Polytope of Type {812}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {812}*1624
Also Known As : 812-gon, {812}. if this polytope has another name.
Group : SmallGroup(1624,37)
Rank : 2
Schlafli Type : {812}
Number of vertices, edges, etc : 812, 812
Order of s₀s₁ : 812
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 : {406}*812
   4-fold quotients : {203}*406
   7-fold quotients : {116}*232
   14-fold quotients : {58}*116
   28-fold quotients : {29}*58
   29-fold quotients : {28}*56
   58-fold quotients : {14}*28
   116-fold quotients : {7}*14
   203-fold quotients : {4}*8
   406-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)(  9, 22)
( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 30,175)( 31,203)
( 32,202)( 33,201)( 34,200)( 35,199)( 36,198)( 37,197)( 38,196)( 39,195)
( 40,194)( 41,193)( 42,192)( 43,191)( 44,190)( 45,189)( 46,188)( 47,187)
( 48,186)( 49,185)( 50,184)( 51,183)( 52,182)( 53,181)( 54,180)( 55,179)
( 56,178)( 57,177)( 58,176)( 59,146)( 60,174)( 61,173)( 62,172)( 63,171)
( 64,170)( 65,169)( 66,168)( 67,167)( 68,166)( 69,165)( 70,164)( 71,163)
( 72,162)( 73,161)( 74,160)( 75,159)( 76,158)( 77,157)( 78,156)( 79,155)
( 80,154)( 81,153)( 82,152)( 83,151)( 84,150)( 85,149)( 86,148)( 87,147)
( 88,117)( 89,145)( 90,144)( 91,143)( 92,142)( 93,141)( 94,140)( 95,139)
( 96,138)( 97,137)( 98,136)( 99,135)(100,134)(101,133)(102,132)(103,131)
(104,130)(105,129)(106,128)(107,127)(108,126)(109,125)(110,124)(111,123)
(112,122)(113,121)(114,120)(115,119)(116,118)(205,232)(206,231)(207,230)
(208,229)(209,228)(210,227)(211,226)(212,225)(213,224)(214,223)(215,222)
(216,221)(217,220)(218,219)(233,378)(234,406)(235,405)(236,404)(237,403)
(238,402)(239,401)(240,400)(241,399)(242,398)(243,397)(244,396)(245,395)
(246,394)(247,393)(248,392)(249,391)(250,390)(251,389)(252,388)(253,387)
(254,386)(255,385)(256,384)(257,383)(258,382)(259,381)(260,380)(261,379)
(262,349)(263,377)(264,376)(265,375)(266,374)(267,373)(268,372)(269,371)
(270,370)(271,369)(272,368)(273,367)(274,366)(275,365)(276,364)(277,363)
(278,362)(279,361)(280,360)(281,359)(282,358)(283,357)(284,356)(285,355)
(286,354)(287,353)(288,352)(289,351)(290,350)(291,320)(292,348)(293,347)
(294,346)(295,345)(296,344)(297,343)(298,342)(299,341)(300,340)(301,339)
(302,338)(303,337)(304,336)(305,335)(306,334)(307,333)(308,332)(309,331)
(310,330)(311,329)(312,328)(313,327)(314,326)(315,325)(316,324)(317,323)
(318,322)(319,321)(407,610)(408,638)(409,637)(410,636)(411,635)(412,634)
(413,633)(414,632)(415,631)(416,630)(417,629)(418,628)(419,627)(420,626)
(421,625)(422,624)(423,623)(424,622)(425,621)(426,620)(427,619)(428,618)
(429,617)(430,616)(431,615)(432,614)(433,613)(434,612)(435,611)(436,784)
(437,812)(438,811)(439,810)(440,809)(441,808)(442,807)(443,806)(444,805)
(445,804)(446,803)(447,802)(448,801)(449,800)(450,799)(451,798)(452,797)
(453,796)(454,795)(455,794)(456,793)(457,792)(458,791)(459,790)(460,789)
(461,788)(462,787)(463,786)(464,785)(465,755)(466,783)(467,782)(468,781)
(469,780)(470,779)(471,778)(472,777)(473,776)(474,775)(475,774)(476,773)
(477,772)(478,771)(479,770)(480,769)(481,768)(482,767)(483,766)(484,765)
(485,764)(486,763)(487,762)(488,761)(489,760)(490,759)(491,758)(492,757)
(493,756)(494,726)(495,754)(496,753)(497,752)(498,751)(499,750)(500,749)
(501,748)(502,747)(503,746)(504,745)(505,744)(506,743)(507,742)(508,741)
(509,740)(510,739)(511,738)(512,737)(513,736)(514,735)(515,734)(516,733)
(517,732)(518,731)(519,730)(520,729)(521,728)(522,727)(523,697)(524,725)
(525,724)(526,723)(527,722)(528,721)(529,720)(530,719)(531,718)(532,717)
(533,716)(534,715)(535,714)(536,713)(537,712)(538,711)(539,710)(540,709)
(541,708)(542,707)(543,706)(544,705)(545,704)(546,703)(547,702)(548,701)
(549,700)(550,699)(551,698)(552,668)(553,696)(554,695)(555,694)(556,693)
(557,692)(558,691)(559,690)(560,689)(561,688)(562,687)(563,686)(564,685)
(565,684)(566,683)(567,682)(568,681)(569,680)(570,679)(571,678)(572,677)
(573,676)(574,675)(575,674)(576,673)(577,672)(578,671)(579,670)(580,669)
(581,639)(582,667)(583,666)(584,665)(585,664)(586,663)(587,662)(588,661)
(589,660)(590,659)(591,658)(592,657)(593,656)(594,655)(595,654)(596,653)
(597,652)(598,651)(599,650)(600,649)(601,648)(602,647)(603,646)(604,645)
(605,644)(606,643)(607,642)(608,641)(609,640);;
s1 := (  1,437)(  2,436)(  3,464)(  4,463)(  5,462)(  6,461)(  7,460)(  8,459)
(  9,458)( 10,457)( 11,456)( 12,455)( 13,454)( 14,453)( 15,452)( 16,451)
( 17,450)( 18,449)( 19,448)( 20,447)( 21,446)( 22,445)( 23,444)( 24,443)
( 25,442)( 26,441)( 27,440)( 28,439)( 29,438)( 30,408)( 31,407)( 32,435)
( 33,434)( 34,433)( 35,432)( 36,431)( 37,430)( 38,429)( 39,428)( 40,427)
( 41,426)( 42,425)( 43,424)( 44,423)( 45,422)( 46,421)( 47,420)( 48,419)
( 49,418)( 50,417)( 51,416)( 52,415)( 53,414)( 54,413)( 55,412)( 56,411)
( 57,410)( 58,409)( 59,582)( 60,581)( 61,609)( 62,608)( 63,607)( 64,606)
( 65,605)( 66,604)( 67,603)( 68,602)( 69,601)( 70,600)( 71,599)( 72,598)
( 73,597)( 74,596)( 75,595)( 76,594)( 77,593)( 78,592)( 79,591)( 80,590)
( 81,589)( 82,588)( 83,587)( 84,586)( 85,585)( 86,584)( 87,583)( 88,553)
( 89,552)( 90,580)( 91,579)( 92,578)( 93,577)( 94,576)( 95,575)( 96,574)
( 97,573)( 98,572)( 99,571)(100,570)(101,569)(102,568)(103,567)(104,566)
(105,565)(106,564)(107,563)(108,562)(109,561)(110,560)(111,559)(112,558)
(113,557)(114,556)(115,555)(116,554)(117,524)(118,523)(119,551)(120,550)
(121,549)(122,548)(123,547)(124,546)(125,545)(126,544)(127,543)(128,542)
(129,541)(130,540)(131,539)(132,538)(133,537)(134,536)(135,535)(136,534)
(137,533)(138,532)(139,531)(140,530)(141,529)(142,528)(143,527)(144,526)
(145,525)(146,495)(147,494)(148,522)(149,521)(150,520)(151,519)(152,518)
(153,517)(154,516)(155,515)(156,514)(157,513)(158,512)(159,511)(160,510)
(161,509)(162,508)(163,507)(164,506)(165,505)(166,504)(167,503)(168,502)
(169,501)(170,500)(171,499)(172,498)(173,497)(174,496)(175,466)(176,465)
(177,493)(178,492)(179,491)(180,490)(181,489)(182,488)(183,487)(184,486)
(185,485)(186,484)(187,483)(188,482)(189,481)(190,480)(191,479)(192,478)
(193,477)(194,476)(195,475)(196,474)(197,473)(198,472)(199,471)(200,470)
(201,469)(202,468)(203,467)(204,640)(205,639)(206,667)(207,666)(208,665)
(209,664)(210,663)(211,662)(212,661)(213,660)(214,659)(215,658)(216,657)
(217,656)(218,655)(219,654)(220,653)(221,652)(222,651)(223,650)(224,649)
(225,648)(226,647)(227,646)(228,645)(229,644)(230,643)(231,642)(232,641)
(233,611)(234,610)(235,638)(236,637)(237,636)(238,635)(239,634)(240,633)
(241,632)(242,631)(243,630)(244,629)(245,628)(246,627)(247,626)(248,625)
(249,624)(250,623)(251,622)(252,621)(253,620)(254,619)(255,618)(256,617)
(257,616)(258,615)(259,614)(260,613)(261,612)(262,785)(263,784)(264,812)
(265,811)(266,810)(267,809)(268,808)(269,807)(270,806)(271,805)(272,804)
(273,803)(274,802)(275,801)(276,800)(277,799)(278,798)(279,797)(280,796)
(281,795)(282,794)(283,793)(284,792)(285,791)(286,790)(287,789)(288,788)
(289,787)(290,786)(291,756)(292,755)(293,783)(294,782)(295,781)(296,780)
(297,779)(298,778)(299,777)(300,776)(301,775)(302,774)(303,773)(304,772)
(305,771)(306,770)(307,769)(308,768)(309,767)(310,766)(311,765)(312,764)
(313,763)(314,762)(315,761)(316,760)(317,759)(318,758)(319,757)(320,727)
(321,726)(322,754)(323,753)(324,752)(325,751)(326,750)(327,749)(328,748)
(329,747)(330,746)(331,745)(332,744)(333,743)(334,742)(335,741)(336,740)
(337,739)(338,738)(339,737)(340,736)(341,735)(342,734)(343,733)(344,732)
(345,731)(346,730)(347,729)(348,728)(349,698)(350,697)(351,725)(352,724)
(353,723)(354,722)(355,721)(356,720)(357,719)(358,718)(359,717)(360,716)
(361,715)(362,714)(363,713)(364,712)(365,711)(366,710)(367,709)(368,708)
(369,707)(370,706)(371,705)(372,704)(373,703)(374,702)(375,701)(376,700)
(377,699)(378,669)(379,668)(380,696)(381,695)(382,694)(383,693)(384,692)
(385,691)(386,690)(387,689)(388,688)(389,687)(390,686)(391,685)(392,684)
(393,683)(394,682)(395,681)(396,680)(397,679)(398,678)(399,677)(400,676)
(401,675)(402,674)(403,673)(404,672)(405,671)(406,670);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(812)!(  2, 29)(  3, 28)(  4, 27)(  5, 26)(  6, 25)(  7, 24)(  8, 23)
(  9, 22)( 10, 21)( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 30,175)
( 31,203)( 32,202)( 33,201)( 34,200)( 35,199)( 36,198)( 37,197)( 38,196)
( 39,195)( 40,194)( 41,193)( 42,192)( 43,191)( 44,190)( 45,189)( 46,188)
( 47,187)( 48,186)( 49,185)( 50,184)( 51,183)( 52,182)( 53,181)( 54,180)
( 55,179)( 56,178)( 57,177)( 58,176)( 59,146)( 60,174)( 61,173)( 62,172)
( 63,171)( 64,170)( 65,169)( 66,168)( 67,167)( 68,166)( 69,165)( 70,164)
( 71,163)( 72,162)( 73,161)( 74,160)( 75,159)( 76,158)( 77,157)( 78,156)
( 79,155)( 80,154)( 81,153)( 82,152)( 83,151)( 84,150)( 85,149)( 86,148)
( 87,147)( 88,117)( 89,145)( 90,144)( 91,143)( 92,142)( 93,141)( 94,140)
( 95,139)( 96,138)( 97,137)( 98,136)( 99,135)(100,134)(101,133)(102,132)
(103,131)(104,130)(105,129)(106,128)(107,127)(108,126)(109,125)(110,124)
(111,123)(112,122)(113,121)(114,120)(115,119)(116,118)(205,232)(206,231)
(207,230)(208,229)(209,228)(210,227)(211,226)(212,225)(213,224)(214,223)
(215,222)(216,221)(217,220)(218,219)(233,378)(234,406)(235,405)(236,404)
(237,403)(238,402)(239,401)(240,400)(241,399)(242,398)(243,397)(244,396)
(245,395)(246,394)(247,393)(248,392)(249,391)(250,390)(251,389)(252,388)
(253,387)(254,386)(255,385)(256,384)(257,383)(258,382)(259,381)(260,380)
(261,379)(262,349)(263,377)(264,376)(265,375)(266,374)(267,373)(268,372)
(269,371)(270,370)(271,369)(272,368)(273,367)(274,366)(275,365)(276,364)
(277,363)(278,362)(279,361)(280,360)(281,359)(282,358)(283,357)(284,356)
(285,355)(286,354)(287,353)(288,352)(289,351)(290,350)(291,320)(292,348)
(293,347)(294,346)(295,345)(296,344)(297,343)(298,342)(299,341)(300,340)
(301,339)(302,338)(303,337)(304,336)(305,335)(306,334)(307,333)(308,332)
(309,331)(310,330)(311,329)(312,328)(313,327)(314,326)(315,325)(316,324)
(317,323)(318,322)(319,321)(407,610)(408,638)(409,637)(410,636)(411,635)
(412,634)(413,633)(414,632)(415,631)(416,630)(417,629)(418,628)(419,627)
(420,626)(421,625)(422,624)(423,623)(424,622)(425,621)(426,620)(427,619)
(428,618)(429,617)(430,616)(431,615)(432,614)(433,613)(434,612)(435,611)
(436,784)(437,812)(438,811)(439,810)(440,809)(441,808)(442,807)(443,806)
(444,805)(445,804)(446,803)(447,802)(448,801)(449,800)(450,799)(451,798)
(452,797)(453,796)(454,795)(455,794)(456,793)(457,792)(458,791)(459,790)
(460,789)(461,788)(462,787)(463,786)(464,785)(465,755)(466,783)(467,782)
(468,781)(469,780)(470,779)(471,778)(472,777)(473,776)(474,775)(475,774)
(476,773)(477,772)(478,771)(479,770)(480,769)(481,768)(482,767)(483,766)
(484,765)(485,764)(486,763)(487,762)(488,761)(489,760)(490,759)(491,758)
(492,757)(493,756)(494,726)(495,754)(496,753)(497,752)(498,751)(499,750)
(500,749)(501,748)(502,747)(503,746)(504,745)(505,744)(506,743)(507,742)
(508,741)(509,740)(510,739)(511,738)(512,737)(513,736)(514,735)(515,734)
(516,733)(517,732)(518,731)(519,730)(520,729)(521,728)(522,727)(523,697)
(524,725)(525,724)(526,723)(527,722)(528,721)(529,720)(530,719)(531,718)
(532,717)(533,716)(534,715)(535,714)(536,713)(537,712)(538,711)(539,710)
(540,709)(541,708)(542,707)(543,706)(544,705)(545,704)(546,703)(547,702)
(548,701)(549,700)(550,699)(551,698)(552,668)(553,696)(554,695)(555,694)
(556,693)(557,692)(558,691)(559,690)(560,689)(561,688)(562,687)(563,686)
(564,685)(565,684)(566,683)(567,682)(568,681)(569,680)(570,679)(571,678)
(572,677)(573,676)(574,675)(575,674)(576,673)(577,672)(578,671)(579,670)
(580,669)(581,639)(582,667)(583,666)(584,665)(585,664)(586,663)(587,662)
(588,661)(589,660)(590,659)(591,658)(592,657)(593,656)(594,655)(595,654)
(596,653)(597,652)(598,651)(599,650)(600,649)(601,648)(602,647)(603,646)
(604,645)(605,644)(606,643)(607,642)(608,641)(609,640);
s1 := Sym(812)!(  1,437)(  2,436)(  3,464)(  4,463)(  5,462)(  6,461)(  7,460)
(  8,459)(  9,458)( 10,457)( 11,456)( 12,455)( 13,454)( 14,453)( 15,452)
( 16,451)( 17,450)( 18,449)( 19,448)( 20,447)( 21,446)( 22,445)( 23,444)
( 24,443)( 25,442)( 26,441)( 27,440)( 28,439)( 29,438)( 30,408)( 31,407)
( 32,435)( 33,434)( 34,433)( 35,432)( 36,431)( 37,430)( 38,429)( 39,428)
( 40,427)( 41,426)( 42,425)( 43,424)( 44,423)( 45,422)( 46,421)( 47,420)
( 48,419)( 49,418)( 50,417)( 51,416)( 52,415)( 53,414)( 54,413)( 55,412)
( 56,411)( 57,410)( 58,409)( 59,582)( 60,581)( 61,609)( 62,608)( 63,607)
( 64,606)( 65,605)( 66,604)( 67,603)( 68,602)( 69,601)( 70,600)( 71,599)
( 72,598)( 73,597)( 74,596)( 75,595)( 76,594)( 77,593)( 78,592)( 79,591)
( 80,590)( 81,589)( 82,588)( 83,587)( 84,586)( 85,585)( 86,584)( 87,583)
( 88,553)( 89,552)( 90,580)( 91,579)( 92,578)( 93,577)( 94,576)( 95,575)
( 96,574)( 97,573)( 98,572)( 99,571)(100,570)(101,569)(102,568)(103,567)
(104,566)(105,565)(106,564)(107,563)(108,562)(109,561)(110,560)(111,559)
(112,558)(113,557)(114,556)(115,555)(116,554)(117,524)(118,523)(119,551)
(120,550)(121,549)(122,548)(123,547)(124,546)(125,545)(126,544)(127,543)
(128,542)(129,541)(130,540)(131,539)(132,538)(133,537)(134,536)(135,535)
(136,534)(137,533)(138,532)(139,531)(140,530)(141,529)(142,528)(143,527)
(144,526)(145,525)(146,495)(147,494)(148,522)(149,521)(150,520)(151,519)
(152,518)(153,517)(154,516)(155,515)(156,514)(157,513)(158,512)(159,511)
(160,510)(161,509)(162,508)(163,507)(164,506)(165,505)(166,504)(167,503)
(168,502)(169,501)(170,500)(171,499)(172,498)(173,497)(174,496)(175,466)
(176,465)(177,493)(178,492)(179,491)(180,490)(181,489)(182,488)(183,487)
(184,486)(185,485)(186,484)(187,483)(188,482)(189,481)(190,480)(191,479)
(192,478)(193,477)(194,476)(195,475)(196,474)(197,473)(198,472)(199,471)
(200,470)(201,469)(202,468)(203,467)(204,640)(205,639)(206,667)(207,666)
(208,665)(209,664)(210,663)(211,662)(212,661)(213,660)(214,659)(215,658)
(216,657)(217,656)(218,655)(219,654)(220,653)(221,652)(222,651)(223,650)
(224,649)(225,648)(226,647)(227,646)(228,645)(229,644)(230,643)(231,642)
(232,641)(233,611)(234,610)(235,638)(236,637)(237,636)(238,635)(239,634)
(240,633)(241,632)(242,631)(243,630)(244,629)(245,628)(246,627)(247,626)
(248,625)(249,624)(250,623)(251,622)(252,621)(253,620)(254,619)(255,618)
(256,617)(257,616)(258,615)(259,614)(260,613)(261,612)(262,785)(263,784)
(264,812)(265,811)(266,810)(267,809)(268,808)(269,807)(270,806)(271,805)
(272,804)(273,803)(274,802)(275,801)(276,800)(277,799)(278,798)(279,797)
(280,796)(281,795)(282,794)(283,793)(284,792)(285,791)(286,790)(287,789)
(288,788)(289,787)(290,786)(291,756)(292,755)(293,783)(294,782)(295,781)
(296,780)(297,779)(298,778)(299,777)(300,776)(301,775)(302,774)(303,773)
(304,772)(305,771)(306,770)(307,769)(308,768)(309,767)(310,766)(311,765)
(312,764)(313,763)(314,762)(315,761)(316,760)(317,759)(318,758)(319,757)
(320,727)(321,726)(322,754)(323,753)(324,752)(325,751)(326,750)(327,749)
(328,748)(329,747)(330,746)(331,745)(332,744)(333,743)(334,742)(335,741)
(336,740)(337,739)(338,738)(339,737)(340,736)(341,735)(342,734)(343,733)
(344,732)(345,731)(346,730)(347,729)(348,728)(349,698)(350,697)(351,725)
(352,724)(353,723)(354,722)(355,721)(356,720)(357,719)(358,718)(359,717)
(360,716)(361,715)(362,714)(363,713)(364,712)(365,711)(366,710)(367,709)
(368,708)(369,707)(370,706)(371,705)(372,704)(373,703)(374,702)(375,701)
(376,700)(377,699)(378,669)(379,668)(380,696)(381,695)(382,694)(383,693)
(384,692)(385,691)(386,690)(387,689)(388,688)(389,687)(390,686)(391,685)
(392,684)(393,683)(394,682)(395,681)(396,680)(397,679)(398,678)(399,677)
(400,676)(401,675)(402,674)(403,673)(404,672)(405,671)(406,670);
poly := sub<Sym(812)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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