Polytope of Type {744}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {744}*1488
Also Known As : 744-gon, {744}. if this polytope has another name.
Group : SmallGroup(1488,93)
Rank : 2
Schlafli Type : {744}
Number of vertices, edges, etc : 744, 744
Order of s₀s₁ : 744
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 : {372}*744
   3-fold quotients : {248}*496
   4-fold quotients : {186}*372
   6-fold quotients : {124}*248
   8-fold quotients : {93}*186
   12-fold quotients : {62}*124
   24-fold quotients : {31}*62
   31-fold quotients : {24}*48
   62-fold quotients : {12}*24
   93-fold quotients : {8}*16
   124-fold quotients : {6}*12
   186-fold quotients : {4}*8
   248-fold quotients : {3}*6
   372-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope