Polytope of Type {862}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {862}*1724
Also Known As : 862-gon, {862}. if this polytope has another name.
Group : SmallGroup(1724,3)
Rank : 2
Schlafli Type : {862}
Number of vertices, edges, etc : 862, 862
Order of s₀s₁ : 862
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 : {431}*862
   431-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,431)(  3,430)(  4,429)(  5,428)(  6,427)(  7,426)(  8,425)(  9,424)
( 10,423)( 11,422)( 12,421)( 13,420)( 14,419)( 15,418)( 16,417)( 17,416)
( 18,415)( 19,414)( 20,413)( 21,412)( 22,411)( 23,410)( 24,409)( 25,408)
( 26,407)( 27,406)( 28,405)( 29,404)( 30,403)( 31,402)( 32,401)( 33,400)
( 34,399)( 35,398)( 36,397)( 37,396)( 38,395)( 39,394)( 40,393)( 41,392)
( 42,391)( 43,390)( 44,389)( 45,388)( 46,387)( 47,386)( 48,385)( 49,384)
( 50,383)( 51,382)( 52,381)( 53,380)( 54,379)( 55,378)( 56,377)( 57,376)
( 58,375)( 59,374)( 60,373)( 61,372)( 62,371)( 63,370)( 64,369)( 65,368)
( 66,367)( 67,366)( 68,365)( 69,364)( 70,363)( 71,362)( 72,361)( 73,360)
( 74,359)( 75,358)( 76,357)( 77,356)( 78,355)( 79,354)( 80,353)( 81,352)
( 82,351)( 83,350)( 84,349)( 85,348)( 86,347)( 87,346)( 88,345)( 89,344)
( 90,343)( 91,342)( 92,341)( 93,340)( 94,339)( 95,338)( 96,337)( 97,336)
( 98,335)( 99,334)(100,333)(101,332)(102,331)(103,330)(104,329)(105,328)
(106,327)(107,326)(108,325)(109,324)(110,323)(111,322)(112,321)(113,320)
(114,319)(115,318)(116,317)(117,316)(118,315)(119,314)(120,313)(121,312)
(122,311)(123,310)(124,309)(125,308)(126,307)(127,306)(128,305)(129,304)
(130,303)(131,302)(132,301)(133,300)(134,299)(135,298)(136,297)(137,296)
(138,295)(139,294)(140,293)(141,292)(142,291)(143,290)(144,289)(145,288)
(146,287)(147,286)(148,285)(149,284)(150,283)(151,282)(152,281)(153,280)
(154,279)(155,278)(156,277)(157,276)(158,275)(159,274)(160,273)(161,272)
(162,271)(163,270)(164,269)(165,268)(166,267)(167,266)(168,265)(169,264)
(170,263)(171,262)(172,261)(173,260)(174,259)(175,258)(176,257)(177,256)
(178,255)(179,254)(180,253)(181,252)(182,251)(183,250)(184,249)(185,248)
(186,247)(187,246)(188,245)(189,244)(190,243)(191,242)(192,241)(193,240)
(194,239)(195,238)(196,237)(197,236)(198,235)(199,234)(200,233)(201,232)
(202,231)(203,230)(204,229)(205,228)(206,227)(207,226)(208,225)(209,224)
(210,223)(211,222)(212,221)(213,220)(214,219)(215,218)(216,217)(433,862)
(434,861)(435,860)(436,859)(437,858)(438,857)(439,856)(440,855)(441,854)
(442,853)(443,852)(444,851)(445,850)(446,849)(447,848)(448,847)(449,846)
(450,845)(451,844)(452,843)(453,842)(454,841)(455,840)(456,839)(457,838)
(458,837)(459,836)(460,835)(461,834)(462,833)(463,832)(464,831)(465,830)
(466,829)(467,828)(468,827)(469,826)(470,825)(471,824)(472,823)(473,822)
(474,821)(475,820)(476,819)(477,818)(478,817)(479,816)(480,815)(481,814)
(482,813)(483,812)(484,811)(485,810)(486,809)(487,808)(488,807)(489,806)
(490,805)(491,804)(492,803)(493,802)(494,801)(495,800)(496,799)(497,798)
(498,797)(499,796)(500,795)(501,794)(502,793)(503,792)(504,791)(505,790)
(506,789)(507,788)(508,787)(509,786)(510,785)(511,784)(512,783)(513,782)
(514,781)(515,780)(516,779)(517,778)(518,777)(519,776)(520,775)(521,774)
(522,773)(523,772)(524,771)(525,770)(526,769)(527,768)(528,767)(529,766)
(530,765)(531,764)(532,763)(533,762)(534,761)(535,760)(536,759)(537,758)
(538,757)(539,756)(540,755)(541,754)(542,753)(543,752)(544,751)(545,750)
(546,749)(547,748)(548,747)(549,746)(550,745)(551,744)(552,743)(553,742)
(554,741)(555,740)(556,739)(557,738)(558,737)(559,736)(560,735)(561,734)
(562,733)(563,732)(564,731)(565,730)(566,729)(567,728)(568,727)(569,726)
(570,725)(571,724)(572,723)(573,722)(574,721)(575,720)(576,719)(577,718)
(578,717)(579,716)(580,715)(581,714)(582,713)(583,712)(584,711)(585,710)
(586,709)(587,708)(588,707)(589,706)(590,705)(591,704)(592,703)(593,702)
(594,701)(595,700)(596,699)(597,698)(598,697)(599,696)(600,695)(601,694)
(602,693)(603,692)(604,691)(605,690)(606,689)(607,688)(608,687)(609,686)
(610,685)(611,684)(612,683)(613,682)(614,681)(615,680)(616,679)(617,678)
(618,677)(619,676)(620,675)(621,674)(622,673)(623,672)(624,671)(625,670)
(626,669)(627,668)(628,667)(629,666)(630,665)(631,664)(632,663)(633,662)
(634,661)(635,660)(636,659)(637,658)(638,657)(639,656)(640,655)(641,654)
(642,653)(643,652)(644,651)(645,650)(646,649)(647,648);;
s1 := (  1,433)(  2,432)(  3,862)(  4,861)(  5,860)(  6,859)(  7,858)(  8,857)
(  9,856)( 10,855)( 11,854)( 12,853)( 13,852)( 14,851)( 15,850)( 16,849)
( 17,848)( 18,847)( 19,846)( 20,845)( 21,844)( 22,843)( 23,842)( 24,841)
( 25,840)( 26,839)( 27,838)( 28,837)( 29,836)( 30,835)( 31,834)( 32,833)
( 33,832)( 34,831)( 35,830)( 36,829)( 37,828)( 38,827)( 39,826)( 40,825)
( 41,824)( 42,823)( 43,822)( 44,821)( 45,820)( 46,819)( 47,818)( 48,817)
( 49,816)( 50,815)( 51,814)( 52,813)( 53,812)( 54,811)( 55,810)( 56,809)
( 57,808)( 58,807)( 59,806)( 60,805)( 61,804)( 62,803)( 63,802)( 64,801)
( 65,800)( 66,799)( 67,798)( 68,797)( 69,796)( 70,795)( 71,794)( 72,793)
( 73,792)( 74,791)( 75,790)( 76,789)( 77,788)( 78,787)( 79,786)( 80,785)
( 81,784)( 82,783)( 83,782)( 84,781)( 85,780)( 86,779)( 87,778)( 88,777)
( 89,776)( 90,775)( 91,774)( 92,773)( 93,772)( 94,771)( 95,770)( 96,769)
( 97,768)( 98,767)( 99,766)(100,765)(101,764)(102,763)(103,762)(104,761)
(105,760)(106,759)(107,758)(108,757)(109,756)(110,755)(111,754)(112,753)
(113,752)(114,751)(115,750)(116,749)(117,748)(118,747)(119,746)(120,745)
(121,744)(122,743)(123,742)(124,741)(125,740)(126,739)(127,738)(128,737)
(129,736)(130,735)(131,734)(132,733)(133,732)(134,731)(135,730)(136,729)
(137,728)(138,727)(139,726)(140,725)(141,724)(142,723)(143,722)(144,721)
(145,720)(146,719)(147,718)(148,717)(149,716)(150,715)(151,714)(152,713)
(153,712)(154,711)(155,710)(156,709)(157,708)(158,707)(159,706)(160,705)
(161,704)(162,703)(163,702)(164,701)(165,700)(166,699)(167,698)(168,697)
(169,696)(170,695)(171,694)(172,693)(173,692)(174,691)(175,690)(176,689)
(177,688)(178,687)(179,686)(180,685)(181,684)(182,683)(183,682)(184,681)
(185,680)(186,679)(187,678)(188,677)(189,676)(190,675)(191,674)(192,673)
(193,672)(194,671)(195,670)(196,669)(197,668)(198,667)(199,666)(200,665)
(201,664)(202,663)(203,662)(204,661)(205,660)(206,659)(207,658)(208,657)
(209,656)(210,655)(211,654)(212,653)(213,652)(214,651)(215,650)(216,649)
(217,648)(218,647)(219,646)(220,645)(221,644)(222,643)(223,642)(224,641)
(225,640)(226,639)(227,638)(228,637)(229,636)(230,635)(231,634)(232,633)
(233,632)(234,631)(235,630)(236,629)(237,628)(238,627)(239,626)(240,625)
(241,624)(242,623)(243,622)(244,621)(245,620)(246,619)(247,618)(248,617)
(249,616)(250,615)(251,614)(252,613)(253,612)(254,611)(255,610)(256,609)
(257,608)(258,607)(259,606)(260,605)(261,604)(262,603)(263,602)(264,601)
(265,600)(266,599)(267,598)(268,597)(269,596)(270,595)(271,594)(272,593)
(273,592)(274,591)(275,590)(276,589)(277,588)(278,587)(279,586)(280,585)
(281,584)(282,583)(283,582)(284,581)(285,580)(286,579)(287,578)(288,577)
(289,576)(290,575)(291,574)(292,573)(293,572)(294,571)(295,570)(296,569)
(297,568)(298,567)(299,566)(300,565)(301,564)(302,563)(303,562)(304,561)
(305,560)(306,559)(307,558)(308,557)(309,556)(310,555)(311,554)(312,553)
(313,552)(314,551)(315,550)(316,549)(317,548)(318,547)(319,546)(320,545)
(321,544)(322,543)(323,542)(324,541)(325,540)(326,539)(327,538)(328,537)
(329,536)(330,535)(331,534)(332,533)(333,532)(334,531)(335,530)(336,529)
(337,528)(338,527)(339,526)(340,525)(341,524)(342,523)(343,522)(344,521)
(345,520)(346,519)(347,518)(348,517)(349,516)(350,515)(351,514)(352,513)
(353,512)(354,511)(355,510)(356,509)(357,508)(358,507)(359,506)(360,505)
(361,504)(362,503)(363,502)(364,501)(365,500)(366,499)(367,498)(368,497)
(369,496)(370,495)(371,494)(372,493)(373,492)(374,491)(375,490)(376,489)
(377,488)(378,487)(379,486)(380,485)(381,484)(382,483)(383,482)(384,481)
(385,480)(386,479)(387,478)(388,477)(389,476)(390,475)(391,474)(392,473)
(393,472)(394,471)(395,470)(396,469)(397,468)(398,467)(399,466)(400,465)
(401,464)(402,463)(403,462)(404,461)(405,460)(406,459)(407,458)(408,457)
(409,456)(410,455)(411,454)(412,453)(413,452)(414,451)(415,450)(416,449)
(417,448)(418,447)(419,446)(420,445)(421,444)(422,443)(423,442)(424,441)
(425,440)(426,439)(427,438)(428,437)(429,436)(430,435)(431,434);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(862)!(  2,431)(  3,430)(  4,429)(  5,428)(  6,427)(  7,426)(  8,425)
(  9,424)( 10,423)( 11,422)( 12,421)( 13,420)( 14,419)( 15,418)( 16,417)
( 17,416)( 18,415)( 19,414)( 20,413)( 21,412)( 22,411)( 23,410)( 24,409)
( 25,408)( 26,407)( 27,406)( 28,405)( 29,404)( 30,403)( 31,402)( 32,401)
( 33,400)( 34,399)( 35,398)( 36,397)( 37,396)( 38,395)( 39,394)( 40,393)
( 41,392)( 42,391)( 43,390)( 44,389)( 45,388)( 46,387)( 47,386)( 48,385)
( 49,384)( 50,383)( 51,382)( 52,381)( 53,380)( 54,379)( 55,378)( 56,377)
( 57,376)( 58,375)( 59,374)( 60,373)( 61,372)( 62,371)( 63,370)( 64,369)
( 65,368)( 66,367)( 67,366)( 68,365)( 69,364)( 70,363)( 71,362)( 72,361)
( 73,360)( 74,359)( 75,358)( 76,357)( 77,356)( 78,355)( 79,354)( 80,353)
( 81,352)( 82,351)( 83,350)( 84,349)( 85,348)( 86,347)( 87,346)( 88,345)
( 89,344)( 90,343)( 91,342)( 92,341)( 93,340)( 94,339)( 95,338)( 96,337)
( 97,336)( 98,335)( 99,334)(100,333)(101,332)(102,331)(103,330)(104,329)
(105,328)(106,327)(107,326)(108,325)(109,324)(110,323)(111,322)(112,321)
(113,320)(114,319)(115,318)(116,317)(117,316)(118,315)(119,314)(120,313)
(121,312)(122,311)(123,310)(124,309)(125,308)(126,307)(127,306)(128,305)
(129,304)(130,303)(131,302)(132,301)(133,300)(134,299)(135,298)(136,297)
(137,296)(138,295)(139,294)(140,293)(141,292)(142,291)(143,290)(144,289)
(145,288)(146,287)(147,286)(148,285)(149,284)(150,283)(151,282)(152,281)
(153,280)(154,279)(155,278)(156,277)(157,276)(158,275)(159,274)(160,273)
(161,272)(162,271)(163,270)(164,269)(165,268)(166,267)(167,266)(168,265)
(169,264)(170,263)(171,262)(172,261)(173,260)(174,259)(175,258)(176,257)
(177,256)(178,255)(179,254)(180,253)(181,252)(182,251)(183,250)(184,249)
(185,248)(186,247)(187,246)(188,245)(189,244)(190,243)(191,242)(192,241)
(193,240)(194,239)(195,238)(196,237)(197,236)(198,235)(199,234)(200,233)
(201,232)(202,231)(203,230)(204,229)(205,228)(206,227)(207,226)(208,225)
(209,224)(210,223)(211,222)(212,221)(213,220)(214,219)(215,218)(216,217)
(433,862)(434,861)(435,860)(436,859)(437,858)(438,857)(439,856)(440,855)
(441,854)(442,853)(443,852)(444,851)(445,850)(446,849)(447,848)(448,847)
(449,846)(450,845)(451,844)(452,843)(453,842)(454,841)(455,840)(456,839)
(457,838)(458,837)(459,836)(460,835)(461,834)(462,833)(463,832)(464,831)
(465,830)(466,829)(467,828)(468,827)(469,826)(470,825)(471,824)(472,823)
(473,822)(474,821)(475,820)(476,819)(477,818)(478,817)(479,816)(480,815)
(481,814)(482,813)(483,812)(484,811)(485,810)(486,809)(487,808)(488,807)
(489,806)(490,805)(491,804)(492,803)(493,802)(494,801)(495,800)(496,799)
(497,798)(498,797)(499,796)(500,795)(501,794)(502,793)(503,792)(504,791)
(505,790)(506,789)(507,788)(508,787)(509,786)(510,785)(511,784)(512,783)
(513,782)(514,781)(515,780)(516,779)(517,778)(518,777)(519,776)(520,775)
(521,774)(522,773)(523,772)(524,771)(525,770)(526,769)(527,768)(528,767)
(529,766)(530,765)(531,764)(532,763)(533,762)(534,761)(535,760)(536,759)
(537,758)(538,757)(539,756)(540,755)(541,754)(542,753)(543,752)(544,751)
(545,750)(546,749)(547,748)(548,747)(549,746)(550,745)(551,744)(552,743)
(553,742)(554,741)(555,740)(556,739)(557,738)(558,737)(559,736)(560,735)
(561,734)(562,733)(563,732)(564,731)(565,730)(566,729)(567,728)(568,727)
(569,726)(570,725)(571,724)(572,723)(573,722)(574,721)(575,720)(576,719)
(577,718)(578,717)(579,716)(580,715)(581,714)(582,713)(583,712)(584,711)
(585,710)(586,709)(587,708)(588,707)(589,706)(590,705)(591,704)(592,703)
(593,702)(594,701)(595,700)(596,699)(597,698)(598,697)(599,696)(600,695)
(601,694)(602,693)(603,692)(604,691)(605,690)(606,689)(607,688)(608,687)
(609,686)(610,685)(611,684)(612,683)(613,682)(614,681)(615,680)(616,679)
(617,678)(618,677)(619,676)(620,675)(621,674)(622,673)(623,672)(624,671)
(625,670)(626,669)(627,668)(628,667)(629,666)(630,665)(631,664)(632,663)
(633,662)(634,661)(635,660)(636,659)(637,658)(638,657)(639,656)(640,655)
(641,654)(642,653)(643,652)(644,651)(645,650)(646,649)(647,648);
s1 := Sym(862)!(  1,433)(  2,432)(  3,862)(  4,861)(  5,860)(  6,859)(  7,858)
(  8,857)(  9,856)( 10,855)( 11,854)( 12,853)( 13,852)( 14,851)( 15,850)
( 16,849)( 17,848)( 18,847)( 19,846)( 20,845)( 21,844)( 22,843)( 23,842)
( 24,841)( 25,840)( 26,839)( 27,838)( 28,837)( 29,836)( 30,835)( 31,834)
( 32,833)( 33,832)( 34,831)( 35,830)( 36,829)( 37,828)( 38,827)( 39,826)
( 40,825)( 41,824)( 42,823)( 43,822)( 44,821)( 45,820)( 46,819)( 47,818)
( 48,817)( 49,816)( 50,815)( 51,814)( 52,813)( 53,812)( 54,811)( 55,810)
( 56,809)( 57,808)( 58,807)( 59,806)( 60,805)( 61,804)( 62,803)( 63,802)
( 64,801)( 65,800)( 66,799)( 67,798)( 68,797)( 69,796)( 70,795)( 71,794)
( 72,793)( 73,792)( 74,791)( 75,790)( 76,789)( 77,788)( 78,787)( 79,786)
( 80,785)( 81,784)( 82,783)( 83,782)( 84,781)( 85,780)( 86,779)( 87,778)
( 88,777)( 89,776)( 90,775)( 91,774)( 92,773)( 93,772)( 94,771)( 95,770)
( 96,769)( 97,768)( 98,767)( 99,766)(100,765)(101,764)(102,763)(103,762)
(104,761)(105,760)(106,759)(107,758)(108,757)(109,756)(110,755)(111,754)
(112,753)(113,752)(114,751)(115,750)(116,749)(117,748)(118,747)(119,746)
(120,745)(121,744)(122,743)(123,742)(124,741)(125,740)(126,739)(127,738)
(128,737)(129,736)(130,735)(131,734)(132,733)(133,732)(134,731)(135,730)
(136,729)(137,728)(138,727)(139,726)(140,725)(141,724)(142,723)(143,722)
(144,721)(145,720)(146,719)(147,718)(148,717)(149,716)(150,715)(151,714)
(152,713)(153,712)(154,711)(155,710)(156,709)(157,708)(158,707)(159,706)
(160,705)(161,704)(162,703)(163,702)(164,701)(165,700)(166,699)(167,698)
(168,697)(169,696)(170,695)(171,694)(172,693)(173,692)(174,691)(175,690)
(176,689)(177,688)(178,687)(179,686)(180,685)(181,684)(182,683)(183,682)
(184,681)(185,680)(186,679)(187,678)(188,677)(189,676)(190,675)(191,674)
(192,673)(193,672)(194,671)(195,670)(196,669)(197,668)(198,667)(199,666)
(200,665)(201,664)(202,663)(203,662)(204,661)(205,660)(206,659)(207,658)
(208,657)(209,656)(210,655)(211,654)(212,653)(213,652)(214,651)(215,650)
(216,649)(217,648)(218,647)(219,646)(220,645)(221,644)(222,643)(223,642)
(224,641)(225,640)(226,639)(227,638)(228,637)(229,636)(230,635)(231,634)
(232,633)(233,632)(234,631)(235,630)(236,629)(237,628)(238,627)(239,626)
(240,625)(241,624)(242,623)(243,622)(244,621)(245,620)(246,619)(247,618)
(248,617)(249,616)(250,615)(251,614)(252,613)(253,612)(254,611)(255,610)
(256,609)(257,608)(258,607)(259,606)(260,605)(261,604)(262,603)(263,602)
(264,601)(265,600)(266,599)(267,598)(268,597)(269,596)(270,595)(271,594)
(272,593)(273,592)(274,591)(275,590)(276,589)(277,588)(278,587)(279,586)
(280,585)(281,584)(282,583)(283,582)(284,581)(285,580)(286,579)(287,578)
(288,577)(289,576)(290,575)(291,574)(292,573)(293,572)(294,571)(295,570)
(296,569)(297,568)(298,567)(299,566)(300,565)(301,564)(302,563)(303,562)
(304,561)(305,560)(306,559)(307,558)(308,557)(309,556)(310,555)(311,554)
(312,553)(313,552)(314,551)(315,550)(316,549)(317,548)(318,547)(319,546)
(320,545)(321,544)(322,543)(323,542)(324,541)(325,540)(326,539)(327,538)
(328,537)(329,536)(330,535)(331,534)(332,533)(333,532)(334,531)(335,530)
(336,529)(337,528)(338,527)(339,526)(340,525)(341,524)(342,523)(343,522)
(344,521)(345,520)(346,519)(347,518)(348,517)(349,516)(350,515)(351,514)
(352,513)(353,512)(354,511)(355,510)(356,509)(357,508)(358,507)(359,506)
(360,505)(361,504)(362,503)(363,502)(364,501)(365,500)(366,499)(367,498)
(368,497)(369,496)(370,495)(371,494)(372,493)(373,492)(374,491)(375,490)
(376,489)(377,488)(378,487)(379,486)(380,485)(381,484)(382,483)(383,482)
(384,481)(385,480)(386,479)(387,478)(388,477)(389,476)(390,475)(391,474)
(392,473)(393,472)(394,471)(395,470)(396,469)(397,468)(398,467)(399,466)
(400,465)(401,464)(402,463)(403,462)(404,461)(405,460)(406,459)(407,458)
(408,457)(409,456)(410,455)(411,454)(412,453)(413,452)(414,451)(415,450)
(416,449)(417,448)(418,447)(419,446)(420,445)(421,444)(422,443)(423,442)
(424,441)(425,440)(426,439)(427,438)(428,437)(429,436)(430,435)(431,434);
poly := sub<Sym(862)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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