Polytope of Type {874}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {874}*1748
Also Known As : 874-gon, {874}. if this polytope has another name.
Group : SmallGroup(1748,8)
Rank : 2
Schlafli Type : {874}
Number of vertices, edges, etc : 874, 874
Order of s₀s₁ : 874
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 : {437}*874
   19-fold quotients : {46}*92
   23-fold quotients : {38}*76
   38-fold quotients : {23}*46
   46-fold quotients : {19}*38
   437-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)
( 10, 15)( 11, 14)( 12, 13)( 24,415)( 25,437)( 26,436)( 27,435)( 28,434)
( 29,433)( 30,432)( 31,431)( 32,430)( 33,429)( 34,428)( 35,427)( 36,426)
( 37,425)( 38,424)( 39,423)( 40,422)( 41,421)( 42,420)( 43,419)( 44,418)
( 45,417)( 46,416)( 47,392)( 48,414)( 49,413)( 50,412)( 51,411)( 52,410)
( 53,409)( 54,408)( 55,407)( 56,406)( 57,405)( 58,404)( 59,403)( 60,402)
( 61,401)( 62,400)( 63,399)( 64,398)( 65,397)( 66,396)( 67,395)( 68,394)
( 69,393)( 70,369)( 71,391)( 72,390)( 73,389)( 74,388)( 75,387)( 76,386)
( 77,385)( 78,384)( 79,383)( 80,382)( 81,381)( 82,380)( 83,379)( 84,378)
( 85,377)( 86,376)( 87,375)( 88,374)( 89,373)( 90,372)( 91,371)( 92,370)
( 93,346)( 94,368)( 95,367)( 96,366)( 97,365)( 98,364)( 99,363)(100,362)
(101,361)(102,360)(103,359)(104,358)(105,357)(106,356)(107,355)(108,354)
(109,353)(110,352)(111,351)(112,350)(113,349)(114,348)(115,347)(116,323)
(117,345)(118,344)(119,343)(120,342)(121,341)(122,340)(123,339)(124,338)
(125,337)(126,336)(127,335)(128,334)(129,333)(130,332)(131,331)(132,330)
(133,329)(134,328)(135,327)(136,326)(137,325)(138,324)(139,300)(140,322)
(141,321)(142,320)(143,319)(144,318)(145,317)(146,316)(147,315)(148,314)
(149,313)(150,312)(151,311)(152,310)(153,309)(154,308)(155,307)(156,306)
(157,305)(158,304)(159,303)(160,302)(161,301)(162,277)(163,299)(164,298)
(165,297)(166,296)(167,295)(168,294)(169,293)(170,292)(171,291)(172,290)
(173,289)(174,288)(175,287)(176,286)(177,285)(178,284)(179,283)(180,282)
(181,281)(182,280)(183,279)(184,278)(185,254)(186,276)(187,275)(188,274)
(189,273)(190,272)(191,271)(192,270)(193,269)(194,268)(195,267)(196,266)
(197,265)(198,264)(199,263)(200,262)(201,261)(202,260)(203,259)(204,258)
(205,257)(206,256)(207,255)(208,231)(209,253)(210,252)(211,251)(212,250)
(213,249)(214,248)(215,247)(216,246)(217,245)(218,244)(219,243)(220,242)
(221,241)(222,240)(223,239)(224,238)(225,237)(226,236)(227,235)(228,234)
(229,233)(230,232)(439,460)(440,459)(441,458)(442,457)(443,456)(444,455)
(445,454)(446,453)(447,452)(448,451)(449,450)(461,852)(462,874)(463,873)
(464,872)(465,871)(466,870)(467,869)(468,868)(469,867)(470,866)(471,865)
(472,864)(473,863)(474,862)(475,861)(476,860)(477,859)(478,858)(479,857)
(480,856)(481,855)(482,854)(483,853)(484,829)(485,851)(486,850)(487,849)
(488,848)(489,847)(490,846)(491,845)(492,844)(493,843)(494,842)(495,841)
(496,840)(497,839)(498,838)(499,837)(500,836)(501,835)(502,834)(503,833)
(504,832)(505,831)(506,830)(507,806)(508,828)(509,827)(510,826)(511,825)
(512,824)(513,823)(514,822)(515,821)(516,820)(517,819)(518,818)(519,817)
(520,816)(521,815)(522,814)(523,813)(524,812)(525,811)(526,810)(527,809)
(528,808)(529,807)(530,783)(531,805)(532,804)(533,803)(534,802)(535,801)
(536,800)(537,799)(538,798)(539,797)(540,796)(541,795)(542,794)(543,793)
(544,792)(545,791)(546,790)(547,789)(548,788)(549,787)(550,786)(551,785)
(552,784)(553,760)(554,782)(555,781)(556,780)(557,779)(558,778)(559,777)
(560,776)(561,775)(562,774)(563,773)(564,772)(565,771)(566,770)(567,769)
(568,768)(569,767)(570,766)(571,765)(572,764)(573,763)(574,762)(575,761)
(576,737)(577,759)(578,758)(579,757)(580,756)(581,755)(582,754)(583,753)
(584,752)(585,751)(586,750)(587,749)(588,748)(589,747)(590,746)(591,745)
(592,744)(593,743)(594,742)(595,741)(596,740)(597,739)(598,738)(599,714)
(600,736)(601,735)(602,734)(603,733)(604,732)(605,731)(606,730)(607,729)
(608,728)(609,727)(610,726)(611,725)(612,724)(613,723)(614,722)(615,721)
(616,720)(617,719)(618,718)(619,717)(620,716)(621,715)(622,691)(623,713)
(624,712)(625,711)(626,710)(627,709)(628,708)(629,707)(630,706)(631,705)
(632,704)(633,703)(634,702)(635,701)(636,700)(637,699)(638,698)(639,697)
(640,696)(641,695)(642,694)(643,693)(644,692)(645,668)(646,690)(647,689)
(648,688)(649,687)(650,686)(651,685)(652,684)(653,683)(654,682)(655,681)
(656,680)(657,679)(658,678)(659,677)(660,676)(661,675)(662,674)(663,673)
(664,672)(665,671)(666,670)(667,669);;
s1 := (  1,462)(  2,461)(  3,483)(  4,482)(  5,481)(  6,480)(  7,479)(  8,478)
(  9,477)( 10,476)( 11,475)( 12,474)( 13,473)( 14,472)( 15,471)( 16,470)
( 17,469)( 18,468)( 19,467)( 20,466)( 21,465)( 22,464)( 23,463)( 24,439)
( 25,438)( 26,460)( 27,459)( 28,458)( 29,457)( 30,456)( 31,455)( 32,454)
( 33,453)( 34,452)( 35,451)( 36,450)( 37,449)( 38,448)( 39,447)( 40,446)
( 41,445)( 42,444)( 43,443)( 44,442)( 45,441)( 46,440)( 47,853)( 48,852)
( 49,874)( 50,873)( 51,872)( 52,871)( 53,870)( 54,869)( 55,868)( 56,867)
( 57,866)( 58,865)( 59,864)( 60,863)( 61,862)( 62,861)( 63,860)( 64,859)
( 65,858)( 66,857)( 67,856)( 68,855)( 69,854)( 70,830)( 71,829)( 72,851)
( 73,850)( 74,849)( 75,848)( 76,847)( 77,846)( 78,845)( 79,844)( 80,843)
( 81,842)( 82,841)( 83,840)( 84,839)( 85,838)( 86,837)( 87,836)( 88,835)
( 89,834)( 90,833)( 91,832)( 92,831)( 93,807)( 94,806)( 95,828)( 96,827)
( 97,826)( 98,825)( 99,824)(100,823)(101,822)(102,821)(103,820)(104,819)
(105,818)(106,817)(107,816)(108,815)(109,814)(110,813)(111,812)(112,811)
(113,810)(114,809)(115,808)(116,784)(117,783)(118,805)(119,804)(120,803)
(121,802)(122,801)(123,800)(124,799)(125,798)(126,797)(127,796)(128,795)
(129,794)(130,793)(131,792)(132,791)(133,790)(134,789)(135,788)(136,787)
(137,786)(138,785)(139,761)(140,760)(141,782)(142,781)(143,780)(144,779)
(145,778)(146,777)(147,776)(148,775)(149,774)(150,773)(151,772)(152,771)
(153,770)(154,769)(155,768)(156,767)(157,766)(158,765)(159,764)(160,763)
(161,762)(162,738)(163,737)(164,759)(165,758)(166,757)(167,756)(168,755)
(169,754)(170,753)(171,752)(172,751)(173,750)(174,749)(175,748)(176,747)
(177,746)(178,745)(179,744)(180,743)(181,742)(182,741)(183,740)(184,739)
(185,715)(186,714)(187,736)(188,735)(189,734)(190,733)(191,732)(192,731)
(193,730)(194,729)(195,728)(196,727)(197,726)(198,725)(199,724)(200,723)
(201,722)(202,721)(203,720)(204,719)(205,718)(206,717)(207,716)(208,692)
(209,691)(210,713)(211,712)(212,711)(213,710)(214,709)(215,708)(216,707)
(217,706)(218,705)(219,704)(220,703)(221,702)(222,701)(223,700)(224,699)
(225,698)(226,697)(227,696)(228,695)(229,694)(230,693)(231,669)(232,668)
(233,690)(234,689)(235,688)(236,687)(237,686)(238,685)(239,684)(240,683)
(241,682)(242,681)(243,680)(244,679)(245,678)(246,677)(247,676)(248,675)
(249,674)(250,673)(251,672)(252,671)(253,670)(254,646)(255,645)(256,667)
(257,666)(258,665)(259,664)(260,663)(261,662)(262,661)(263,660)(264,659)
(265,658)(266,657)(267,656)(268,655)(269,654)(270,653)(271,652)(272,651)
(273,650)(274,649)(275,648)(276,647)(277,623)(278,622)(279,644)(280,643)
(281,642)(282,641)(283,640)(284,639)(285,638)(286,637)(287,636)(288,635)
(289,634)(290,633)(291,632)(292,631)(293,630)(294,629)(295,628)(296,627)
(297,626)(298,625)(299,624)(300,600)(301,599)(302,621)(303,620)(304,619)
(305,618)(306,617)(307,616)(308,615)(309,614)(310,613)(311,612)(312,611)
(313,610)(314,609)(315,608)(316,607)(317,606)(318,605)(319,604)(320,603)
(321,602)(322,601)(323,577)(324,576)(325,598)(326,597)(327,596)(328,595)
(329,594)(330,593)(331,592)(332,591)(333,590)(334,589)(335,588)(336,587)
(337,586)(338,585)(339,584)(340,583)(341,582)(342,581)(343,580)(344,579)
(345,578)(346,554)(347,553)(348,575)(349,574)(350,573)(351,572)(352,571)
(353,570)(354,569)(355,568)(356,567)(357,566)(358,565)(359,564)(360,563)
(361,562)(362,561)(363,560)(364,559)(365,558)(366,557)(367,556)(368,555)
(369,531)(370,530)(371,552)(372,551)(373,550)(374,549)(375,548)(376,547)
(377,546)(378,545)(379,544)(380,543)(381,542)(382,541)(383,540)(384,539)
(385,538)(386,537)(387,536)(388,535)(389,534)(390,533)(391,532)(392,508)
(393,507)(394,529)(395,528)(396,527)(397,526)(398,525)(399,524)(400,523)
(401,522)(402,521)(403,520)(404,519)(405,518)(406,517)(407,516)(408,515)
(409,514)(410,513)(411,512)(412,511)(413,510)(414,509)(415,485)(416,484)
(417,506)(418,505)(419,504)(420,503)(421,502)(422,501)(423,500)(424,499)
(425,498)(426,497)(427,496)(428,495)(429,494)(430,493)(431,492)(432,491)
(433,490)(434,489)(435,488)(436,487)(437,486);;
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*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(874)!(  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)
(  9, 16)( 10, 15)( 11, 14)( 12, 13)( 24,415)( 25,437)( 26,436)( 27,435)
( 28,434)( 29,433)( 30,432)( 31,431)( 32,430)( 33,429)( 34,428)( 35,427)
( 36,426)( 37,425)( 38,424)( 39,423)( 40,422)( 41,421)( 42,420)( 43,419)
( 44,418)( 45,417)( 46,416)( 47,392)( 48,414)( 49,413)( 50,412)( 51,411)
( 52,410)( 53,409)( 54,408)( 55,407)( 56,406)( 57,405)( 58,404)( 59,403)
( 60,402)( 61,401)( 62,400)( 63,399)( 64,398)( 65,397)( 66,396)( 67,395)
( 68,394)( 69,393)( 70,369)( 71,391)( 72,390)( 73,389)( 74,388)( 75,387)
( 76,386)( 77,385)( 78,384)( 79,383)( 80,382)( 81,381)( 82,380)( 83,379)
( 84,378)( 85,377)( 86,376)( 87,375)( 88,374)( 89,373)( 90,372)( 91,371)
( 92,370)( 93,346)( 94,368)( 95,367)( 96,366)( 97,365)( 98,364)( 99,363)
(100,362)(101,361)(102,360)(103,359)(104,358)(105,357)(106,356)(107,355)
(108,354)(109,353)(110,352)(111,351)(112,350)(113,349)(114,348)(115,347)
(116,323)(117,345)(118,344)(119,343)(120,342)(121,341)(122,340)(123,339)
(124,338)(125,337)(126,336)(127,335)(128,334)(129,333)(130,332)(131,331)
(132,330)(133,329)(134,328)(135,327)(136,326)(137,325)(138,324)(139,300)
(140,322)(141,321)(142,320)(143,319)(144,318)(145,317)(146,316)(147,315)
(148,314)(149,313)(150,312)(151,311)(152,310)(153,309)(154,308)(155,307)
(156,306)(157,305)(158,304)(159,303)(160,302)(161,301)(162,277)(163,299)
(164,298)(165,297)(166,296)(167,295)(168,294)(169,293)(170,292)(171,291)
(172,290)(173,289)(174,288)(175,287)(176,286)(177,285)(178,284)(179,283)
(180,282)(181,281)(182,280)(183,279)(184,278)(185,254)(186,276)(187,275)
(188,274)(189,273)(190,272)(191,271)(192,270)(193,269)(194,268)(195,267)
(196,266)(197,265)(198,264)(199,263)(200,262)(201,261)(202,260)(203,259)
(204,258)(205,257)(206,256)(207,255)(208,231)(209,253)(210,252)(211,251)
(212,250)(213,249)(214,248)(215,247)(216,246)(217,245)(218,244)(219,243)
(220,242)(221,241)(222,240)(223,239)(224,238)(225,237)(226,236)(227,235)
(228,234)(229,233)(230,232)(439,460)(440,459)(441,458)(442,457)(443,456)
(444,455)(445,454)(446,453)(447,452)(448,451)(449,450)(461,852)(462,874)
(463,873)(464,872)(465,871)(466,870)(467,869)(468,868)(469,867)(470,866)
(471,865)(472,864)(473,863)(474,862)(475,861)(476,860)(477,859)(478,858)
(479,857)(480,856)(481,855)(482,854)(483,853)(484,829)(485,851)(486,850)
(487,849)(488,848)(489,847)(490,846)(491,845)(492,844)(493,843)(494,842)
(495,841)(496,840)(497,839)(498,838)(499,837)(500,836)(501,835)(502,834)
(503,833)(504,832)(505,831)(506,830)(507,806)(508,828)(509,827)(510,826)
(511,825)(512,824)(513,823)(514,822)(515,821)(516,820)(517,819)(518,818)
(519,817)(520,816)(521,815)(522,814)(523,813)(524,812)(525,811)(526,810)
(527,809)(528,808)(529,807)(530,783)(531,805)(532,804)(533,803)(534,802)
(535,801)(536,800)(537,799)(538,798)(539,797)(540,796)(541,795)(542,794)
(543,793)(544,792)(545,791)(546,790)(547,789)(548,788)(549,787)(550,786)
(551,785)(552,784)(553,760)(554,782)(555,781)(556,780)(557,779)(558,778)
(559,777)(560,776)(561,775)(562,774)(563,773)(564,772)(565,771)(566,770)
(567,769)(568,768)(569,767)(570,766)(571,765)(572,764)(573,763)(574,762)
(575,761)(576,737)(577,759)(578,758)(579,757)(580,756)(581,755)(582,754)
(583,753)(584,752)(585,751)(586,750)(587,749)(588,748)(589,747)(590,746)
(591,745)(592,744)(593,743)(594,742)(595,741)(596,740)(597,739)(598,738)
(599,714)(600,736)(601,735)(602,734)(603,733)(604,732)(605,731)(606,730)
(607,729)(608,728)(609,727)(610,726)(611,725)(612,724)(613,723)(614,722)
(615,721)(616,720)(617,719)(618,718)(619,717)(620,716)(621,715)(622,691)
(623,713)(624,712)(625,711)(626,710)(627,709)(628,708)(629,707)(630,706)
(631,705)(632,704)(633,703)(634,702)(635,701)(636,700)(637,699)(638,698)
(639,697)(640,696)(641,695)(642,694)(643,693)(644,692)(645,668)(646,690)
(647,689)(648,688)(649,687)(650,686)(651,685)(652,684)(653,683)(654,682)
(655,681)(656,680)(657,679)(658,678)(659,677)(660,676)(661,675)(662,674)
(663,673)(664,672)(665,671)(666,670)(667,669);
s1 := Sym(874)!(  1,462)(  2,461)(  3,483)(  4,482)(  5,481)(  6,480)(  7,479)
(  8,478)(  9,477)( 10,476)( 11,475)( 12,474)( 13,473)( 14,472)( 15,471)
( 16,470)( 17,469)( 18,468)( 19,467)( 20,466)( 21,465)( 22,464)( 23,463)
( 24,439)( 25,438)( 26,460)( 27,459)( 28,458)( 29,457)( 30,456)( 31,455)
( 32,454)( 33,453)( 34,452)( 35,451)( 36,450)( 37,449)( 38,448)( 39,447)
( 40,446)( 41,445)( 42,444)( 43,443)( 44,442)( 45,441)( 46,440)( 47,853)
( 48,852)( 49,874)( 50,873)( 51,872)( 52,871)( 53,870)( 54,869)( 55,868)
( 56,867)( 57,866)( 58,865)( 59,864)( 60,863)( 61,862)( 62,861)( 63,860)
( 64,859)( 65,858)( 66,857)( 67,856)( 68,855)( 69,854)( 70,830)( 71,829)
( 72,851)( 73,850)( 74,849)( 75,848)( 76,847)( 77,846)( 78,845)( 79,844)
( 80,843)( 81,842)( 82,841)( 83,840)( 84,839)( 85,838)( 86,837)( 87,836)
( 88,835)( 89,834)( 90,833)( 91,832)( 92,831)( 93,807)( 94,806)( 95,828)
( 96,827)( 97,826)( 98,825)( 99,824)(100,823)(101,822)(102,821)(103,820)
(104,819)(105,818)(106,817)(107,816)(108,815)(109,814)(110,813)(111,812)
(112,811)(113,810)(114,809)(115,808)(116,784)(117,783)(118,805)(119,804)
(120,803)(121,802)(122,801)(123,800)(124,799)(125,798)(126,797)(127,796)
(128,795)(129,794)(130,793)(131,792)(132,791)(133,790)(134,789)(135,788)
(136,787)(137,786)(138,785)(139,761)(140,760)(141,782)(142,781)(143,780)
(144,779)(145,778)(146,777)(147,776)(148,775)(149,774)(150,773)(151,772)
(152,771)(153,770)(154,769)(155,768)(156,767)(157,766)(158,765)(159,764)
(160,763)(161,762)(162,738)(163,737)(164,759)(165,758)(166,757)(167,756)
(168,755)(169,754)(170,753)(171,752)(172,751)(173,750)(174,749)(175,748)
(176,747)(177,746)(178,745)(179,744)(180,743)(181,742)(182,741)(183,740)
(184,739)(185,715)(186,714)(187,736)(188,735)(189,734)(190,733)(191,732)
(192,731)(193,730)(194,729)(195,728)(196,727)(197,726)(198,725)(199,724)
(200,723)(201,722)(202,721)(203,720)(204,719)(205,718)(206,717)(207,716)
(208,692)(209,691)(210,713)(211,712)(212,711)(213,710)(214,709)(215,708)
(216,707)(217,706)(218,705)(219,704)(220,703)(221,702)(222,701)(223,700)
(224,699)(225,698)(226,697)(227,696)(228,695)(229,694)(230,693)(231,669)
(232,668)(233,690)(234,689)(235,688)(236,687)(237,686)(238,685)(239,684)
(240,683)(241,682)(242,681)(243,680)(244,679)(245,678)(246,677)(247,676)
(248,675)(249,674)(250,673)(251,672)(252,671)(253,670)(254,646)(255,645)
(256,667)(257,666)(258,665)(259,664)(260,663)(261,662)(262,661)(263,660)
(264,659)(265,658)(266,657)(267,656)(268,655)(269,654)(270,653)(271,652)
(272,651)(273,650)(274,649)(275,648)(276,647)(277,623)(278,622)(279,644)
(280,643)(281,642)(282,641)(283,640)(284,639)(285,638)(286,637)(287,636)
(288,635)(289,634)(290,633)(291,632)(292,631)(293,630)(294,629)(295,628)
(296,627)(297,626)(298,625)(299,624)(300,600)(301,599)(302,621)(303,620)
(304,619)(305,618)(306,617)(307,616)(308,615)(309,614)(310,613)(311,612)
(312,611)(313,610)(314,609)(315,608)(316,607)(317,606)(318,605)(319,604)
(320,603)(321,602)(322,601)(323,577)(324,576)(325,598)(326,597)(327,596)
(328,595)(329,594)(330,593)(331,592)(332,591)(333,590)(334,589)(335,588)
(336,587)(337,586)(338,585)(339,584)(340,583)(341,582)(342,581)(343,580)
(344,579)(345,578)(346,554)(347,553)(348,575)(349,574)(350,573)(351,572)
(352,571)(353,570)(354,569)(355,568)(356,567)(357,566)(358,565)(359,564)
(360,563)(361,562)(362,561)(363,560)(364,559)(365,558)(366,557)(367,556)
(368,555)(369,531)(370,530)(371,552)(372,551)(373,550)(374,549)(375,548)
(376,547)(377,546)(378,545)(379,544)(380,543)(381,542)(382,541)(383,540)
(384,539)(385,538)(386,537)(387,536)(388,535)(389,534)(390,533)(391,532)
(392,508)(393,507)(394,529)(395,528)(396,527)(397,526)(398,525)(399,524)
(400,523)(401,522)(402,521)(403,520)(404,519)(405,518)(406,517)(407,516)
(408,515)(409,514)(410,513)(411,512)(412,511)(413,510)(414,509)(415,485)
(416,484)(417,506)(418,505)(419,504)(420,503)(421,502)(422,501)(423,500)
(424,499)(425,498)(426,497)(427,496)(428,495)(429,494)(430,493)(431,492)
(432,491)(433,490)(434,489)(435,488)(436,487)(437,486);
poly := sub<Sym(874)|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*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