Polytope of Type {790}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {790}*1580
Also Known As : 790-gon, {790}. if this polytope has another name.
Group : SmallGroup(1580,10)
Rank : 2
Schlafli Type : {790}
Number of vertices, edges, etc : 790, 790
Order of s0s1 : 790
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 : {395}*790
5-fold quotients : {158}*316
10-fold quotients : {79}*158
79-fold quotients : {10}*20
158-fold quotients : {5}*10
395-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, 79)( 3, 78)( 4, 77)( 5, 76)( 6, 75)( 7, 74)( 8, 73)( 9, 72)( 10, 71)( 11, 70)( 12, 69)( 13, 68)( 14, 67)( 15, 66)( 16, 65)( 17, 64)( 18, 63)( 19, 62)( 20, 61)( 21, 60)( 22, 59)( 23, 58)( 24, 57)( 25, 56)( 26, 55)( 27, 54)( 28, 53)( 29, 52)( 30, 51)( 31, 50)( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)( 80,317)( 81,395)( 82,394)( 83,393)( 84,392)( 85,391)( 86,390)( 87,389)( 88,388)( 89,387)( 90,386)( 91,385)( 92,384)( 93,383)( 94,382)( 95,381)( 96,380)( 97,379)( 98,378)( 99,377)(100,376)(101,375)(102,374)(103,373)(104,372)(105,371)(106,370)(107,369)(108,368)(109,367)(110,366)(111,365)(112,364)(113,363)(114,362)(115,361)(116,360)(117,359)(118,358)(119,357)(120,356)(121,355)(122,354)(123,353)(124,352)(125,351)(126,350)(127,349)(128,348)(129,347)(130,346)(131,345)(132,344)(133,343)(134,342)(135,341)(136,340)(137,339)(138,338)(139,337)(140,336)(141,335)(142,334)(143,333)(144,332)(145,331)(146,330)(147,329)(148,328)(149,327)(150,326)(151,325)(152,324)(153,323)(154,322)(155,321)(156,320)(157,319)(158,318)(159,238)(160,316)(161,315)(162,314)(163,313)(164,312)(165,311)(166,310)(167,309)(168,308)(169,307)(170,306)(171,305)(172,304)(173,303)(174,302)(175,301)(176,300)(177,299)(178,298)(179,297)(180,296)(181,295)(182,294)(183,293)(184,292)(185,291)(186,290)(187,289)(188,288)(189,287)(190,286)(191,285)(192,284)(193,283)(194,282)(195,281)(196,280)(197,279)(198,278)(199,277)(200,276)(201,275)(202,274)(203,273)(204,272)(205,271)(206,270)(207,269)(208,268)(209,267)(210,266)(211,265)(212,264)(213,263)(214,262)(215,261)(216,260)(217,259)(218,258)(219,257)(220,256)(221,255)(222,254)(223,253)(224,252)(225,251)(226,250)(227,249)(228,248)(229,247)(230,246)(231,245)(232,244)(233,243)(234,242)(235,241)(236,240)(237,239)(397,474)(398,473)(399,472)(400,471)(401,470)(402,469)(403,468)(404,467)(405,466)(406,465)(407,464)(408,463)(409,462)(410,461)(411,460)(412,459)(413,458)(414,457)(415,456)(416,455)(417,454)(418,453)(419,452)(420,451)(421,450)(422,449)(423,448)(424,447)(425,446)(426,445)(427,444)(428,443)(429,442)(430,441)(431,440)(432,439)(433,438)(434,437)(435,436)(475,712)(476,790)(477,789)(478,788)(479,787)(480,786)(481,785)(482,784)(483,783)(484,782)(485,781)(486,780)(487,779)(488,778)(489,777)(490,776)(491,775)(492,774)(493,773)(494,772)(495,771)(496,770)(497,769)(498,768)(499,767)(500,766)(501,765)(502,764)(503,763)(504,762)(505,761)(506,760)(507,759)(508,758)(509,757)(510,756)(511,755)(512,754)(513,753)(514,752)(515,751)(516,750)(517,749)(518,748)(519,747)(520,746)(521,745)(522,744)(523,743)(524,742)(525,741)(526,740)(527,739)(528,738)(529,737)(530,736)(531,735)(532,734)(533,733)(534,732)(535,731)(536,730)(537,729)(538,728)(539,727)(540,726)(541,725)(542,724)(543,723)(544,722)(545,721)(546,720)(547,719)(548,718)(549,717)(550,716)(551,715)(552,714)(553,713)(554,633)(555,711)(556,710)(557,709)(558,708)(559,707)(560,706)(561,705)(562,704)(563,703)(564,702)(565,701)(566,700)(567,699)(568,698)(569,697)(570,696)(571,695)(572,694)(573,693)(574,692)(575,691)(576,690)(577,689)(578,688)(579,687)(580,686)(581,685)(582,684)(583,683)(584,682)(585,681)(586,680)(587,679)(588,678)(589,677)(590,676)(591,675)(592,674)(593,673)(594,672)(595,671)(596,670)(597,669)(598,668)(599,667)(600,666)(601,665)(602,664)(603,663)(604,662)(605,661)(606,660)(607,659)(608,658)(609,657)(610,656)(611,655)(612,654)(613,653)(614,652)(615,651)(616,650)(617,649)(618,648)(619,647)(620,646)(621,645)(622,644)(623,643)(624,642)(625,641)(626,640)(627,639)(628,638)(629,637)(630,636)(631,635)(632,634);;
s1 := ( 1,476)( 2,475)( 3,553)( 4,552)( 5,551)( 6,550)( 7,549)( 8,548)( 9,547)( 10,546)( 11,545)( 12,544)( 13,543)( 14,542)( 15,541)( 16,540)( 17,539)( 18,538)( 19,537)( 20,536)( 21,535)( 22,534)( 23,533)( 24,532)( 25,531)( 26,530)( 27,529)( 28,528)( 29,527)( 30,526)( 31,525)( 32,524)( 33,523)( 34,522)( 35,521)( 36,520)( 37,519)( 38,518)( 39,517)( 40,516)( 41,515)( 42,514)( 43,513)( 44,512)( 45,511)( 46,510)( 47,509)( 48,508)( 49,507)( 50,506)( 51,505)( 52,504)( 53,503)( 54,502)( 55,501)( 56,500)( 57,499)( 58,498)( 59,497)( 60,496)( 61,495)( 62,494)( 63,493)( 64,492)( 65,491)( 66,490)( 67,489)( 68,488)( 69,487)( 70,486)( 71,485)( 72,484)( 73,483)( 74,482)( 75,481)( 76,480)( 77,479)( 78,478)( 79,477)( 80,397)( 81,396)( 82,474)( 83,473)( 84,472)( 85,471)( 86,470)( 87,469)( 88,468)( 89,467)( 90,466)( 91,465)( 92,464)( 93,463)( 94,462)( 95,461)( 96,460)( 97,459)( 98,458)( 99,457)(100,456)(101,455)(102,454)(103,453)(104,452)(105,451)(106,450)(107,449)(108,448)(109,447)(110,446)(111,445)(112,444)(113,443)(114,442)(115,441)(116,440)(117,439)(118,438)(119,437)(120,436)(121,435)(122,434)(123,433)(124,432)(125,431)(126,430)(127,429)(128,428)(129,427)(130,426)(131,425)(132,424)(133,423)(134,422)(135,421)(136,420)(137,419)(138,418)(139,417)(140,416)(141,415)(142,414)(143,413)(144,412)(145,411)(146,410)(147,409)(148,408)(149,407)(150,406)(151,405)(152,404)(153,403)(154,402)(155,401)(156,400)(157,399)(158,398)(159,713)(160,712)(161,790)(162,789)(163,788)(164,787)(165,786)(166,785)(167,784)(168,783)(169,782)(170,781)(171,780)(172,779)(173,778)(174,777)(175,776)(176,775)(177,774)(178,773)(179,772)(180,771)(181,770)(182,769)(183,768)(184,767)(185,766)(186,765)(187,764)(188,763)(189,762)(190,761)(191,760)(192,759)(193,758)(194,757)(195,756)(196,755)(197,754)(198,753)(199,752)(200,751)(201,750)(202,749)(203,748)(204,747)(205,746)(206,745)(207,744)(208,743)(209,742)(210,741)(211,740)(212,739)(213,738)(214,737)(215,736)(216,735)(217,734)(218,733)(219,732)(220,731)(221,730)(222,729)(223,728)(224,727)(225,726)(226,725)(227,724)(228,723)(229,722)(230,721)(231,720)(232,719)(233,718)(234,717)(235,716)(236,715)(237,714)(238,634)(239,633)(240,711)(241,710)(242,709)(243,708)(244,707)(245,706)(246,705)(247,704)(248,703)(249,702)(250,701)(251,700)(252,699)(253,698)(254,697)(255,696)(256,695)(257,694)(258,693)(259,692)(260,691)(261,690)(262,689)(263,688)(264,687)(265,686)(266,685)(267,684)(268,683)(269,682)(270,681)(271,680)(272,679)(273,678)(274,677)(275,676)(276,675)(277,674)(278,673)(279,672)(280,671)(281,670)(282,669)(283,668)(284,667)(285,666)(286,665)(287,664)(288,663)(289,662)(290,661)(291,660)(292,659)(293,658)(294,657)(295,656)(296,655)(297,654)(298,653)(299,652)(300,651)(301,650)(302,649)(303,648)(304,647)(305,646)(306,645)(307,644)(308,643)(309,642)(310,641)(311,640)(312,639)(313,638)(314,637)(315,636)(316,635)(317,555)(318,554)(319,632)(320,631)(321,630)(322,629)(323,628)(324,627)(325,626)(326,625)(327,624)(328,623)(329,622)(330,621)(331,620)(332,619)(333,618)(334,617)(335,616)(336,615)(337,614)(338,613)(339,612)(340,611)(341,610)(342,609)(343,608)(344,607)(345,606)(346,605)(347,604)(348,603)(349,602)(350,601)(351,600)(352,599)(353,598)(354,597)(355,596)(356,595)(357,594)(358,593)(359,592)(360,591)(361,590)(362,589)(363,588)(364,587)(365,586)(366,585)(367,584)(368,583)(369,582)(370,581)(371,580)(372,579)(373,578)(374,577)(375,576)(376,575)(377,574)(378,573)(379,572)(380,571)(381,570)(382,569)(383,568)(384,567)(385,566)(386,565)(387,564)(388,563)(389,562)(390,561)(391,560)(392,559)(393,558)(394,557)(395,556);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(790)!( 2, 79)( 3, 78)( 4, 77)( 5, 76)( 6, 75)( 7, 74)( 8, 73)( 9, 72)( 10, 71)( 11, 70)( 12, 69)( 13, 68)( 14, 67)( 15, 66)( 16, 65)( 17, 64)( 18, 63)( 19, 62)( 20, 61)( 21, 60)( 22, 59)( 23, 58)( 24, 57)( 25, 56)( 26, 55)( 27, 54)( 28, 53)( 29, 52)( 30, 51)( 31, 50)( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)( 80,317)( 81,395)( 82,394)( 83,393)( 84,392)( 85,391)( 86,390)( 87,389)( 88,388)( 89,387)( 90,386)( 91,385)( 92,384)( 93,383)( 94,382)( 95,381)( 96,380)( 97,379)( 98,378)( 99,377)(100,376)(101,375)(102,374)(103,373)(104,372)(105,371)(106,370)(107,369)(108,368)(109,367)(110,366)(111,365)(112,364)(113,363)(114,362)(115,361)(116,360)(117,359)(118,358)(119,357)(120,356)(121,355)(122,354)(123,353)(124,352)(125,351)(126,350)(127,349)(128,348)(129,347)(130,346)(131,345)(132,344)(133,343)(134,342)(135,341)(136,340)(137,339)(138,338)(139,337)(140,336)(141,335)(142,334)(143,333)(144,332)(145,331)(146,330)(147,329)(148,328)(149,327)(150,326)(151,325)(152,324)(153,323)(154,322)(155,321)(156,320)(157,319)(158,318)(159,238)(160,316)(161,315)(162,314)(163,313)(164,312)(165,311)(166,310)(167,309)(168,308)(169,307)(170,306)(171,305)(172,304)(173,303)(174,302)(175,301)(176,300)(177,299)(178,298)(179,297)(180,296)(181,295)(182,294)(183,293)(184,292)(185,291)(186,290)(187,289)(188,288)(189,287)(190,286)(191,285)(192,284)(193,283)(194,282)(195,281)(196,280)(197,279)(198,278)(199,277)(200,276)(201,275)(202,274)(203,273)(204,272)(205,271)(206,270)(207,269)(208,268)(209,267)(210,266)(211,265)(212,264)(213,263)(214,262)(215,261)(216,260)(217,259)(218,258)(219,257)(220,256)(221,255)(222,254)(223,253)(224,252)(225,251)(226,250)(227,249)(228,248)(229,247)(230,246)(231,245)(232,244)(233,243)(234,242)(235,241)(236,240)(237,239)(397,474)(398,473)(399,472)(400,471)(401,470)(402,469)(403,468)(404,467)(405,466)(406,465)(407,464)(408,463)(409,462)(410,461)(411,460)(412,459)(413,458)(414,457)(415,456)(416,455)(417,454)(418,453)(419,452)(420,451)(421,450)(422,449)(423,448)(424,447)(425,446)(426,445)(427,444)(428,443)(429,442)(430,441)(431,440)(432,439)(433,438)(434,437)(435,436)(475,712)(476,790)(477,789)(478,788)(479,787)(480,786)(481,785)(482,784)(483,783)(484,782)(485,781)(486,780)(487,779)(488,778)(489,777)(490,776)(491,775)(492,774)(493,773)(494,772)(495,771)(496,770)(497,769)(498,768)(499,767)(500,766)(501,765)(502,764)(503,763)(504,762)(505,761)(506,760)(507,759)(508,758)(509,757)(510,756)(511,755)(512,754)(513,753)(514,752)(515,751)(516,750)(517,749)(518,748)(519,747)(520,746)(521,745)(522,744)(523,743)(524,742)(525,741)(526,740)(527,739)(528,738)(529,737)(530,736)(531,735)(532,734)(533,733)(534,732)(535,731)(536,730)(537,729)(538,728)(539,727)(540,726)(541,725)(542,724)(543,723)(544,722)(545,721)(546,720)(547,719)(548,718)(549,717)(550,716)(551,715)(552,714)(553,713)(554,633)(555,711)(556,710)(557,709)(558,708)(559,707)(560,706)(561,705)(562,704)(563,703)(564,702)(565,701)(566,700)(567,699)(568,698)(569,697)(570,696)(571,695)(572,694)(573,693)(574,692)(575,691)(576,690)(577,689)(578,688)(579,687)(580,686)(581,685)(582,684)(583,683)(584,682)(585,681)(586,680)(587,679)(588,678)(589,677)(590,676)(591,675)(592,674)(593,673)(594,672)(595,671)(596,670)(597,669)(598,668)(599,667)(600,666)(601,665)(602,664)(603,663)(604,662)(605,661)(606,660)(607,659)(608,658)(609,657)(610,656)(611,655)(612,654)(613,653)(614,652)(615,651)(616,650)(617,649)(618,648)(619,647)(620,646)(621,645)(622,644)(623,643)(624,642)(625,641)(626,640)(627,639)(628,638)(629,637)(630,636)(631,635)(632,634);
s1 := Sym(790)!( 1,476)( 2,475)( 3,553)( 4,552)( 5,551)( 6,550)( 7,549)( 8,548)( 9,547)( 10,546)( 11,545)( 12,544)( 13,543)( 14,542)( 15,541)( 16,540)( 17,539)( 18,538)( 19,537)( 20,536)( 21,535)( 22,534)( 23,533)( 24,532)( 25,531)( 26,530)( 27,529)( 28,528)( 29,527)( 30,526)( 31,525)( 32,524)( 33,523)( 34,522)( 35,521)( 36,520)( 37,519)( 38,518)( 39,517)( 40,516)( 41,515)( 42,514)( 43,513)( 44,512)( 45,511)( 46,510)( 47,509)( 48,508)( 49,507)( 50,506)( 51,505)( 52,504)( 53,503)( 54,502)( 55,501)( 56,500)( 57,499)( 58,498)( 59,497)( 60,496)( 61,495)( 62,494)( 63,493)( 64,492)( 65,491)( 66,490)( 67,489)( 68,488)( 69,487)( 70,486)( 71,485)( 72,484)( 73,483)( 74,482)( 75,481)( 76,480)( 77,479)( 78,478)( 79,477)( 80,397)( 81,396)( 82,474)( 83,473)( 84,472)( 85,471)( 86,470)( 87,469)( 88,468)( 89,467)( 90,466)( 91,465)( 92,464)( 93,463)( 94,462)( 95,461)( 96,460)( 97,459)( 98,458)( 99,457)(100,456)(101,455)(102,454)(103,453)(104,452)(105,451)(106,450)(107,449)(108,448)(109,447)(110,446)(111,445)(112,444)(113,443)(114,442)(115,441)(116,440)(117,439)(118,438)(119,437)(120,436)(121,435)(122,434)(123,433)(124,432)(125,431)(126,430)(127,429)(128,428)(129,427)(130,426)(131,425)(132,424)(133,423)(134,422)(135,421)(136,420)(137,419)(138,418)(139,417)(140,416)(141,415)(142,414)(143,413)(144,412)(145,411)(146,410)(147,409)(148,408)(149,407)(150,406)(151,405)(152,404)(153,403)(154,402)(155,401)(156,400)(157,399)(158,398)(159,713)(160,712)(161,790)(162,789)(163,788)(164,787)(165,786)(166,785)(167,784)(168,783)(169,782)(170,781)(171,780)(172,779)(173,778)(174,777)(175,776)(176,775)(177,774)(178,773)(179,772)(180,771)(181,770)(182,769)(183,768)(184,767)(185,766)(186,765)(187,764)(188,763)(189,762)(190,761)(191,760)(192,759)(193,758)(194,757)(195,756)(196,755)(197,754)(198,753)(199,752)(200,751)(201,750)(202,749)(203,748)(204,747)(205,746)(206,745)(207,744)(208,743)(209,742)(210,741)(211,740)(212,739)(213,738)(214,737)(215,736)(216,735)(217,734)(218,733)(219,732)(220,731)(221,730)(222,729)(223,728)(224,727)(225,726)(226,725)(227,724)(228,723)(229,722)(230,721)(231,720)(232,719)(233,718)(234,717)(235,716)(236,715)(237,714)(238,634)(239,633)(240,711)(241,710)(242,709)(243,708)(244,707)(245,706)(246,705)(247,704)(248,703)(249,702)(250,701)(251,700)(252,699)(253,698)(254,697)(255,696)(256,695)(257,694)(258,693)(259,692)(260,691)(261,690)(262,689)(263,688)(264,687)(265,686)(266,685)(267,684)(268,683)(269,682)(270,681)(271,680)(272,679)(273,678)(274,677)(275,676)(276,675)(277,674)(278,673)(279,672)(280,671)(281,670)(282,669)(283,668)(284,667)(285,666)(286,665)(287,664)(288,663)(289,662)(290,661)(291,660)(292,659)(293,658)(294,657)(295,656)(296,655)(297,654)(298,653)(299,652)(300,651)(301,650)(302,649)(303,648)(304,647)(305,646)(306,645)(307,644)(308,643)(309,642)(310,641)(311,640)(312,639)(313,638)(314,637)(315,636)(316,635)(317,555)(318,554)(319,632)(320,631)(321,630)(322,629)(323,628)(324,627)(325,626)(326,625)(327,624)(328,623)(329,622)(330,621)(331,620)(332,619)(333,618)(334,617)(335,616)(336,615)(337,614)(338,613)(339,612)(340,611)(341,610)(342,609)(343,608)(344,607)(345,606)(346,605)(347,604)(348,603)(349,602)(350,601)(351,600)(352,599)(353,598)(354,597)(355,596)(356,595)(357,594)(358,593)(359,592)(360,591)(361,590)(362,589)(363,588)(364,587)(365,586)(366,585)(367,584)(368,583)(369,582)(370,581)(371,580)(372,579)(373,578)(374,577)(375,576)(376,575)(377,574)(378,573)(379,572)(380,571)(381,570)(382,569)(383,568)(384,567)(385,566)(386,565)(387,564)(388,563)(389,562)(390,561)(391,560)(392,559)(393,558)(394,557)(395,556);
poly := sub<Sym(790)|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 >;
References : None.
to this polytope