Polytope of Type {796}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {796}*1592
Also Known As : 796-gon, {796}. if this polytope has another name.
Group : SmallGroup(1592,10)
Rank : 2
Schlafli Type : {796}
Number of vertices, edges, etc : 796, 796
Order of s₀s₁ : 796
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 : {398}*796
   4-fold quotients : {199}*398
   199-fold quotients : {4}*8
   398-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope