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.
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