Polytope of Type {734}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {734}*1468
Also Known As : 734-gon, {734}. if this polytope has another name.
Group : SmallGroup(1468,3)
Rank : 2
Schlafli Type : {734}
Number of vertices, edges, etc : 734, 734
Order of s₀s₁ : 734
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 : {367}*734
   367-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope