Polytope of Type {792}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {792}*1584
Also Known As : 792-gon, {792}. if this polytope has another name.
Group : SmallGroup(1584,67)
Rank : 2
Schlafli Type : {792}
Number of vertices, edges, etc : 792, 792
Order of s₀s₁ : 792
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 : {396}*792
   3-fold quotients : {264}*528
   4-fold quotients : {198}*396
   6-fold quotients : {132}*264
   8-fold quotients : {99}*198
   9-fold quotients : {88}*176
   11-fold quotients : {72}*144
   12-fold quotients : {66}*132
   18-fold quotients : {44}*88
   22-fold quotients : {36}*72
   24-fold quotients : {33}*66
   33-fold quotients : {24}*48
   36-fold quotients : {22}*44
   44-fold quotients : {18}*36
   66-fold quotients : {12}*24
   72-fold quotients : {11}*22
   88-fold quotients : {9}*18
   99-fold quotients : {8}*16
   132-fold quotients : {6}*12
   198-fold quotients : {4}*8
   264-fold quotients : {3}*6
   396-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  3)(  4, 31)(  5, 33)(  6, 32)(  7, 28)(  8, 30)(  9, 29)( 10, 25)
( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 16, 19)( 17, 21)( 18, 20)
( 34, 69)( 35, 68)( 36, 67)( 37, 99)( 38, 98)( 39, 97)( 40, 96)( 41, 95)
( 42, 94)( 43, 93)( 44, 92)( 45, 91)( 46, 90)( 47, 89)( 48, 88)( 49, 87)
( 50, 86)( 51, 85)( 52, 84)( 53, 83)( 54, 82)( 55, 81)( 56, 80)( 57, 79)
( 58, 78)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 73)( 64, 72)( 65, 71)
( 66, 70)(101,102)(103,130)(104,132)(105,131)(106,127)(107,129)(108,128)
(109,124)(110,126)(111,125)(112,121)(113,123)(114,122)(115,118)(116,120)
(117,119)(133,168)(134,167)(135,166)(136,198)(137,197)(138,196)(139,195)
(140,194)(141,193)(142,192)(143,191)(144,190)(145,189)(146,188)(147,187)
(148,186)(149,185)(150,184)(151,183)(152,182)(153,181)(154,180)(155,179)
(156,178)(157,177)(158,176)(159,175)(160,174)(161,173)(162,172)(163,171)
(164,170)(165,169)(199,298)(200,300)(201,299)(202,328)(203,330)(204,329)
(205,325)(206,327)(207,326)(208,322)(209,324)(210,323)(211,319)(212,321)
(213,320)(214,316)(215,318)(216,317)(217,313)(218,315)(219,314)(220,310)
(221,312)(222,311)(223,307)(224,309)(225,308)(226,304)(227,306)(228,305)
(229,301)(230,303)(231,302)(232,366)(233,365)(234,364)(235,396)(236,395)
(237,394)(238,393)(239,392)(240,391)(241,390)(242,389)(243,388)(244,387)
(245,386)(246,385)(247,384)(248,383)(249,382)(250,381)(251,380)(252,379)
(253,378)(254,377)(255,376)(256,375)(257,374)(258,373)(259,372)(260,371)
(261,370)(262,369)(263,368)(264,367)(265,333)(266,332)(267,331)(268,363)
(269,362)(270,361)(271,360)(272,359)(273,358)(274,357)(275,356)(276,355)
(277,354)(278,353)(279,352)(280,351)(281,350)(282,349)(283,348)(284,347)
(285,346)(286,345)(287,344)(288,343)(289,342)(290,341)(291,340)(292,339)
(293,338)(294,337)(295,336)(296,335)(297,334)(397,595)(398,597)(399,596)
(400,625)(401,627)(402,626)(403,622)(404,624)(405,623)(406,619)(407,621)
(408,620)(409,616)(410,618)(411,617)(412,613)(413,615)(414,614)(415,610)
(416,612)(417,611)(418,607)(419,609)(420,608)(421,604)(422,606)(423,605)
(424,601)(425,603)(426,602)(427,598)(428,600)(429,599)(430,663)(431,662)
(432,661)(433,693)(434,692)(435,691)(436,690)(437,689)(438,688)(439,687)
(440,686)(441,685)(442,684)(443,683)(444,682)(445,681)(446,680)(447,679)
(448,678)(449,677)(450,676)(451,675)(452,674)(453,673)(454,672)(455,671)
(456,670)(457,669)(458,668)(459,667)(460,666)(461,665)(462,664)(463,630)
(464,629)(465,628)(466,660)(467,659)(468,658)(469,657)(470,656)(471,655)
(472,654)(473,653)(474,652)(475,651)(476,650)(477,649)(478,648)(479,647)
(480,646)(481,645)(482,644)(483,643)(484,642)(485,641)(486,640)(487,639)
(488,638)(489,637)(490,636)(491,635)(492,634)(493,633)(494,632)(495,631)
(496,694)(497,696)(498,695)(499,724)(500,726)(501,725)(502,721)(503,723)
(504,722)(505,718)(506,720)(507,719)(508,715)(509,717)(510,716)(511,712)
(512,714)(513,713)(514,709)(515,711)(516,710)(517,706)(518,708)(519,707)
(520,703)(521,705)(522,704)(523,700)(524,702)(525,701)(526,697)(527,699)
(528,698)(529,762)(530,761)(531,760)(532,792)(533,791)(534,790)(535,789)
(536,788)(537,787)(538,786)(539,785)(540,784)(541,783)(542,782)(543,781)
(544,780)(545,779)(546,778)(547,777)(548,776)(549,775)(550,774)(551,773)
(552,772)(553,771)(554,770)(555,769)(556,768)(557,767)(558,766)(559,765)
(560,764)(561,763)(562,729)(563,728)(564,727)(565,759)(566,758)(567,757)
(568,756)(569,755)(570,754)(571,753)(572,752)(573,751)(574,750)(575,749)
(576,748)(577,747)(578,746)(579,745)(580,744)(581,743)(582,742)(583,741)
(584,740)(585,739)(586,738)(587,737)(588,736)(589,735)(590,734)(591,733)
(592,732)(593,731)(594,730);;
s1 := (  1,433)(  2,435)(  3,434)(  4,430)(  5,432)(  6,431)(  7,460)(  8,462)
(  9,461)( 10,457)( 11,459)( 12,458)( 13,454)( 14,456)( 15,455)( 16,451)
( 17,453)( 18,452)( 19,448)( 20,450)( 21,449)( 22,445)( 23,447)( 24,446)
( 25,442)( 26,444)( 27,443)( 28,439)( 29,441)( 30,440)( 31,436)( 32,438)
( 33,437)( 34,400)( 35,402)( 36,401)( 37,397)( 38,399)( 39,398)( 40,427)
( 41,429)( 42,428)( 43,424)( 44,426)( 45,425)( 46,421)( 47,423)( 48,422)
( 49,418)( 50,420)( 51,419)( 52,415)( 53,417)( 54,416)( 55,412)( 56,414)
( 57,413)( 58,409)( 59,411)( 60,410)( 61,406)( 62,408)( 63,407)( 64,403)
( 65,405)( 66,404)( 67,468)( 68,467)( 69,466)( 70,465)( 71,464)( 72,463)
( 73,495)( 74,494)( 75,493)( 76,492)( 77,491)( 78,490)( 79,489)( 80,488)
( 81,487)( 82,486)( 83,485)( 84,484)( 85,483)( 86,482)( 87,481)( 88,480)
( 89,479)( 90,478)( 91,477)( 92,476)( 93,475)( 94,474)( 95,473)( 96,472)
( 97,471)( 98,470)( 99,469)(100,532)(101,534)(102,533)(103,529)(104,531)
(105,530)(106,559)(107,561)(108,560)(109,556)(110,558)(111,557)(112,553)
(113,555)(114,554)(115,550)(116,552)(117,551)(118,547)(119,549)(120,548)
(121,544)(122,546)(123,545)(124,541)(125,543)(126,542)(127,538)(128,540)
(129,539)(130,535)(131,537)(132,536)(133,499)(134,501)(135,500)(136,496)
(137,498)(138,497)(139,526)(140,528)(141,527)(142,523)(143,525)(144,524)
(145,520)(146,522)(147,521)(148,517)(149,519)(150,518)(151,514)(152,516)
(153,515)(154,511)(155,513)(156,512)(157,508)(158,510)(159,509)(160,505)
(161,507)(162,506)(163,502)(164,504)(165,503)(166,567)(167,566)(168,565)
(169,564)(170,563)(171,562)(172,594)(173,593)(174,592)(175,591)(176,590)
(177,589)(178,588)(179,587)(180,586)(181,585)(182,584)(183,583)(184,582)
(185,581)(186,580)(187,579)(188,578)(189,577)(190,576)(191,575)(192,574)
(193,573)(194,572)(195,571)(196,570)(197,569)(198,568)(199,730)(200,732)
(201,731)(202,727)(203,729)(204,728)(205,757)(206,759)(207,758)(208,754)
(209,756)(210,755)(211,751)(212,753)(213,752)(214,748)(215,750)(216,749)
(217,745)(218,747)(219,746)(220,742)(221,744)(222,743)(223,739)(224,741)
(225,740)(226,736)(227,738)(228,737)(229,733)(230,735)(231,734)(232,697)
(233,699)(234,698)(235,694)(236,696)(237,695)(238,724)(239,726)(240,725)
(241,721)(242,723)(243,722)(244,718)(245,720)(246,719)(247,715)(248,717)
(249,716)(250,712)(251,714)(252,713)(253,709)(254,711)(255,710)(256,706)
(257,708)(258,707)(259,703)(260,705)(261,704)(262,700)(263,702)(264,701)
(265,765)(266,764)(267,763)(268,762)(269,761)(270,760)(271,792)(272,791)
(273,790)(274,789)(275,788)(276,787)(277,786)(278,785)(279,784)(280,783)
(281,782)(282,781)(283,780)(284,779)(285,778)(286,777)(287,776)(288,775)
(289,774)(290,773)(291,772)(292,771)(293,770)(294,769)(295,768)(296,767)
(297,766)(298,631)(299,633)(300,632)(301,628)(302,630)(303,629)(304,658)
(305,660)(306,659)(307,655)(308,657)(309,656)(310,652)(311,654)(312,653)
(313,649)(314,651)(315,650)(316,646)(317,648)(318,647)(319,643)(320,645)
(321,644)(322,640)(323,642)(324,641)(325,637)(326,639)(327,638)(328,634)
(329,636)(330,635)(331,598)(332,600)(333,599)(334,595)(335,597)(336,596)
(337,625)(338,627)(339,626)(340,622)(341,624)(342,623)(343,619)(344,621)
(345,620)(346,616)(347,618)(348,617)(349,613)(350,615)(351,614)(352,610)
(353,612)(354,611)(355,607)(356,609)(357,608)(358,604)(359,606)(360,605)
(361,601)(362,603)(363,602)(364,666)(365,665)(366,664)(367,663)(368,662)
(369,661)(370,693)(371,692)(372,691)(373,690)(374,689)(375,688)(376,687)
(377,686)(378,685)(379,684)(380,683)(381,682)(382,681)(383,680)(384,679)
(385,678)(386,677)(387,676)(388,675)(389,674)(390,673)(391,672)(392,671)
(393,670)(394,669)(395,668)(396,667);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(792)!(  2,  3)(  4, 31)(  5, 33)(  6, 32)(  7, 28)(  8, 30)(  9, 29)
( 10, 25)( 11, 27)( 12, 26)( 13, 22)( 14, 24)( 15, 23)( 16, 19)( 17, 21)
( 18, 20)( 34, 69)( 35, 68)( 36, 67)( 37, 99)( 38, 98)( 39, 97)( 40, 96)
( 41, 95)( 42, 94)( 43, 93)( 44, 92)( 45, 91)( 46, 90)( 47, 89)( 48, 88)
( 49, 87)( 50, 86)( 51, 85)( 52, 84)( 53, 83)( 54, 82)( 55, 81)( 56, 80)
( 57, 79)( 58, 78)( 59, 77)( 60, 76)( 61, 75)( 62, 74)( 63, 73)( 64, 72)
( 65, 71)( 66, 70)(101,102)(103,130)(104,132)(105,131)(106,127)(107,129)
(108,128)(109,124)(110,126)(111,125)(112,121)(113,123)(114,122)(115,118)
(116,120)(117,119)(133,168)(134,167)(135,166)(136,198)(137,197)(138,196)
(139,195)(140,194)(141,193)(142,192)(143,191)(144,190)(145,189)(146,188)
(147,187)(148,186)(149,185)(150,184)(151,183)(152,182)(153,181)(154,180)
(155,179)(156,178)(157,177)(158,176)(159,175)(160,174)(161,173)(162,172)
(163,171)(164,170)(165,169)(199,298)(200,300)(201,299)(202,328)(203,330)
(204,329)(205,325)(206,327)(207,326)(208,322)(209,324)(210,323)(211,319)
(212,321)(213,320)(214,316)(215,318)(216,317)(217,313)(218,315)(219,314)
(220,310)(221,312)(222,311)(223,307)(224,309)(225,308)(226,304)(227,306)
(228,305)(229,301)(230,303)(231,302)(232,366)(233,365)(234,364)(235,396)
(236,395)(237,394)(238,393)(239,392)(240,391)(241,390)(242,389)(243,388)
(244,387)(245,386)(246,385)(247,384)(248,383)(249,382)(250,381)(251,380)
(252,379)(253,378)(254,377)(255,376)(256,375)(257,374)(258,373)(259,372)
(260,371)(261,370)(262,369)(263,368)(264,367)(265,333)(266,332)(267,331)
(268,363)(269,362)(270,361)(271,360)(272,359)(273,358)(274,357)(275,356)
(276,355)(277,354)(278,353)(279,352)(280,351)(281,350)(282,349)(283,348)
(284,347)(285,346)(286,345)(287,344)(288,343)(289,342)(290,341)(291,340)
(292,339)(293,338)(294,337)(295,336)(296,335)(297,334)(397,595)(398,597)
(399,596)(400,625)(401,627)(402,626)(403,622)(404,624)(405,623)(406,619)
(407,621)(408,620)(409,616)(410,618)(411,617)(412,613)(413,615)(414,614)
(415,610)(416,612)(417,611)(418,607)(419,609)(420,608)(421,604)(422,606)
(423,605)(424,601)(425,603)(426,602)(427,598)(428,600)(429,599)(430,663)
(431,662)(432,661)(433,693)(434,692)(435,691)(436,690)(437,689)(438,688)
(439,687)(440,686)(441,685)(442,684)(443,683)(444,682)(445,681)(446,680)
(447,679)(448,678)(449,677)(450,676)(451,675)(452,674)(453,673)(454,672)
(455,671)(456,670)(457,669)(458,668)(459,667)(460,666)(461,665)(462,664)
(463,630)(464,629)(465,628)(466,660)(467,659)(468,658)(469,657)(470,656)
(471,655)(472,654)(473,653)(474,652)(475,651)(476,650)(477,649)(478,648)
(479,647)(480,646)(481,645)(482,644)(483,643)(484,642)(485,641)(486,640)
(487,639)(488,638)(489,637)(490,636)(491,635)(492,634)(493,633)(494,632)
(495,631)(496,694)(497,696)(498,695)(499,724)(500,726)(501,725)(502,721)
(503,723)(504,722)(505,718)(506,720)(507,719)(508,715)(509,717)(510,716)
(511,712)(512,714)(513,713)(514,709)(515,711)(516,710)(517,706)(518,708)
(519,707)(520,703)(521,705)(522,704)(523,700)(524,702)(525,701)(526,697)
(527,699)(528,698)(529,762)(530,761)(531,760)(532,792)(533,791)(534,790)
(535,789)(536,788)(537,787)(538,786)(539,785)(540,784)(541,783)(542,782)
(543,781)(544,780)(545,779)(546,778)(547,777)(548,776)(549,775)(550,774)
(551,773)(552,772)(553,771)(554,770)(555,769)(556,768)(557,767)(558,766)
(559,765)(560,764)(561,763)(562,729)(563,728)(564,727)(565,759)(566,758)
(567,757)(568,756)(569,755)(570,754)(571,753)(572,752)(573,751)(574,750)
(575,749)(576,748)(577,747)(578,746)(579,745)(580,744)(581,743)(582,742)
(583,741)(584,740)(585,739)(586,738)(587,737)(588,736)(589,735)(590,734)
(591,733)(592,732)(593,731)(594,730);
s1 := Sym(792)!(  1,433)(  2,435)(  3,434)(  4,430)(  5,432)(  6,431)(  7,460)
(  8,462)(  9,461)( 10,457)( 11,459)( 12,458)( 13,454)( 14,456)( 15,455)
( 16,451)( 17,453)( 18,452)( 19,448)( 20,450)( 21,449)( 22,445)( 23,447)
( 24,446)( 25,442)( 26,444)( 27,443)( 28,439)( 29,441)( 30,440)( 31,436)
( 32,438)( 33,437)( 34,400)( 35,402)( 36,401)( 37,397)( 38,399)( 39,398)
( 40,427)( 41,429)( 42,428)( 43,424)( 44,426)( 45,425)( 46,421)( 47,423)
( 48,422)( 49,418)( 50,420)( 51,419)( 52,415)( 53,417)( 54,416)( 55,412)
( 56,414)( 57,413)( 58,409)( 59,411)( 60,410)( 61,406)( 62,408)( 63,407)
( 64,403)( 65,405)( 66,404)( 67,468)( 68,467)( 69,466)( 70,465)( 71,464)
( 72,463)( 73,495)( 74,494)( 75,493)( 76,492)( 77,491)( 78,490)( 79,489)
( 80,488)( 81,487)( 82,486)( 83,485)( 84,484)( 85,483)( 86,482)( 87,481)
( 88,480)( 89,479)( 90,478)( 91,477)( 92,476)( 93,475)( 94,474)( 95,473)
( 96,472)( 97,471)( 98,470)( 99,469)(100,532)(101,534)(102,533)(103,529)
(104,531)(105,530)(106,559)(107,561)(108,560)(109,556)(110,558)(111,557)
(112,553)(113,555)(114,554)(115,550)(116,552)(117,551)(118,547)(119,549)
(120,548)(121,544)(122,546)(123,545)(124,541)(125,543)(126,542)(127,538)
(128,540)(129,539)(130,535)(131,537)(132,536)(133,499)(134,501)(135,500)
(136,496)(137,498)(138,497)(139,526)(140,528)(141,527)(142,523)(143,525)
(144,524)(145,520)(146,522)(147,521)(148,517)(149,519)(150,518)(151,514)
(152,516)(153,515)(154,511)(155,513)(156,512)(157,508)(158,510)(159,509)
(160,505)(161,507)(162,506)(163,502)(164,504)(165,503)(166,567)(167,566)
(168,565)(169,564)(170,563)(171,562)(172,594)(173,593)(174,592)(175,591)
(176,590)(177,589)(178,588)(179,587)(180,586)(181,585)(182,584)(183,583)
(184,582)(185,581)(186,580)(187,579)(188,578)(189,577)(190,576)(191,575)
(192,574)(193,573)(194,572)(195,571)(196,570)(197,569)(198,568)(199,730)
(200,732)(201,731)(202,727)(203,729)(204,728)(205,757)(206,759)(207,758)
(208,754)(209,756)(210,755)(211,751)(212,753)(213,752)(214,748)(215,750)
(216,749)(217,745)(218,747)(219,746)(220,742)(221,744)(222,743)(223,739)
(224,741)(225,740)(226,736)(227,738)(228,737)(229,733)(230,735)(231,734)
(232,697)(233,699)(234,698)(235,694)(236,696)(237,695)(238,724)(239,726)
(240,725)(241,721)(242,723)(243,722)(244,718)(245,720)(246,719)(247,715)
(248,717)(249,716)(250,712)(251,714)(252,713)(253,709)(254,711)(255,710)
(256,706)(257,708)(258,707)(259,703)(260,705)(261,704)(262,700)(263,702)
(264,701)(265,765)(266,764)(267,763)(268,762)(269,761)(270,760)(271,792)
(272,791)(273,790)(274,789)(275,788)(276,787)(277,786)(278,785)(279,784)
(280,783)(281,782)(282,781)(283,780)(284,779)(285,778)(286,777)(287,776)
(288,775)(289,774)(290,773)(291,772)(292,771)(293,770)(294,769)(295,768)
(296,767)(297,766)(298,631)(299,633)(300,632)(301,628)(302,630)(303,629)
(304,658)(305,660)(306,659)(307,655)(308,657)(309,656)(310,652)(311,654)
(312,653)(313,649)(314,651)(315,650)(316,646)(317,648)(318,647)(319,643)
(320,645)(321,644)(322,640)(323,642)(324,641)(325,637)(326,639)(327,638)
(328,634)(329,636)(330,635)(331,598)(332,600)(333,599)(334,595)(335,597)
(336,596)(337,625)(338,627)(339,626)(340,622)(341,624)(342,623)(343,619)
(344,621)(345,620)(346,616)(347,618)(348,617)(349,613)(350,615)(351,614)
(352,610)(353,612)(354,611)(355,607)(356,609)(357,608)(358,604)(359,606)
(360,605)(361,601)(362,603)(363,602)(364,666)(365,665)(366,664)(367,663)
(368,662)(369,661)(370,693)(371,692)(372,691)(373,690)(374,689)(375,688)
(376,687)(377,686)(378,685)(379,684)(380,683)(381,682)(382,681)(383,680)
(384,679)(385,678)(386,677)(387,676)(388,675)(389,674)(390,673)(391,672)
(392,671)(393,670)(394,669)(395,668)(396,667);
poly := sub<Sym(792)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope