,603)(219,602)(220,601)(221,600)(222,599)(223,598)(224,597)
(225,596)(226,595)(227,594)(228,593)(229,592)(230,591)(231,590)(232,589)
(233,588)(234,587)(235,586)(236,585)(237,584)(238,583)(239,582)(240,581)
(241,580)(242,579)(243,578)(244,577)(245,576)(246,575)(247,574)(248,573)
(249,572)(250,571)(251,570)(252,569)(253,568)(254,567)(255,566)(256,565)
(257,564)(258,563)(259,562)(260,561)(261,560)(262,559)(263,558)(264,557)
(265,556)(266,555)(267,554)(268,553)(269,552)(270,551)(271,550)(272,549)
(273,548)(274,547)(275,546)(276,545)(277,544)(278,543)(279,542)(280,541)
(281,540)(282,539)(283,538)(284,537)(285,536)(286,535)(287,534)(288,533)
(289,532)(290,531)(291,530)(292,529)(293,528)(294,527)(295,526)(296,525)
(297,524)(298,523)(299,522)(300,521)(301,520)(302,519)(303,518)(304,517)
(305,516)(306,515)(307,514)(308,513)(309,512)(310,511)(311,510)(312,509)
(313,508)(314,507)(315,506)(316,505)(317,504)(318,503)(319,502)(320,501)
(321,500)(322,499)(323,498)(324,497)(325,496)(326,495)(327,494)(328,493)
(329,492)(330,491)(331,490)(332,489)(333,488)(334,487)(335,486)(336,485)
(337,484)(338,483)(339,482)(340,481)(341,480)(342,479)(343,478)(344,477)
(345,476)(346,475)(347,474)(348,473)(349,472)(350,471)(351,470)(352,469)
(353,468)(354,467)(355,466)(356,465)(357,464)(358,463)(359,462)(360,461)
(361,460)(362,459)(363,458)(364,457)(365,456)(366,455)(367,454)(368,453)
(369,452)(370,451)(371,450)(372,449)(373,448)(374,447)(375,446)(376,445)
(377,444)(378,443)(379,442)(380,441)(381,440)(382,439)(383,438)(384,437)
(385,436)(386,435)(387,434)(388,433)(389,432)(390,431)(391,430)(392,429)
(393,428)(394,427)(395,426)(396,425)(397,424)(398,423)(399,422)(400,421)
(401,420)(402,419)(403,418)(404,417)(405,416)(406,415)(407,414)(408,413)
(409,412);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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*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*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*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*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*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*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*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*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*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(818)!(  2,409)(  3,408)(  4,407)(  5,406)(  6,405)(  7,404)(  8,403)
(  9,402)( 10,401)( 11,400)( 12,399)( 13,398)( 14,397)( 15,396)( 16,395)
( 17,394)( 18,393)( 19,392)( 20,391)( 21,390)( 22,389)( 23,388)( 24,387)
( 25,386)( 26,385)( 27,384)( 28,383)( 29,382)( 30,381)( 31,380)( 32,379)
( 33,378)( 34,377)( 35,376)( 36,375)( 37,374)( 38,373)( 39,372)( 40,371)
( 41,370)( 42,369)( 43,368)( 44,367)( 45,366)( 46,365)( 47,364)( 48,363)
( 49,362)( 50,361)( 51,360)( 52,359)( 53,358)( 54,357)( 55,356)( 56,355)
( 57,354)( 58,353)( 59,352)( 60,351)( 61,350)( 62,349)( 63,348)( 64,347)
( 65,346)( 66,345)( 67,344)( 68,343)( 69,342)( 70,341)( 71,340)( 72,339)
( 73,338)( 74,337)( 75,336)( 76,335)( 77,334)( 78,333)( 79,332)( 80,331)
( 81,330)( 82,329)( 83,328)( 84,327)( 85,326)( 86,325)( 87,324)( 88,323)
( 89,322)( 90,321)( 91,320)( 92,319)( 93,318)( 94,317)( 95,316)( 96,315)
( 97,314)( 98,313)( 99,312)(100,311)(101,310)(102,309)(103,308)(104,307)
(105,306)(106,305)(107,304)(108,303)(109,302)(110,301)(111,300)(112,299)
(113,298)(114,297)(115,296)(116,295)(117,294)(118,293)(119,292)(120,291)
(121,290)(122,289)(123,288)(124,287)(125,286)(126,285)(127,284)(128,283)
(129,282)(130,281)(131,280)(132,279)(133,278)(134,277)(135,276)(136,275)
(137,274)(138,273)(139,272)(140,271)(141,270)(142,269)(143,268)(144,267)
(145,266)(146,265)(147,264)(148,263)(149,262)(150,261)(151,260)(152,259)
(153,258)(154,257)(155,256)(156,255)(157,254)(158,253)(159,252)(160,251)
(161,250)(162,249)(163,248)(164,247)(165,246)(166,245)(167,244)(168,243)
(169,242)(170,241)(171,240)(172,239)(173,238)(174,237)(175,236)(176,235)
(177,234)(178,233)(179,232)(180,231)(181,230)(182,229)(183,228)(184,227)
(185,226)(186,225)(187,224)(188,223)(189,222)(190,221)(191,220)(192,219)
(193,218)(194,217)(195,216)(196,215)(197,214)(198,213)(199,212)(200,211)
(201,210)(202,209)(203,208)(204,207)(205,206)(411,818)(412,817)(413,816)
(414,815)(415,814)(416,813)(417,812)(418,811)(419,810)(420,809)(421,808)
(422,807)(423,806)(424,805)(425,804)(426,803)(427,802)(428,801)(429,800)
(430,799)(431,798)(432,797)(433,796)(434,795)(435,794)(436,793)(437,792)
(438,791)(439,790)(440,789)(441,788)(442,787)(443,786)(444,785)(445,784)
(446,783)(447,782)(448,781)(449,780)(450,779)(451,778)(452,777)(453,776)
(454,775)(455,774)(456,773)(457,772)(458,771)(459,770)(460,769)(461,768)
(462,767)(463,766)(464,765)(465,764)(466,763)(467,762)(468,761)(469,760)
(470,759)(471,758)(472,757)(473,756)(474,755)(475,754)(476,753)(477,752)
(478,751)(479,750)(480,749)(481,748)(482,747)(483,746)(484,745)(485,744)
(486,743)(487,742)(488,741)(489,740)(490,739)(491,738)(492,737)(493,736)
(494,735)(495,734)(496,733)(497,732)(498,731)(499,730)(500,729)(501,728)
(502,727)(503,726)(504,725)(505,724)(506,723)(507,722)(508,721)(509,720)
(510,719)(511,718)(512,717)(513,716)(514,715)(515,714)(516,713)(517,712)
(518,711)(519,710)(520,709)(521,708)(522,707)(523,706)(524,705)(525,704)
(526,703)(527,702)(528,701)(529,700)(530,699)(531,698)(532,697)(533,696)
(534,695)(535,694)(536,693)(537,692)(538,691)(539,690)(540,689)(541,688)
(542,687)(543,686)(544,685)(545,684)(546,683)(547,682)(548,681)(549,680)
(550,679)(551,678)(552,677)(553,676)(554,675)(555,674)(556,673)(557,672)
(558,671)(559,670)(560,669)(561,668)(562,667)(563,666)(564,665)(565,664)
(566,663)(567,662)(568,661)(569,660)(570,659)(571,658)(572,657)(573,656)
(574,655)(575,654)(576,653)(577,652)(578,651)(579,650)(580,649)(581,648)
(582,647)(583,646)(584,645)(585,644)(586,643)(587,642)(588,641)(589,640)
(590,639)(591,638)(592,637)(593,636)(594,635)(595,634)(596,633)(597,632)
(598,631)(599,630)(600,629)(601,628)(602,627)(603,626)(604,625)(605,624)
(606,623)(607,622)(608,621)(609,620)(610,619)(611,618)(612,617)(613,616)
(614,615);
s1 := Sym(818)!(  1,411)(  2,410)(  3,818)(  4,817)(  5,816)(  6,815)(  7,814)
(  8,813)(  9,812)( 10,811)( 11,810)( 12,809)( 13,808)( 14,807)( 15,806)
( 16,805)( 17,804)( 18,803)( 19,802)( 20,801)( 21,800)( 22,799)( 23,798)
( 24,797)( 25,796)( 26,795)( 27,794)( 28,793)( 29,792)( 30,791)( 31,790)
( 32,789)( 33,788)( 34,787)( 35,786)( 36,785)( 37,784)( 38,783)( 39,782)
( 40,781)( 41,780)( 42,779)( 43,778)( 44,777)( 45,776)( 46,775)( 47,774)
( 48,773)( 49,772)( 50,771)( 51,770)( 52,769)( 53,768)( 54,767)( 55,766)
( 56,765)( 57,764)( 58,763)( 59,762)( 60,761)( 61,760)( 62,759)( 63,758)
( 64,757)( 65,756)( 66,755)( 67,754)( 68,753)( 69,752)( 70,751)( 71,750)
( 72,749)( 73,748)( 74,747)( 75,746)( 76,745)( 77,744)( 78,743)( 79,742)
( 80,741)( 81,740)( 82,739)( 83,738)( 84,737)( 85,736)( 86,735)( 87,734)
( 88,733)( 89,732)( 90,731)( 91,730)( 92,729)( 93,728)( 94,727)( 95,726)
( 96,725)( 97,724)( 98,723)( 99,722)(100,721)(101,720)(102,719)(103,718)
(104,717)(105,716)(106,715)(107,714)(108,713)(109,712)(110,711)(111,710)
(112,709)(113,708)(114,707)(115,706)(116,705)(117,704)(118,703)(119,702)
(120,701)(121,700)(122,699)(123,698)(124,697)(125,696)(126,695)(127,694)
(128,693)(129,692)(130,691)(131,690)(132,689)(133,688)(134,687)(135,686)
(136,685)(137,684)(138,683)(139,682)(140,681)(141,680)(142,679)(143,678)
(144,677)(145,676)(146,675)(147,674)(148,673)(149,672)(150,671)(151,670)
(152,669)(153,668)(154,667)(155,666)(156,665)(157,664)(158,663)(159,662)
(160,661)(161,660)(162,659)(163,658)(164,657)(165,656)(166,655)(167,654)
(168,653)(169,652)(170,651)(171,650)(172,649)(173,648)(174,647)(175,646)
(176,645)(177,644)(178,643)(179,642)(180,641)(181,640)(182,639)(183,638)
(184,637)(185,636)(186,635)(187,634)(188,633)(189,632)(190,631)(191,630)
(192,629)(193,628)(194,627)(195,626)(196,625)(197,624)(198,623)(199,622)
(200,621)(201,620)(202,619)(203,618)(204,617)(205,616)(206,615)(207,614)
(208,613)(209,612)(210,611)(211,610)(212,609)(213,608)(214,607)(215,606)
(216,605)(217,604)(218,603)(219,602)(220,601)(221,600)(222,599)(223,598)
(224,597)(225,596)(226,595)(227,594)(228,593)(229,592)(230,591)(231,590)
(232,589)(233,588)(234,587)(235,586)(236,585)(237,584)(238,583)(239,582)
(240,581)(241,580)(242,579)(243,578)(244,577)(245,576)(246,575)(247,574)
(248,573)(249,572)(250,571)(251,570)(252,569)(253,568)(254,567)(255,566)
(256,565)(257,564)(258,563)(259,562)(260,561)(261,560)(262,559)(263,558)
(264,557)(265,556)(266,555)(267,554)(268,553)(269,552)(270,551)(271,550)
(272,549)(273,548)(274,547)(275,546)(276,545)(277,544)(278,543)(279,542)
(280,541)(281,540)(282,539)(283,538)(284,537)(285,536)(286,535)(287,534)
(288,533)(289,532)(290,531)(291,530)(292,529)(293,528)(294,527)(295,526)
(296,525)(297,524)(298,523)(299,522)(300,521)(301,520)(302,519)(303,518)
(304,517)(305,516)(306,515)(307,514)(308,513)(309,512)(310,511)(311,510)
(312,509)(313,508)(314,507)(315,506)(316,505)(317,504)(318,503)(319,502)
(320,501)(321,500)(322,499)(323,498)(324,497)(325,496)(326,495)(327,494)
(328,493)(329,492)(330,491)(331,490)(332,489)(333,488)(334,487)(335,486)
(336,485)(337,484)(338,483)(339,482)(340,481)(341,480)(342,479)(343,478)
(344,477)(345,476)(346,475)(347,474)(348,473)(349,472)(350,471)(351,470)
(352,469)(353,468)(354,467)(355,466)(356,465)(357,464)(358,463)(359,462)
(360,461)(361,460)(362,459)(363,458)(364,457)(365,456)(366,455)(367,454)
(368,453)(369,452)(370,451)(371,450)(372,449)(373,448)(374,447)(375,446)
(376,445)(377,444)(378,443)(379,442)(380,441)(381,440)(382,439)(383,438)
(384,437)(385,436)(386,435)(387,434)(388,433)(389,432)(390,431)(391,430)
(392,429)(393,428)(394,427)(395,426)(396,425)(397,424)(398,423)(399,422)
(400,421)(401,420)(402,419)(403,418)(404,417)(405,416)(406,415)(407,414)
(408,413)(409,412);
poly := sub<Sym(818)|s0,s1>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*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*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*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*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*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*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*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*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