Polytope of Type {774}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {774}*1548
Also Known As : 774-gon, {774}. if this polytope has another name.
Group : SmallGroup(1548,14)
Rank : 2
Schlafli Type : {774}
Number of vertices, edges, etc : 774, 774
Order of s₀s₁ : 774
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 : {387}*774
   3-fold quotients : {258}*516
   6-fold quotients : {129}*258
   9-fold quotients : {86}*172
   18-fold quotients : {43}*86
   43-fold quotients : {18}*36
   86-fold quotients : {9}*18
   129-fold quotients : {6}*12
   258-fold quotients : {3}*6
   387-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope