Polytope of Type {750}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {750}*1500
Also Known As : 750-gon, {750}. if this polytope has another name.
Group : SmallGroup(1500,11)
Rank : 2
Schlafli Type : {750}
Number of vertices, edges, etc : 750, 750
Order of s₀s₁ : 750
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 : {375}*750
   3-fold quotients : {250}*500
   5-fold quotients : {150}*300
   6-fold quotients : {125}*250
   10-fold quotients : {75}*150
   15-fold quotients : {50}*100
   25-fold quotients : {30}*60
   30-fold quotients : {25}*50
   50-fold quotients : {15}*30
   75-fold quotients : {10}*20
   125-fold quotients : {6}*12
   150-fold quotients : {5}*10
   250-fold quotients : {3}*6
   375-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope