Polytope of Type {766}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {766}*1532
Also Known As : 766-gon, {766}. if this polytope has another name.
Group : SmallGroup(1532,3)
Rank : 2
Schlafli Type : {766}
Number of vertices, edges, etc : 766, 766
Order of s₀s₁ : 766
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 : {383}*766
   383-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope