Polytope of Type {782}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {782}*1564
Also Known As : 782-gon, {782}. if this polytope has another name.
Group : SmallGroup(1564,10)
Rank : 2
Schlafli Type : {782}
Number of vertices, edges, etc : 782, 782
Order of s₀s₁ : 782
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 : {391}*782
   17-fold quotients : {46}*92
   23-fold quotients : {34}*68
   34-fold quotients : {23}*46
   46-fold quotients : {17}*34
   391-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope