Polytope of Type {754}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {754}*1508
Also Known As : 754-gon, {754}. if this polytope has another name.
Group : SmallGroup(1508,14)
Rank : 2
Schlafli Type : {754}
Number of vertices, edges, etc : 754, 754
Order of s₀s₁ : 754
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 : {377}*754
   13-fold quotients : {58}*116
   26-fold quotients : {29}*58
   29-fold quotients : {26}*52
   58-fold quotients : {13}*26
   377-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope