Polytope of Type {778}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {778}*1556
Also Known As : 778-gon, {778}. if this polytope has another name.
Group : SmallGroup(1556,4)
Rank : 2
Schlafli Type : {778}
Number of vertices, edges, etc : 778, 778
Order of s₀s₁ : 778
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 : {389}*778
   389-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope