Polytope of Type {854}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {854}*1708
Also Known As : 854-gon, {854}. if this polytope has another name.
Group : SmallGroup(1708,10)
Rank : 2
Schlafli Type : {854}
Number of vertices, edges, etc : 854, 854
Order of s₀s₁ : 854
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 : {427}*854
   7-fold quotients : {122}*244
   14-fold quotients : {61}*122
   61-fold quotients : {14}*28
   122-fold quotients : {7}*14
   427-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope