Polytope of Type {808}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {808}*1616
Also Known As : 808-gon, {808}. if this polytope has another name.
Group : SmallGroup(1616,26)
Rank : 2
Schlafli Type : {808}
Number of vertices, edges, etc : 808, 808
Order of s₀s₁ : 808
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 : {404}*808
   4-fold quotients : {202}*404
   8-fold quotients : {101}*202
   101-fold quotients : {8}*16
   202-fold quotients : {4}*8
   404-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope