Polytope of Type {806}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {806}*1612
Also Known As : 806-gon, {806}. if this polytope has another name.
Group : SmallGroup(1612,10)
Rank : 2
Schlafli Type : {806}
Number of vertices, edges, etc : 806, 806
Order of s₀s₁ : 806
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 : {403}*806
   13-fold quotients : {62}*124
   26-fold quotients : {31}*62
   31-fold quotients : {26}*52
   62-fold quotients : {13}*26
   403-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope