Polytope of Type {838}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {838}*1676
Also Known As : 838-gon, {838}. if this polytope has another name.
Group : SmallGroup(1676,3)
Rank : 2
Schlafli Type : {838}
Number of vertices, edges, etc : 838, 838
Order of s₀s₁ : 838
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 : {419}*838
   419-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope