Polytope of Type {786}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {786}*1572
Also Known As : 786-gon, {786}. if this polytope has another name.
Group : SmallGroup(1572,9)
Rank : 2
Schlafli Type : {786}
Number of vertices, edges, etc : 786, 786
Order of s₀s₁ : 786
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 : {393}*786
   3-fold quotients : {262}*524
   6-fold quotients : {131}*262
   131-fold quotients : {6}*12
   262-fold quotients : {3}*6
   393-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,131)(  3,130)(  4,129)(  5,128)(  6,127)(  7,126)(  8,125)(  9,124)
( 10,123)( 11,122)( 12,121)( 13,120)( 14,119)( 15,118)( 16,117)( 17,116)
( 18,115)( 19,114)( 20,113)( 21,112)( 22,111)( 23,110)( 24,109)( 25,108)
( 26,107)( 27,106)( 28,105)( 29,104)( 30,103)( 31,102)( 32,101)( 33,100)
( 34, 99)( 35, 98)( 36, 97)( 37, 96)( 38, 95)( 39, 94)( 40, 93)( 41, 92)
( 42, 91)( 43, 90)( 44, 89)( 45, 88)( 46, 87)( 47, 86)( 48, 85)( 49, 84)
( 50, 83)( 51, 82)( 52, 81)( 53, 80)( 54, 79)( 55, 78)( 56, 77)( 57, 76)
( 58, 75)( 59, 74)( 60, 73)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)
( 66, 67)(132,263)(133,393)(134,392)(135,391)(136,390)(137,389)(138,388)
(139,387)(140,386)(141,385)(142,384)(143,383)(144,382)(145,381)(146,380)
(147,379)(148,378)(149,377)(150,376)(151,375)(152,374)(153,373)(154,372)
(155,371)(156,370)(157,369)(158,368)(159,367)(160,366)(161,365)(162,364)
(163,363)(164,362)(165,361)(166,360)(167,359)(168,358)(169,357)(170,356)
(171,355)(172,354)(173,353)(174,352)(175,351)(176,350)(177,349)(178,348)
(179,347)(180,346)(181,345)(182,344)(183,343)(184,342)(185,341)(186,340)
(187,339)(188,338)(189,337)(190,336)(191,335)(192,334)(193,333)(194,332)
(195,331)(196,330)(197,329)(198,328)(199,327)(200,326)(201,325)(202,324)
(203,323)(204,322)(205,321)(206,320)(207,319)(208,318)(209,317)(210,316)
(211,315)(212,314)(213,313)(214,312)(215,311)(216,310)(217,309)(218,308)
(219,307)(220,306)(221,305)(222,304)(223,303)(224,302)(225,301)(226,300)
(227,299)(228,298)(229,297)(230,296)(231,295)(232,294)(233,293)(234,292)
(235,291)(236,290)(237,289)(238,288)(239,287)(240,286)(241,285)(242,284)
(243,283)(244,282)(245,281)(246,280)(247,279)(248,278)(249,277)(250,276)
(251,275)(252,274)(253,273)(254,272)(255,271)(256,270)(257,269)(258,268)
(259,267)(260,266)(261,265)(262,264)(395,524)(396,523)(397,522)(398,521)
(399,520)(400,519)(401,518)(402,517)(403,516)(404,515)(405,514)(406,513)
(407,512)(408,511)(409,510)(410,509)(411,508)(412,507)(413,506)(414,505)
(415,504)(416,503)(417,502)(418,501)(419,500)(420,499)(421,498)(422,497)
(423,496)(424,495)(425,494)(426,493)(427,492)(428,491)(429,490)(430,489)
(431,488)(432,487)(433,486)(434,485)(435,484)(436,483)(437,482)(438,481)
(439,480)(440,479)(441,478)(442,477)(443,476)(444,475)(445,474)(446,473)
(447,472)(448,471)(449,470)(450,469)(451,468)(452,467)(453,466)(454,465)
(455,464)(456,463)(457,462)(458,461)(459,460)(525,656)(526,786)(527,785)
(528,784)(529,783)(530,782)(531,781)(532,780)(533,779)(534,778)(535,777)
(536,776)(537,775)(538,774)(539,773)(540,772)(541,771)(542,770)(543,769)
(544,768)(545,767)(546,766)(547,765)(548,764)(549,763)(550,762)(551,761)
(552,760)(553,759)(554,758)(555,757)(556,756)(557,755)(558,754)(559,753)
(560,752)(561,751)(562,750)(563,749)(564,748)(565,747)(566,746)(567,745)
(568,744)(569,743)(570,742)(571,741)(572,740)(573,739)(574,738)(575,737)
(576,736)(577,735)(578,734)(579,733)(580,732)(581,731)(582,730)(583,729)
(584,728)(585,727)(586,726)(587,725)(588,724)(589,723)(590,722)(591,721)
(592,720)(593,719)(594,718)(595,717)(596,716)(597,715)(598,714)(599,713)
(600,712)(601,711)(602,710)(603,709)(604,708)(605,707)(606,706)(607,705)
(608,704)(609,703)(610,702)(611,701)(612,700)(613,699)(614,698)(615,697)
(616,696)(617,695)(618,694)(619,693)(620,692)(621,691)(622,690)(623,689)
(624,688)(625,687)(626,686)(627,685)(628,684)(629,683)(630,682)(631,681)
(632,680)(633,679)(634,678)(635,677)(636,676)(637,675)(638,674)(639,673)
(640,672)(641,671)(642,670)(643,669)(644,668)(645,667)(646,666)(647,665)
(648,664)(649,663)(650,662)(651,661)(652,660)(653,659)(654,658)(655,657);;
s1 := (  1,526)(  2,525)(  3,655)(  4,654)(  5,653)(  6,652)(  7,651)(  8,650)
(  9,649)( 10,648)( 11,647)( 12,646)( 13,645)( 14,644)( 15,643)( 16,642)
( 17,641)( 18,640)( 19,639)( 20,638)( 21,637)( 22,636)( 23,635)( 24,634)
( 25,633)( 26,632)( 27,631)( 28,630)( 29,629)( 30,628)( 31,627)( 32,626)
( 33,625)( 34,624)( 35,623)( 36,622)( 37,621)( 38,620)( 39,619)( 40,618)
( 41,617)( 42,616)( 43,615)( 44,614)( 45,613)( 46,612)( 47,611)( 48,610)
( 49,609)( 50,608)( 51,607)( 52,606)( 53,605)( 54,604)( 55,603)( 56,602)
( 57,601)( 58,600)( 59,599)( 60,598)( 61,597)( 62,596)( 63,595)( 64,594)
( 65,593)( 66,592)( 67,591)( 68,590)( 69,589)( 70,588)( 71,587)( 72,586)
( 73,585)( 74,584)( 75,583)( 76,582)( 77,581)( 78,580)( 79,579)( 80,578)
( 81,577)( 82,576)( 83,575)( 84,574)( 85,573)( 86,572)( 87,571)( 88,570)
( 89,569)( 90,568)( 91,567)( 92,566)( 93,565)( 94,564)( 95,563)( 96,562)
( 97,561)( 98,560)( 99,559)(100,558)(101,557)(102,556)(103,555)(104,554)
(105,553)(106,552)(107,551)(108,550)(109,549)(110,548)(111,547)(112,546)
(113,545)(114,544)(115,543)(116,542)(117,541)(118,540)(119,539)(120,538)
(121,537)(122,536)(123,535)(124,534)(125,533)(126,532)(127,531)(128,530)
(129,529)(130,528)(131,527)(132,395)(133,394)(134,524)(135,523)(136,522)
(137,521)(138,520)(139,519)(140,518)(141,517)(142,516)(143,515)(144,514)
(145,513)(146,512)(147,511)(148,510)(149,509)(150,508)(151,507)(152,506)
(153,505)(154,504)(155,503)(156,502)(157,501)(158,500)(159,499)(160,498)
(161,497)(162,496)(163,495)(164,494)(165,493)(166,492)(167,491)(168,490)
(169,489)(170,488)(171,487)(172,486)(173,485)(174,484)(175,483)(176,482)
(177,481)(178,480)(179,479)(180,478)(181,477)(182,476)(183,475)(184,474)
(185,473)(186,472)(187,471)(188,470)(189,469)(190,468)(191,467)(192,466)
(193,465)(194,464)(195,463)(196,462)(197,461)(198,460)(199,459)(200,458)
(201,457)(202,456)(203,455)(204,454)(205,453)(206,452)(207,451)(208,450)
(209,449)(210,448)(211,447)(212,446)(213,445)(214,444)(215,443)(216,442)
(217,441)(218,440)(219,439)(220,438)(221,437)(222,436)(223,435)(224,434)
(225,433)(226,432)(227,431)(228,430)(229,429)(230,428)(231,427)(232,426)
(233,425)(234,424)(235,423)(236,422)(237,421)(238,420)(239,419)(240,418)
(241,417)(242,416)(243,415)(244,414)(245,413)(246,412)(247,411)(248,410)
(249,409)(250,408)(251,407)(252,406)(253,405)(254,404)(255,403)(256,402)
(257,401)(258,400)(259,399)(260,398)(261,397)(262,396)(263,657)(264,656)
(265,786)(266,785)(267,784)(268,783)(269,782)(270,781)(271,780)(272,779)
(273,778)(274,777)(275,776)(276,775)(277,774)(278,773)(279,772)(280,771)
(281,770)(282,769)(283,768)(284,767)(285,766)(286,765)(287,764)(288,763)
(289,762)(290,761)(291,760)(292,759)(293,758)(294,757)(295,756)(296,755)
(297,754)(298,753)(299,752)(300,751)(301,750)(302,749)(303,748)(304,747)
(305,746)(306,745)(307,744)(308,743)(309,742)(310,741)(311,740)(312,739)
(313,738)(314,737)(315,736)(316,735)(317,734)(318,733)(319,732)(320,731)
(321,730)(322,729)(323,728)(324,727)(325,726)(326,725)(327,724)(328,723)
(329,722)(330,721)(331,720)(332,719)(333,718)(334,717)(335,716)(336,715)
(337,714)(338,713)(339,712)(340,711)(341,710)(342,709)(343,708)(344,707)
(345,706)(346,705)(347,704)(348,703)(349,702)(350,701)(351,700)(352,699)
(353,698)(354,697)(355,696)(356,695)(357,694)(358,693)(359,692)(360,691)
(361,690)(362,689)(363,688)(364,687)(365,686)(366,685)(367,684)(368,683)
(369,682)(370,681)(371,680)(372,679)(373,678)(374,677)(375,676)(376,675)
(377,674)(378,673)(379,672)(380,671)(381,670)(382,669)(383,668)(384,667)
(385,666)(386,665)(387,664)(388,663)(389,662)(390,661)(391,660)(392,659)
(393,658);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(786)!(  2,131)(  3,130)(  4,129)(  5,128)(  6,127)(  7,126)(  8,125)
(  9,124)( 10,123)( 11,122)( 12,121)( 13,120)( 14,119)( 15,118)( 16,117)
( 17,116)( 18,115)( 19,114)( 20,113)( 21,112)( 22,111)( 23,110)( 24,109)
( 25,108)( 26,107)( 27,106)( 28,105)( 29,104)( 30,103)( 31,102)( 32,101)
( 33,100)( 34, 99)( 35, 98)( 36, 97)( 37, 96)( 38, 95)( 39, 94)( 40, 93)
( 41, 92)( 42, 91)( 43, 90)( 44, 89)( 45, 88)( 46, 87)( 47, 86)( 48, 85)
( 49, 84)( 50, 83)( 51, 82)( 52, 81)( 53, 80)( 54, 79)( 55, 78)( 56, 77)
( 57, 76)( 58, 75)( 59, 74)( 60, 73)( 61, 72)( 62, 71)( 63, 70)( 64, 69)
( 65, 68)( 66, 67)(132,263)(133,393)(134,392)(135,391)(136,390)(137,389)
(138,388)(139,387)(140,386)(141,385)(142,384)(143,383)(144,382)(145,381)
(146,380)(147,379)(148,378)(149,377)(150,376)(151,375)(152,374)(153,373)
(154,372)(155,371)(156,370)(157,369)(158,368)(159,367)(160,366)(161,365)
(162,364)(163,363)(164,362)(165,361)(166,360)(167,359)(168,358)(169,357)
(170,356)(171,355)(172,354)(173,353)(174,352)(175,351)(176,350)(177,349)
(178,348)(179,347)(180,346)(181,345)(182,344)(183,343)(184,342)(185,341)
(186,340)(187,339)(188,338)(189,337)(190,336)(191,335)(192,334)(193,333)
(194,332)(195,331)(196,330)(197,329)(198,328)(199,327)(200,326)(201,325)
(202,324)(203,323)(204,322)(205,321)(206,320)(207,319)(208,318)(209,317)
(210,316)(211,315)(212,314)(213,313)(214,312)(215,311)(216,310)(217,309)
(218,308)(219,307)(220,306)(221,305)(222,304)(223,303)(224,302)(225,301)
(226,300)(227,299)(228,298)(229,297)(230,296)(231,295)(232,294)(233,293)
(234,292)(235,291)(236,290)(237,289)(238,288)(239,287)(240,286)(241,285)
(242,284)(243,283)(244,282)(245,281)(246,280)(247,279)(248,278)(249,277)
(250,276)(251,275)(252,274)(253,273)(254,272)(255,271)(256,270)(257,269)
(258,268)(259,267)(260,266)(261,265)(262,264)(395,524)(396,523)(397,522)
(398,521)(399,520)(400,519)(401,518)(402,517)(403,516)(404,515)(405,514)
(406,513)(407,512)(408,511)(409,510)(410,509)(411,508)(412,507)(413,506)
(414,505)(415,504)(416,503)(417,502)(418,501)(419,500)(420,499)(421,498)
(422,497)(423,496)(424,495)(425,494)(426,493)(427,492)(428,491)(429,490)
(430,489)(431,488)(432,487)(433,486)(434,485)(435,484)(436,483)(437,482)
(438,481)(439,480)(440,479)(441,478)(442,477)(443,476)(444,475)(445,474)
(446,473)(447,472)(448,471)(449,470)(450,469)(451,468)(452,467)(453,466)
(454,465)(455,464)(456,463)(457,462)(458,461)(459,460)(525,656)(526,786)
(527,785)(528,784)(529,783)(530,782)(531,781)(532,780)(533,779)(534,778)
(535,777)(536,776)(537,775)(538,774)(539,773)(540,772)(541,771)(542,770)
(543,769)(544,768)(545,767)(546,766)(547,765)(548,764)(549,763)(550,762)
(551,761)(552,760)(553,759)(554,758)(555,757)(556,756)(557,755)(558,754)
(559,753)(560,752)(561,751)(562,750)(563,749)(564,748)(565,747)(566,746)
(567,745)(568,744)(569,743)(570,742)(571,741)(572,740)(573,739)(574,738)
(575,737)(576,736)(577,735)(578,734)(579,733)(580,732)(581,731)(582,730)
(583,729)(584,728)(585,727)(586,726)(587,725)(588,724)(589,723)(590,722)
(591,721)(592,720)(593,719)(594,718)(595,717)(596,716)(597,715)(598,714)
(599,713)(600,712)(601,711)(602,710)(603,709)(604,708)(605,707)(606,706)
(607,705)(608,704)(609,703)(610,702)(611,701)(612,700)(613,699)(614,698)
(615,697)(616,696)(617,695)(618,694)(619,693)(620,692)(621,691)(622,690)
(623,689)(624,688)(625,687)(626,686)(627,685)(628,684)(629,683)(630,682)
(631,681)(632,680)(633,679)(634,678)(635,677)(636,676)(637,675)(638,674)
(639,673)(640,672)(641,671)(642,670)(643,669)(644,668)(645,667)(646,666)
(647,665)(648,664)(649,663)(650,662)(651,661)(652,660)(653,659)(654,658)
(655,657);
s1 := Sym(786)!(  1,526)(  2,525)(  3,655)(  4,654)(  5,653)(  6,652)(  7,651)
(  8,650)(  9,649)( 10,648)( 11,647)( 12,646)( 13,645)( 14,644)( 15,643)
( 16,642)( 17,641)( 18,640)( 19,639)( 20,638)( 21,637)( 22,636)( 23,635)
( 24,634)( 25,633)( 26,632)( 27,631)( 28,630)( 29,629)( 30,628)( 31,627)
( 32,626)( 33,625)( 34,624)( 35,623)( 36,622)( 37,621)( 38,620)( 39,619)
( 40,618)( 41,617)( 42,616)( 43,615)( 44,614)( 45,613)( 46,612)( 47,611)
( 48,610)( 49,609)( 50,608)( 51,607)( 52,606)( 53,605)( 54,604)( 55,603)
( 56,602)( 57,601)( 58,600)( 59,599)( 60,598)( 61,597)( 62,596)( 63,595)
( 64,594)( 65,593)( 66,592)( 67,591)( 68,590)( 69,589)( 70,588)( 71,587)
( 72,586)( 73,585)( 74,584)( 75,583)( 76,582)( 77,581)( 78,580)( 79,579)
( 80,578)( 81,577)( 82,576)( 83,575)( 84,574)( 85,573)( 86,572)( 87,571)
( 88,570)( 89,569)( 90,568)( 91,567)( 92,566)( 93,565)( 94,564)( 95,563)
( 96,562)( 97,561)( 98,560)( 99,559)(100,558)(101,557)(102,556)(103,555)
(104,554)(105,553)(106,552)(107,551)(108,550)(109,549)(110,548)(111,547)
(112,546)(113,545)(114,544)(115,543)(116,542)(117,541)(118,540)(119,539)
(120,538)(121,537)(122,536)(123,535)(124,534)(125,533)(126,532)(127,531)
(128,530)(129,529)(130,528)(131,527)(132,395)(133,394)(134,524)(135,523)
(136,522)(137,521)(138,520)(139,519)(140,518)(141,517)(142,516)(143,515)
(144,514)(145,513)(146,512)(147,511)(148,510)(149,509)(150,508)(151,507)
(152,506)(153,505)(154,504)(155,503)(156,502)(157,501)(158,500)(159,499)
(160,498)(161,497)(162,496)(163,495)(164,494)(165,493)(166,492)(167,491)
(168,490)(169,489)(170,488)(171,487)(172,486)(173,485)(174,484)(175,483)
(176,482)(177,481)(178,480)(179,479)(180,478)(181,477)(182,476)(183,475)
(184,474)(185,473)(186,472)(187,471)(188,470)(189,469)(190,468)(191,467)
(192,466)(193,465)(194,464)(195,463)(196,462)(197,461)(198,460)(199,459)
(200,458)(201,457)(202,456)(203,455)(204,454)(205,453)(206,452)(207,451)
(208,450)(209,449)(210,448)(211,447)(212,446)(213,445)(214,444)(215,443)
(216,442)(217,441)(218,440)(219,439)(220,438)(221,437)(222,436)(223,435)
(224,434)(225,433)(226,432)(227,431)(228,430)(229,429)(230,428)(231,427)
(232,426)(233,425)(234,424)(235,423)(236,422)(237,421)(238,420)(239,419)
(240,418)(241,417)(242,416)(243,415)(244,414)(245,413)(246,412)(247,411)
(248,410)(249,409)(250,408)(251,407)(252,406)(253,405)(254,404)(255,403)
(256,402)(257,401)(258,400)(259,399)(260,398)(261,397)(262,396)(263,657)
(264,656)(265,786)(266,785)(267,784)(268,783)(269,782)(270,781)(271,780)
(272,779)(273,778)(274,777)(275,776)(276,775)(277,774)(278,773)(279,772)
(280,771)(281,770)(282,769)(283,768)(284,767)(285,766)(286,765)(287,764)
(288,763)(289,762)(290,761)(291,760)(292,759)(293,758)(294,757)(295,756)
(296,755)(297,754)(298,753)(299,752)(300,751)(301,750)(302,749)(303,748)
(304,747)(305,746)(306,745)(307,744)(308,743)(309,742)(310,741)(311,740)
(312,739)(313,738)(314,737)(315,736)(316,735)(317,734)(318,733)(319,732)
(320,731)(321,730)(322,729)(323,728)(324,727)(325,726)(326,725)(327,724)
(328,723)(329,722)(330,721)(331,720)(332,719)(333,718)(334,717)(335,716)
(336,715)(337,714)(338,713)(339,712)(340,711)(341,710)(342,709)(343,708)
(344,707)(345,706)(346,705)(347,704)(348,703)(349,702)(350,701)(351,700)
(352,699)(353,698)(354,697)(355,696)(356,695)(357,694)(358,693)(359,692)
(360,691)(361,690)(362,689)(363,688)(364,687)(365,686)(366,685)(367,684)
(368,683)(369,682)(370,681)(371,680)(372,679)(373,678)(374,677)(375,676)
(376,675)(377,674)(378,673)(379,672)(380,671)(381,670)(382,669)(383,668)
(384,667)(385,666)(386,665)(387,664)(388,663)(389,662)(390,661)(391,660)
(392,659)(393,658);
poly := sub<Sym(786)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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