Polytope of Type {802}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {802}*1604
Also Known As : 802-gon, {802}. if this polytope has another name.
Group : SmallGroup(1604,4)
Rank : 2
Schlafli Type : {802}
Number of vertices, edges, etc : 802, 802
Order of s₀s₁ : 802
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 : {401}*802
   401-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope