Polytope of Type {804}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {804}*1608
Also Known As : 804-gon, {804}. if this polytope has another name.
Group : SmallGroup(1608,36)
Rank : 2
Schlafli Type : {804}
Number of vertices, edges, etc : 804, 804
Order of s₀s₁ : 804
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 : {402}*804
   3-fold quotients : {268}*536
   4-fold quotients : {201}*402
   6-fold quotients : {134}*268
   12-fold quotients : {67}*134
   67-fold quotients : {12}*24
   134-fold quotients : {6}*12
   201-fold quotients : {4}*8
   268-fold quotients : {3}*6
   402-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope