Polytope of Type {866}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {866}*1732
Also Known As : 866-gon, {866}. if this polytope has another name.
Group : SmallGroup(1732,4)
Rank : 2
Schlafli Type : {866}
Number of vertices, edges, etc : 866, 866
Order of s₀s₁ : 866
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 : {433}*866
   433-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope