Polytope of Type {776}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {776}*1552
Also Known As : 776-gon, {776}. if this polytope has another name.
Group : SmallGroup(1552,26)
Rank : 2
Schlafli Type : {776}
Number of vertices, edges, etc : 776, 776
Order of s₀s₁ : 776
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 : {388}*776
   4-fold quotients : {194}*388
   8-fold quotients : {97}*194
   97-fold quotients : {8}*16
   194-fold quotients : {4}*8
   388-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope