Polytope of Type {762}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {762}*1524
Also Known As : 762-gon, {762}. if this polytope has another name.
Group : SmallGroup(1524,14)
Rank : 2
Schlafli Type : {762}
Number of vertices, edges, etc : 762, 762
Order of s₀s₁ : 762
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 : {381}*762
   3-fold quotients : {254}*508
   6-fold quotients : {127}*254
   127-fold quotients : {6}*12
   254-fold quotients : {3}*6
   381-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,127)(  3,126)(  4,125)(  5,124)(  6,123)(  7,122)(  8,121)(  9,120)
( 10,119)( 11,118)( 12,117)( 13,116)( 14,115)( 15,114)( 16,113)( 17,112)
( 18,111)( 19,110)( 20,109)( 21,108)( 22,107)( 23,106)( 24,105)( 25,104)
( 26,103)( 27,102)( 28,101)( 29,100)( 30, 99)( 31, 98)( 32, 97)( 33, 96)
( 34, 95)( 35, 94)( 36, 93)( 37, 92)( 38, 91)( 39, 90)( 40, 89)( 41, 88)
( 42, 87)( 43, 86)( 44, 85)( 45, 84)( 46, 83)( 47, 82)( 48, 81)( 49, 80)
( 50, 79)( 51, 78)( 52, 77)( 53, 76)( 54, 75)( 55, 74)( 56, 73)( 57, 72)
( 58, 71)( 59, 70)( 60, 69)( 61, 68)( 62, 67)( 63, 66)( 64, 65)(128,255)
(129,381)(130,380)(131,379)(132,378)(133,377)(134,376)(135,375)(136,374)
(137,373)(138,372)(139,371)(140,370)(141,369)(142,368)(143,367)(144,366)
(145,365)(146,364)(147,363)(148,362)(149,361)(150,360)(151,359)(152,358)
(153,357)(154,356)(155,355)(156,354)(157,353)(158,352)(159,351)(160,350)
(161,349)(162,348)(163,347)(164,346)(165,345)(166,344)(167,343)(168,342)
(169,341)(170,340)(171,339)(172,338)(173,337)(174,336)(175,335)(176,334)
(177,333)(178,332)(179,331)(180,330)(181,329)(182,328)(183,327)(184,326)
(185,325)(186,324)(187,323)(188,322)(189,321)(190,320)(191,319)(192,318)
(193,317)(194,316)(195,315)(196,314)(197,313)(198,312)(199,311)(200,310)
(201,309)(202,308)(203,307)(204,306)(205,305)(206,304)(207,303)(208,302)
(209,301)(210,300)(211,299)(212,298)(213,297)(214,296)(215,295)(216,294)
(217,293)(218,292)(219,291)(220,290)(221,289)(222,288)(223,287)(224,286)
(225,285)(226,284)(227,283)(228,282)(229,281)(230,280)(231,279)(232,278)
(233,277)(234,276)(235,275)(236,274)(237,273)(238,272)(239,271)(240,270)
(241,269)(242,268)(243,267)(244,266)(245,265)(246,264)(247,263)(248,262)
(249,261)(250,260)(251,259)(252,258)(253,257)(254,256)(383,508)(384,507)
(385,506)(386,505)(387,504)(388,503)(389,502)(390,501)(391,500)(392,499)
(393,498)(394,497)(395,496)(396,495)(397,494)(398,493)(399,492)(400,491)
(401,490)(402,489)(403,488)(404,487)(405,486)(406,485)(407,484)(408,483)
(409,482)(410,481)(411,480)(412,479)(413,478)(414,477)(415,476)(416,475)
(417,474)(418,473)(419,472)(420,471)(421,470)(422,469)(423,468)(424,467)
(425,466)(426,465)(427,464)(428,463)(429,462)(430,461)(431,460)(432,459)
(433,458)(434,457)(435,456)(436,455)(437,454)(438,453)(439,452)(440,451)
(441,450)(442,449)(443,448)(444,447)(445,446)(509,636)(510,762)(511,761)
(512,760)(513,759)(514,758)(515,757)(516,756)(517,755)(518,754)(519,753)
(520,752)(521,751)(522,750)(523,749)(524,748)(525,747)(526,746)(527,745)
(528,744)(529,743)(530,742)(531,741)(532,740)(533,739)(534,738)(535,737)
(536,736)(537,735)(538,734)(539,733)(540,732)(541,731)(542,730)(543,729)
(544,728)(545,727)(546,726)(547,725)(548,724)(549,723)(550,722)(551,721)
(552,720)(553,719)(554,718)(555,717)(556,716)(557,715)(558,714)(559,713)
(560,712)(561,711)(562,710)(563,709)(564,708)(565,707)(566,706)(567,705)
(568,704)(569,703)(570,702)(571,701)(572,700)(573,699)(574,698)(575,697)
(576,696)(577,695)(578,694)(579,693)(580,692)(581,691)(582,690)(583,689)
(584,688)(585,687)(586,686)(587,685)(588,684)(589,683)(590,682)(591,681)
(592,680)(593,679)(594,678)(595,677)(596,676)(597,675)(598,674)(599,673)
(600,672)(601,671)(602,670)(603,669)(604,668)(605,667)(606,666)(607,665)
(608,664)(609,663)(610,662)(611,661)(612,660)(613,659)(614,658)(615,657)
(616,656)(617,655)(618,654)(619,653)(620,652)(621,651)(622,650)(623,649)
(624,648)(625,647)(626,646)(627,645)(628,644)(629,643)(630,642)(631,641)
(632,640)(633,639)(634,638)(635,637);;
s1 := (  1,510)(  2,509)(  3,635)(  4,634)(  5,633)(  6,632)(  7,631)(  8,630)
(  9,629)( 10,628)( 11,627)( 12,626)( 13,625)( 14,624)( 15,623)( 16,622)
( 17,621)( 18,620)( 19,619)( 20,618)( 21,617)( 22,616)( 23,615)( 24,614)
( 25,613)( 26,612)( 27,611)( 28,610)( 29,609)( 30,608)( 31,607)( 32,606)
( 33,605)( 34,604)( 35,603)( 36,602)( 37,601)( 38,600)( 39,599)( 40,598)
( 41,597)( 42,596)( 43,595)( 44,594)( 45,593)( 46,592)( 47,591)( 48,590)
( 49,589)( 50,588)( 51,587)( 52,586)( 53,585)( 54,584)( 55,583)( 56,582)
( 57,581)( 58,580)( 59,579)( 60,578)( 61,577)( 62,576)( 63,575)( 64,574)
( 65,573)( 66,572)( 67,571)( 68,570)( 69,569)( 70,568)( 71,567)( 72,566)
( 73,565)( 74,564)( 75,563)( 76,562)( 77,561)( 78,560)( 79,559)( 80,558)
( 81,557)( 82,556)( 83,555)( 84,554)( 85,553)( 86,552)( 87,551)( 88,550)
( 89,549)( 90,548)( 91,547)( 92,546)( 93,545)( 94,544)( 95,543)( 96,542)
( 97,541)( 98,540)( 99,539)(100,538)(101,537)(102,536)(103,535)(104,534)
(105,533)(106,532)(107,531)(108,530)(109,529)(110,528)(111,527)(112,526)
(113,525)(114,524)(115,523)(116,522)(117,521)(118,520)(119,519)(120,518)
(121,517)(122,516)(123,515)(124,514)(125,513)(126,512)(127,511)(128,383)
(129,382)(130,508)(131,507)(132,506)(133,505)(134,504)(135,503)(136,502)
(137,501)(138,500)(139,499)(140,498)(141,497)(142,496)(143,495)(144,494)
(145,493)(146,492)(147,491)(148,490)(149,489)(150,488)(151,487)(152,486)
(153,485)(154,484)(155,483)(156,482)(157,481)(158,480)(159,479)(160,478)
(161,477)(162,476)(163,475)(164,474)(165,473)(166,472)(167,471)(168,470)
(169,469)(170,468)(171,467)(172,466)(173,465)(174,464)(175,463)(176,462)
(177,461)(178,460)(179,459)(180,458)(181,457)(182,456)(183,455)(184,454)
(185,453)(186,452)(187,451)(188,450)(189,449)(190,448)(191,447)(192,446)
(193,445)(194,444)(195,443)(196,442)(197,441)(198,440)(199,439)(200,438)
(201,437)(202,436)(203,435)(204,434)(205,433)(206,432)(207,431)(208,430)
(209,429)(210,428)(211,427)(212,426)(213,425)(214,424)(215,423)(216,422)
(217,421)(218,420)(219,419)(220,418)(221,417)(222,416)(223,415)(224,414)
(225,413)(226,412)(227,411)(228,410)(229,409)(230,408)(231,407)(232,406)
(233,405)(234,404)(235,403)(236,402)(237,401)(238,400)(239,399)(240,398)
(241,397)(242,396)(243,395)(244,394)(245,393)(246,392)(247,391)(248,390)
(249,389)(250,388)(251,387)(252,386)(253,385)(254,384)(255,637)(256,636)
(257,762)(258,761)(259,760)(260,759)(261,758)(262,757)(263,756)(264,755)
(265,754)(266,753)(267,752)(268,751)(269,750)(270,749)(271,748)(272,747)
(273,746)(274,745)(275,744)(276,743)(277,742)(278,741)(279,740)(280,739)
(281,738)(282,737)(283,736)(284,735)(285,734)(286,733)(287,732)(288,731)
(289,730)(290,729)(291,728)(292,727)(293,726)(294,725)(295,724)(296,723)
(297,722)(298,721)(299,720)(300,719)(301,718)(302,717)(303,716)(304,715)
(305,714)(306,713)(307,712)(308,711)(309,710)(310,709)(311,708)(312,707)
(313,706)(314,705)(315,704)(316,703)(317,702)(318,701)(319,700)(320,699)
(321,698)(322,697)(323,696)(324,695)(325,694)(326,693)(327,692)(328,691)
(329,690)(330,689)(331,688)(332,687)(333,686)(334,685)(335,684)(336,683)
(337,682)(338,681)(339,680)(340,679)(341,678)(342,677)(343,676)(344,675)
(345,674)(346,673)(347,672)(348,671)(349,670)(350,669)(351,668)(352,667)
(353,666)(354,665)(355,664)(356,663)(357,662)(358,661)(359,660)(360,659)
(361,658)(362,657)(363,656)(364,655)(365,654)(366,653)(367,652)(368,651)
(369,650)(370,649)(371,648)(372,647)(373,646)(374,645)(375,644)(376,643)
(377,642)(378,641)(379,640)(380,639)(381,638);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(762)!(  2,127)(  3,126)(  4,125)(  5,124)(  6,123)(  7,122)(  8,121)
(  9,120)( 10,119)( 11,118)( 12,117)( 13,116)( 14,115)( 15,114)( 16,113)
( 17,112)( 18,111)( 19,110)( 20,109)( 21,108)( 22,107)( 23,106)( 24,105)
( 25,104)( 26,103)( 27,102)( 28,101)( 29,100)( 30, 99)( 31, 98)( 32, 97)
( 33, 96)( 34, 95)( 35, 94)( 36, 93)( 37, 92)( 38, 91)( 39, 90)( 40, 89)
( 41, 88)( 42, 87)( 43, 86)( 44, 85)( 45, 84)( 46, 83)( 47, 82)( 48, 81)
( 49, 80)( 50, 79)( 51, 78)( 52, 77)( 53, 76)( 54, 75)( 55, 74)( 56, 73)
( 57, 72)( 58, 71)( 59, 70)( 60, 69)( 61, 68)( 62, 67)( 63, 66)( 64, 65)
(128,255)(129,381)(130,380)(131,379)(132,378)(133,377)(134,376)(135,375)
(136,374)(137,373)(138,372)(139,371)(140,370)(141,369)(142,368)(143,367)
(144,366)(145,365)(146,364)(147,363)(148,362)(149,361)(150,360)(151,359)
(152,358)(153,357)(154,356)(155,355)(156,354)(157,353)(158,352)(159,351)
(160,350)(161,349)(162,348)(163,347)(164,346)(165,345)(166,344)(167,343)
(168,342)(169,341)(170,340)(171,339)(172,338)(173,337)(174,336)(175,335)
(176,334)(177,333)(178,332)(179,331)(180,330)(181,329)(182,328)(183,327)
(184,326)(185,325)(186,324)(187,323)(188,322)(189,321)(190,320)(191,319)
(192,318)(193,317)(194,316)(195,315)(196,314)(197,313)(198,312)(199,311)
(200,310)(201,309)(202,308)(203,307)(204,306)(205,305)(206,304)(207,303)
(208,302)(209,301)(210,300)(211,299)(212,298)(213,297)(214,296)(215,295)
(216,294)(217,293)(218,292)(219,291)(220,290)(221,289)(222,288)(223,287)
(224,286)(225,285)(226,284)(227,283)(228,282)(229,281)(230,280)(231,279)
(232,278)(233,277)(234,276)(235,275)(236,274)(237,273)(238,272)(239,271)
(240,270)(241,269)(242,268)(243,267)(244,266)(245,265)(246,264)(247,263)
(248,262)(249,261)(250,260)(251,259)(252,258)(253,257)(254,256)(383,508)
(384,507)(385,506)(386,505)(387,504)(388,503)(389,502)(390,501)(391,500)
(392,499)(393,498)(394,497)(395,496)(396,495)(397,494)(398,493)(399,492)
(400,491)(401,490)(402,489)(403,488)(404,487)(405,486)(406,485)(407,484)
(408,483)(409,482)(410,481)(411,480)(412,479)(413,478)(414,477)(415,476)
(416,475)(417,474)(418,473)(419,472)(420,471)(421,470)(422,469)(423,468)
(424,467)(425,466)(426,465)(427,464)(428,463)(429,462)(430,461)(431,460)
(432,459)(433,458)(434,457)(435,456)(436,455)(437,454)(438,453)(439,452)
(440,451)(441,450)(442,449)(443,448)(444,447)(445,446)(509,636)(510,762)
(511,761)(512,760)(513,759)(514,758)(515,757)(516,756)(517,755)(518,754)
(519,753)(520,752)(521,751)(522,750)(523,749)(524,748)(525,747)(526,746)
(527,745)(528,744)(529,743)(530,742)(531,741)(532,740)(533,739)(534,738)
(535,737)(536,736)(537,735)(538,734)(539,733)(540,732)(541,731)(542,730)
(543,729)(544,728)(545,727)(546,726)(547,725)(548,724)(549,723)(550,722)
(551,721)(552,720)(553,719)(554,718)(555,717)(556,716)(557,715)(558,714)
(559,713)(560,712)(561,711)(562,710)(563,709)(564,708)(565,707)(566,706)
(567,705)(568,704)(569,703)(570,702)(571,701)(572,700)(573,699)(574,698)
(575,697)(576,696)(577,695)(578,694)(579,693)(580,692)(581,691)(582,690)
(583,689)(584,688)(585,687)(586,686)(587,685)(588,684)(589,683)(590,682)
(591,681)(592,680)(593,679)(594,678)(595,677)(596,676)(597,675)(598,674)
(599,673)(600,672)(601,671)(602,670)(603,669)(604,668)(605,667)(606,666)
(607,665)(608,664)(609,663)(610,662)(611,661)(612,660)(613,659)(614,658)
(615,657)(616,656)(617,655)(618,654)(619,653)(620,652)(621,651)(622,650)
(623,649)(624,648)(625,647)(626,646)(627,645)(628,644)(629,643)(630,642)
(631,641)(632,640)(633,639)(634,638)(635,637);
s1 := Sym(762)!(  1,510)(  2,509)(  3,635)(  4,634)(  5,633)(  6,632)(  7,631)
(  8,630)(  9,629)( 10,628)( 11,627)( 12,626)( 13,625)( 14,624)( 15,623)
( 16,622)( 17,621)( 18,620)( 19,619)( 20,618)( 21,617)( 22,616)( 23,615)
( 24,614)( 25,613)( 26,612)( 27,611)( 28,610)( 29,609)( 30,608)( 31,607)
( 32,606)( 33,605)( 34,604)( 35,603)( 36,602)( 37,601)( 38,600)( 39,599)
( 40,598)( 41,597)( 42,596)( 43,595)( 44,594)( 45,593)( 46,592)( 47,591)
( 48,590)( 49,589)( 50,588)( 51,587)( 52,586)( 53,585)( 54,584)( 55,583)
( 56,582)( 57,581)( 58,580)( 59,579)( 60,578)( 61,577)( 62,576)( 63,575)
( 64,574)( 65,573)( 66,572)( 67,571)( 68,570)( 69,569)( 70,568)( 71,567)
( 72,566)( 73,565)( 74,564)( 75,563)( 76,562)( 77,561)( 78,560)( 79,559)
( 80,558)( 81,557)( 82,556)( 83,555)( 84,554)( 85,553)( 86,552)( 87,551)
( 88,550)( 89,549)( 90,548)( 91,547)( 92,546)( 93,545)( 94,544)( 95,543)
( 96,542)( 97,541)( 98,540)( 99,539)(100,538)(101,537)(102,536)(103,535)
(104,534)(105,533)(106,532)(107,531)(108,530)(109,529)(110,528)(111,527)
(112,526)(113,525)(114,524)(115,523)(116,522)(117,521)(118,520)(119,519)
(120,518)(121,517)(122,516)(123,515)(124,514)(125,513)(126,512)(127,511)
(128,383)(129,382)(130,508)(131,507)(132,506)(133,505)(134,504)(135,503)
(136,502)(137,501)(138,500)(139,499)(140,498)(141,497)(142,496)(143,495)
(144,494)(145,493)(146,492)(147,491)(148,490)(149,489)(150,488)(151,487)
(152,486)(153,485)(154,484)(155,483)(156,482)(157,481)(158,480)(159,479)
(160,478)(161,477)(162,476)(163,475)(164,474)(165,473)(166,472)(167,471)
(168,470)(169,469)(170,468)(171,467)(172,466)(173,465)(174,464)(175,463)
(176,462)(177,461)(178,460)(179,459)(180,458)(181,457)(182,456)(183,455)
(184,454)(185,453)(186,452)(187,451)(188,450)(189,449)(190,448)(191,447)
(192,446)(193,445)(194,444)(195,443)(196,442)(197,441)(198,440)(199,439)
(200,438)(201,437)(202,436)(203,435)(204,434)(205,433)(206,432)(207,431)
(208,430)(209,429)(210,428)(211,427)(212,426)(213,425)(214,424)(215,423)
(216,422)(217,421)(218,420)(219,419)(220,418)(221,417)(222,416)(223,415)
(224,414)(225,413)(226,412)(227,411)(228,410)(229,409)(230,408)(231,407)
(232,406)(233,405)(234,404)(235,403)(236,402)(237,401)(238,400)(239,399)
(240,398)(241,397)(242,396)(243,395)(244,394)(245,393)(246,392)(247,391)
(248,390)(249,389)(250,388)(251,387)(252,386)(253,385)(254,384)(255,637)
(256,636)(257,762)(258,761)(259,760)(260,759)(261,758)(262,757)(263,756)
(264,755)(265,754)(266,753)(267,752)(268,751)(269,750)(270,749)(271,748)
(272,747)(273,746)(274,745)(275,744)(276,743)(277,742)(278,741)(279,740)
(280,739)(281,738)(282,737)(283,736)(284,735)(285,734)(286,733)(287,732)
(288,731)(289,730)(290,729)(291,728)(292,727)(293,726)(294,725)(295,724)
(296,723)(297,722)(298,721)(299,720)(300,719)(301,718)(302,717)(303,716)
(304,715)(305,714)(306,713)(307,712)(308,711)(309,710)(310,709)(311,708)
(312,707)(313,706)(314,705)(315,704)(316,703)(317,702)(318,701)(319,700)
(320,699)(321,698)(322,697)(323,696)(324,695)(325,694)(326,693)(327,692)
(328,691)(329,690)(330,689)(331,688)(332,687)(333,686)(334,685)(335,684)
(336,683)(337,682)(338,681)(339,680)(340,679)(341,678)(342,677)(343,676)
(344,675)(345,674)(346,673)(347,672)(348,671)(349,670)(350,669)(351,668)
(352,667)(353,666)(354,665)(355,664)(356,663)(357,662)(358,661)(359,660)
(360,659)(361,658)(362,657)(363,656)(364,655)(365,654)(366,653)(367,652)
(368,651)(369,650)(370,649)(371,648)(372,647)(373,646)(374,645)(375,644)
(376,643)(377,642)(378,641)(379,640)(380,639)(381,638);
poly := sub<Sym(762)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope