Polytope of Type {814}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {814}*1628
Also Known As : 814-gon, {814}. if this polytope has another name.
Group : SmallGroup(1628,10)
Rank : 2
Schlafli Type : {814}
Number of vertices, edges, etc : 814, 814
Order of s₀s₁ : 814
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 : {407}*814
   11-fold quotients : {74}*148
   22-fold quotients : {37}*74
   37-fold quotients : {22}*44
   74-fold quotients : {11}*22
   407-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope