Polytope of Type {794}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {794}*1588
Also Known As : 794-gon, {794}. if this polytope has another name.
Group : SmallGroup(1588,4)
Rank : 2
Schlafli Type : {794}
Number of vertices, edges, etc : 794, 794
Order of s₀s₁ : 794
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 : {397}*794
   397-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope