Polytope of Type {770}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {770}*1540
Also Known As : 770-gon, {770}. if this polytope has another name.
Group : SmallGroup(1540,35)
Rank : 2
Schlafli Type : {770}
Number of vertices, edges, etc : 770, 770
Order of s₀s₁ : 770
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 : {385}*770
   5-fold quotients : {154}*308
   7-fold quotients : {110}*220
   10-fold quotients : {77}*154
   11-fold quotients : {70}*140
   14-fold quotients : {55}*110
   22-fold quotients : {35}*70
   35-fold quotients : {22}*44
   55-fold quotients : {14}*28
   70-fold quotients : {11}*22
   77-fold quotients : {10}*20
   110-fold quotients : {7}*14
   154-fold quotients : {5}*10
   385-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope