Polytope of Type {842}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {842}*1684
Also Known As : 842-gon, {842}. if this polytope has another name.
Group : SmallGroup(1684,4)
Rank : 2
Schlafli Type : {842}
Number of vertices, edges, etc : 842, 842
Order of s₀s₁ : 842
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 : {421}*842
   421-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope