Polytope of Type {742}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {742}*1484
Also Known As : 742-gon, {742}. if this polytope has another name.
Group : SmallGroup(1484,10)
Rank : 2
Schlafli Type : {742}
Number of vertices, edges, etc : 742, 742
Order of s₀s₁ : 742
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 : {371}*742
   7-fold quotients : {106}*212
   14-fold quotients : {53}*106
   53-fold quotients : {14}*28
   106-fold quotients : {7}*14
   371-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope