Polytope of Type {752}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {752}*1504
Also Known As : 752-gon, {752}. if this polytope has another name.
Group : SmallGroup(1504,88)
Rank : 2
Schlafli Type : {752}
Number of vertices, edges, etc : 752, 752
Order of s₀s₁ : 752
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 : {376}*752
   4-fold quotients : {188}*376
   8-fold quotients : {94}*188
   16-fold quotients : {47}*94
   47-fold quotients : {16}*32
   94-fold quotients : {8}*16
   188-fold quotients : {4}*8
   376-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope