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.
Irregular Quotients (of which this is a minimal cover):
None.
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