Polytope of Type {820}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {820}*1640
Also Known As : 820-gon, {820}. if this polytope has another name.
Group : SmallGroup(1640,41)
Rank : 2
Schlafli Type : {820}
Number of vertices, edges, etc : 820, 820
Order of s₀s₁ : 820
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 : {410}*820
   4-fold quotients : {205}*410
   5-fold quotients : {164}*328
   10-fold quotients : {82}*164
   20-fold quotients : {41}*82
   41-fold quotients : {20}*40
   82-fold quotients : {10}*20
   164-fold quotients : {5}*10
   205-fold quotients : {4}*8
   410-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 41)(  3, 40)(  4, 39)(  5, 38)(  6, 37)(  7, 36)(  8, 35)(  9, 34)
( 10, 33)( 11, 32)( 12, 31)( 13, 30)( 14, 29)( 15, 28)( 16, 27)( 17, 26)
( 18, 25)( 19, 24)( 20, 23)( 21, 22)( 42,165)( 43,205)( 44,204)( 45,203)
( 46,202)( 47,201)( 48,200)( 49,199)( 50,198)( 51,197)( 52,196)( 53,195)
( 54,194)( 55,193)( 56,192)( 57,191)( 58,190)( 59,189)( 60,188)( 61,187)
( 62,186)( 63,185)( 64,184)( 65,183)( 66,182)( 67,181)( 68,180)( 69,179)
( 70,178)( 71,177)( 72,176)( 73,175)( 74,174)( 75,173)( 76,172)( 77,171)
( 78,170)( 79,169)( 80,168)( 81,167)( 82,166)( 83,124)( 84,164)( 85,163)
( 86,162)( 87,161)( 88,160)( 89,159)( 90,158)( 91,157)( 92,156)( 93,155)
( 94,154)( 95,153)( 96,152)( 97,151)( 98,150)( 99,149)(100,148)(101,147)
(102,146)(103,145)(104,144)(105,143)(106,142)(107,141)(108,140)(109,139)
(110,138)(111,137)(112,136)(113,135)(114,134)(115,133)(116,132)(117,131)
(118,130)(119,129)(120,128)(121,127)(122,126)(123,125)(207,246)(208,245)
(209,244)(210,243)(211,242)(212,241)(213,240)(214,239)(215,238)(216,237)
(217,236)(218,235)(219,234)(220,233)(221,232)(222,231)(223,230)(224,229)
(225,228)(226,227)(247,370)(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)(263,395)(264,394)(265,393)(266,392)(267,391)(268,390)
(269,389)(270,388)(271,387)(272,386)(273,385)(274,384)(275,383)(276,382)
(277,381)(278,380)(279,379)(280,378)(281,377)(282,376)(283,375)(284,374)
(285,373)(286,372)(287,371)(288,329)(289,369)(290,368)(291,367)(292,366)
(293,365)(294,364)(295,363)(296,362)(297,361)(298,360)(299,359)(300,358)
(301,357)(302,356)(303,355)(304,354)(305,353)(306,352)(307,351)(308,350)
(309,349)(310,348)(311,347)(312,346)(313,345)(314,344)(315,343)(316,342)
(317,341)(318,340)(319,339)(320,338)(321,337)(322,336)(323,335)(324,334)
(325,333)(326,332)(327,331)(328,330)(411,616)(412,656)(413,655)(414,654)
(415,653)(416,652)(417,651)(418,650)(419,649)(420,648)(421,647)(422,646)
(423,645)(424,644)(425,643)(426,642)(427,641)(428,640)(429,639)(430,638)
(431,637)(432,636)(433,635)(434,634)(435,633)(436,632)(437,631)(438,630)
(439,629)(440,628)(441,627)(442,626)(443,625)(444,624)(445,623)(446,622)
(447,621)(448,620)(449,619)(450,618)(451,617)(452,780)(453,820)(454,819)
(455,818)(456,817)(457,816)(458,815)(459,814)(460,813)(461,812)(462,811)
(463,810)(464,809)(465,808)(466,807)(467,806)(468,805)(469,804)(470,803)
(471,802)(472,801)(473,800)(474,799)(475,798)(476,797)(477,796)(478,795)
(479,794)(480,793)(481,792)(482,791)(483,790)(484,789)(485,788)(486,787)
(487,786)(488,785)(489,784)(490,783)(491,782)(492,781)(493,739)(494,779)
(495,778)(496,777)(497,776)(498,775)(499,774)(500,773)(501,772)(502,771)
(503,770)(504,769)(505,768)(506,767)(507,766)(508,765)(509,764)(510,763)
(511,762)(512,761)(513,760)(514,759)(515,758)(516,757)(517,756)(518,755)
(519,754)(520,753)(521,752)(522,751)(523,750)(524,749)(525,748)(526,747)
(527,746)(528,745)(529,744)(530,743)(531,742)(532,741)(533,740)(534,698)
(535,738)(536,737)(537,736)(538,735)(539,734)(540,733)(541,732)(542,731)
(543,730)(544,729)(545,728)(546,727)(547,726)(548,725)(549,724)(550,723)
(551,722)(552,721)(553,720)(554,719)(555,718)(556,717)(557,716)(558,715)
(559,714)(560,713)(561,712)(562,711)(563,710)(564,709)(565,708)(566,707)
(567,706)(568,705)(569,704)(570,703)(571,702)(572,701)(573,700)(574,699)
(575,657)(576,697)(577,696)(578,695)(579,694)(580,693)(581,692)(582,691)
(583,690)(584,689)(585,688)(586,687)(587,686)(588,685)(589,684)(590,683)
(591,682)(592,681)(593,680)(594,679)(595,678)(596,677)(597,676)(598,675)
(599,674)(600,673)(601,672)(602,671)(603,670)(604,669)(605,668)(606,667)
(607,666)(608,665)(609,664)(610,663)(611,662)(612,661)(613,660)(614,659)
(615,658);;
s1 := (  1,453)(  2,452)(  3,492)(  4,491)(  5,490)(  6,489)(  7,488)(  8,487)
(  9,486)( 10,485)( 11,484)( 12,483)( 13,482)( 14,481)( 15,480)( 16,479)
( 17,478)( 18,477)( 19,476)( 20,475)( 21,474)( 22,473)( 23,472)( 24,471)
( 25,470)( 26,469)( 27,468)( 28,467)( 29,466)( 30,465)( 31,464)( 32,463)
( 33,462)( 34,461)( 35,460)( 36,459)( 37,458)( 38,457)( 39,456)( 40,455)
( 41,454)( 42,412)( 43,411)( 44,451)( 45,450)( 46,449)( 47,448)( 48,447)
( 49,446)( 50,445)( 51,444)( 52,443)( 53,442)( 54,441)( 55,440)( 56,439)
( 57,438)( 58,437)( 59,436)( 60,435)( 61,434)( 62,433)( 63,432)( 64,431)
( 65,430)( 66,429)( 67,428)( 68,427)( 69,426)( 70,425)( 71,424)( 72,423)
( 73,422)( 74,421)( 75,420)( 76,419)( 77,418)( 78,417)( 79,416)( 80,415)
( 81,414)( 82,413)( 83,576)( 84,575)( 85,615)( 86,614)( 87,613)( 88,612)
( 89,611)( 90,610)( 91,609)( 92,608)( 93,607)( 94,606)( 95,605)( 96,604)
( 97,603)( 98,602)( 99,601)(100,600)(101,599)(102,598)(103,597)(104,596)
(105,595)(106,594)(107,593)(108,592)(109,591)(110,590)(111,589)(112,588)
(113,587)(114,586)(115,585)(116,584)(117,583)(118,582)(119,581)(120,580)
(121,579)(122,578)(123,577)(124,535)(125,534)(126,574)(127,573)(128,572)
(129,571)(130,570)(131,569)(132,568)(133,567)(134,566)(135,565)(136,564)
(137,563)(138,562)(139,561)(140,560)(141,559)(142,558)(143,557)(144,556)
(145,555)(146,554)(147,553)(148,552)(149,551)(150,550)(151,549)(152,548)
(153,547)(154,546)(155,545)(156,544)(157,543)(158,542)(159,541)(160,540)
(161,539)(162,538)(163,537)(164,536)(165,494)(166,493)(167,533)(168,532)
(169,531)(170,530)(171,529)(172,528)(173,527)(174,526)(175,525)(176,524)
(177,523)(178,522)(179,521)(180,520)(181,519)(182,518)(183,517)(184,516)
(185,515)(186,514)(187,513)(188,512)(189,511)(190,510)(191,509)(192,508)
(193,507)(194,506)(195,505)(196,504)(197,503)(198,502)(199,501)(200,500)
(201,499)(202,498)(203,497)(204,496)(205,495)(206,658)(207,657)(208,697)
(209,696)(210,695)(211,694)(212,693)(213,692)(214,691)(215,690)(216,689)
(217,688)(218,687)(219,686)(220,685)(221,684)(222,683)(223,682)(224,681)
(225,680)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)(232,673)
(233,672)(234,671)(235,670)(236,669)(237,668)(238,667)(239,666)(240,665)
(241,664)(242,663)(243,662)(244,661)(245,660)(246,659)(247,617)(248,616)
(249,656)(250,655)(251,654)(252,653)(253,652)(254,651)(255,650)(256,649)
(257,648)(258,647)(259,646)(260,645)(261,644)(262,643)(263,642)(264,641)
(265,640)(266,639)(267,638)(268,637)(269,636)(270,635)(271,634)(272,633)
(273,632)(274,631)(275,630)(276,629)(277,628)(278,627)(279,626)(280,625)
(281,624)(282,623)(283,622)(284,621)(285,620)(286,619)(287,618)(288,781)
(289,780)(290,820)(291,819)(292,818)(293,817)(294,816)(295,815)(296,814)
(297,813)(298,812)(299,811)(300,810)(301,809)(302,808)(303,807)(304,806)
(305,805)(306,804)(307,803)(308,802)(309,801)(310,800)(311,799)(312,798)
(313,797)(314,796)(315,795)(316,794)(317,793)(318,792)(319,791)(320,790)
(321,789)(322,788)(323,787)(324,786)(325,785)(326,784)(327,783)(328,782)
(329,740)(330,739)(331,779)(332,778)(333,777)(334,776)(335,775)(336,774)
(337,773)(338,772)(339,771)(340,770)(341,769)(342,768)(343,767)(344,766)
(345,765)(346,764)(347,763)(348,762)(349,761)(350,760)(351,759)(352,758)
(353,757)(354,756)(355,755)(356,754)(357,753)(358,752)(359,751)(360,750)
(361,749)(362,748)(363,747)(364,746)(365,745)(366,744)(367,743)(368,742)
(369,741)(370,699)(371,698)(372,738)(373,737)(374,736)(375,735)(376,734)
(377,733)(378,732)(379,731)(380,730)(381,729)(382,728)(383,727)(384,726)
(385,725)(386,724)(387,723)(388,722)(389,721)(390,720)(391,719)(392,718)
(393,717)(394,716)(395,715)(396,714)(397,713)(398,712)(399,711)(400,710)
(401,709)(402,708)(403,707)(404,706)(405,705)(406,704)(407,703)(408,702)
(409,701)(410,700);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(820)!(  2, 41)(  3, 40)(  4, 39)(  5, 38)(  6, 37)(  7, 36)(  8, 35)
(  9, 34)( 10, 33)( 11, 32)( 12, 31)( 13, 30)( 14, 29)( 15, 28)( 16, 27)
( 17, 26)( 18, 25)( 19, 24)( 20, 23)( 21, 22)( 42,165)( 43,205)( 44,204)
( 45,203)( 46,202)( 47,201)( 48,200)( 49,199)( 50,198)( 51,197)( 52,196)
( 53,195)( 54,194)( 55,193)( 56,192)( 57,191)( 58,190)( 59,189)( 60,188)
( 61,187)( 62,186)( 63,185)( 64,184)( 65,183)( 66,182)( 67,181)( 68,180)
( 69,179)( 70,178)( 71,177)( 72,176)( 73,175)( 74,174)( 75,173)( 76,172)
( 77,171)( 78,170)( 79,169)( 80,168)( 81,167)( 82,166)( 83,124)( 84,164)
( 85,163)( 86,162)( 87,161)( 88,160)( 89,159)( 90,158)( 91,157)( 92,156)
( 93,155)( 94,154)( 95,153)( 96,152)( 97,151)( 98,150)( 99,149)(100,148)
(101,147)(102,146)(103,145)(104,144)(105,143)(106,142)(107,141)(108,140)
(109,139)(110,138)(111,137)(112,136)(113,135)(114,134)(115,133)(116,132)
(117,131)(118,130)(119,129)(120,128)(121,127)(122,126)(123,125)(207,246)
(208,245)(209,244)(210,243)(211,242)(212,241)(213,240)(214,239)(215,238)
(216,237)(217,236)(218,235)(219,234)(220,233)(221,232)(222,231)(223,230)
(224,229)(225,228)(226,227)(247,370)(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)(263,395)(264,394)(265,393)(266,392)(267,391)
(268,390)(269,389)(270,388)(271,387)(272,386)(273,385)(274,384)(275,383)
(276,382)(277,381)(278,380)(279,379)(280,378)(281,377)(282,376)(283,375)
(284,374)(285,373)(286,372)(287,371)(288,329)(289,369)(290,368)(291,367)
(292,366)(293,365)(294,364)(295,363)(296,362)(297,361)(298,360)(299,359)
(300,358)(301,357)(302,356)(303,355)(304,354)(305,353)(306,352)(307,351)
(308,350)(309,349)(310,348)(311,347)(312,346)(313,345)(314,344)(315,343)
(316,342)(317,341)(318,340)(319,339)(320,338)(321,337)(322,336)(323,335)
(324,334)(325,333)(326,332)(327,331)(328,330)(411,616)(412,656)(413,655)
(414,654)(415,653)(416,652)(417,651)(418,650)(419,649)(420,648)(421,647)
(422,646)(423,645)(424,644)(425,643)(426,642)(427,641)(428,640)(429,639)
(430,638)(431,637)(432,636)(433,635)(434,634)(435,633)(436,632)(437,631)
(438,630)(439,629)(440,628)(441,627)(442,626)(443,625)(444,624)(445,623)
(446,622)(447,621)(448,620)(449,619)(450,618)(451,617)(452,780)(453,820)
(454,819)(455,818)(456,817)(457,816)(458,815)(459,814)(460,813)(461,812)
(462,811)(463,810)(464,809)(465,808)(466,807)(467,806)(468,805)(469,804)
(470,803)(471,802)(472,801)(473,800)(474,799)(475,798)(476,797)(477,796)
(478,795)(479,794)(480,793)(481,792)(482,791)(483,790)(484,789)(485,788)
(486,787)(487,786)(488,785)(489,784)(490,783)(491,782)(492,781)(493,739)
(494,779)(495,778)(496,777)(497,776)(498,775)(499,774)(500,773)(501,772)
(502,771)(503,770)(504,769)(505,768)(506,767)(507,766)(508,765)(509,764)
(510,763)(511,762)(512,761)(513,760)(514,759)(515,758)(516,757)(517,756)
(518,755)(519,754)(520,753)(521,752)(522,751)(523,750)(524,749)(525,748)
(526,747)(527,746)(528,745)(529,744)(530,743)(531,742)(532,741)(533,740)
(534,698)(535,738)(536,737)(537,736)(538,735)(539,734)(540,733)(541,732)
(542,731)(543,730)(544,729)(545,728)(546,727)(547,726)(548,725)(549,724)
(550,723)(551,722)(552,721)(553,720)(554,719)(555,718)(556,717)(557,716)
(558,715)(559,714)(560,713)(561,712)(562,711)(563,710)(564,709)(565,708)
(566,707)(567,706)(568,705)(569,704)(570,703)(571,702)(572,701)(573,700)
(574,699)(575,657)(576,697)(577,696)(578,695)(579,694)(580,693)(581,692)
(582,691)(583,690)(584,689)(585,688)(586,687)(587,686)(588,685)(589,684)
(590,683)(591,682)(592,681)(593,680)(594,679)(595,678)(596,677)(597,676)
(598,675)(599,674)(600,673)(601,672)(602,671)(603,670)(604,669)(605,668)
(606,667)(607,666)(608,665)(609,664)(610,663)(611,662)(612,661)(613,660)
(614,659)(615,658);
s1 := Sym(820)!(  1,453)(  2,452)(  3,492)(  4,491)(  5,490)(  6,489)(  7,488)
(  8,487)(  9,486)( 10,485)( 11,484)( 12,483)( 13,482)( 14,481)( 15,480)
( 16,479)( 17,478)( 18,477)( 19,476)( 20,475)( 21,474)( 22,473)( 23,472)
( 24,471)( 25,470)( 26,469)( 27,468)( 28,467)( 29,466)( 30,465)( 31,464)
( 32,463)( 33,462)( 34,461)( 35,460)( 36,459)( 37,458)( 38,457)( 39,456)
( 40,455)( 41,454)( 42,412)( 43,411)( 44,451)( 45,450)( 46,449)( 47,448)
( 48,447)( 49,446)( 50,445)( 51,444)( 52,443)( 53,442)( 54,441)( 55,440)
( 56,439)( 57,438)( 58,437)( 59,436)( 60,435)( 61,434)( 62,433)( 63,432)
( 64,431)( 65,430)( 66,429)( 67,428)( 68,427)( 69,426)( 70,425)( 71,424)
( 72,423)( 73,422)( 74,421)( 75,420)( 76,419)( 77,418)( 78,417)( 79,416)
( 80,415)( 81,414)( 82,413)( 83,576)( 84,575)( 85,615)( 86,614)( 87,613)
( 88,612)( 89,611)( 90,610)( 91,609)( 92,608)( 93,607)( 94,606)( 95,605)
( 96,604)( 97,603)( 98,602)( 99,601)(100,600)(101,599)(102,598)(103,597)
(104,596)(105,595)(106,594)(107,593)(108,592)(109,591)(110,590)(111,589)
(112,588)(113,587)(114,586)(115,585)(116,584)(117,583)(118,582)(119,581)
(120,580)(121,579)(122,578)(123,577)(124,535)(125,534)(126,574)(127,573)
(128,572)(129,571)(130,570)(131,569)(132,568)(133,567)(134,566)(135,565)
(136,564)(137,563)(138,562)(139,561)(140,560)(141,559)(142,558)(143,557)
(144,556)(145,555)(146,554)(147,553)(148,552)(149,551)(150,550)(151,549)
(152,548)(153,547)(154,546)(155,545)(156,544)(157,543)(158,542)(159,541)
(160,540)(161,539)(162,538)(163,537)(164,536)(165,494)(166,493)(167,533)
(168,532)(169,531)(170,530)(171,529)(172,528)(173,527)(174,526)(175,525)
(176,524)(177,523)(178,522)(179,521)(180,520)(181,519)(182,518)(183,517)
(184,516)(185,515)(186,514)(187,513)(188,512)(189,511)(190,510)(191,509)
(192,508)(193,507)(194,506)(195,505)(196,504)(197,503)(198,502)(199,501)
(200,500)(201,499)(202,498)(203,497)(204,496)(205,495)(206,658)(207,657)
(208,697)(209,696)(210,695)(211,694)(212,693)(213,692)(214,691)(215,690)
(216,689)(217,688)(218,687)(219,686)(220,685)(221,684)(222,683)(223,682)
(224,681)(225,680)(226,679)(227,678)(228,677)(229,676)(230,675)(231,674)
(232,673)(233,672)(234,671)(235,670)(236,669)(237,668)(238,667)(239,666)
(240,665)(241,664)(242,663)(243,662)(244,661)(245,660)(246,659)(247,617)
(248,616)(249,656)(250,655)(251,654)(252,653)(253,652)(254,651)(255,650)
(256,649)(257,648)(258,647)(259,646)(260,645)(261,644)(262,643)(263,642)
(264,641)(265,640)(266,639)(267,638)(268,637)(269,636)(270,635)(271,634)
(272,633)(273,632)(274,631)(275,630)(276,629)(277,628)(278,627)(279,626)
(280,625)(281,624)(282,623)(283,622)(284,621)(285,620)(286,619)(287,618)
(288,781)(289,780)(290,820)(291,819)(292,818)(293,817)(294,816)(295,815)
(296,814)(297,813)(298,812)(299,811)(300,810)(301,809)(302,808)(303,807)
(304,806)(305,805)(306,804)(307,803)(308,802)(309,801)(310,800)(311,799)
(312,798)(313,797)(314,796)(315,795)(316,794)(317,793)(318,792)(319,791)
(320,790)(321,789)(322,788)(323,787)(324,786)(325,785)(326,784)(327,783)
(328,782)(329,740)(330,739)(331,779)(332,778)(333,777)(334,776)(335,775)
(336,774)(337,773)(338,772)(339,771)(340,770)(341,769)(342,768)(343,767)
(344,766)(345,765)(346,764)(347,763)(348,762)(349,761)(350,760)(351,759)
(352,758)(353,757)(354,756)(355,755)(356,754)(357,753)(358,752)(359,751)
(360,750)(361,749)(362,748)(363,747)(364,746)(365,745)(366,744)(367,743)
(368,742)(369,741)(370,699)(371,698)(372,738)(373,737)(374,736)(375,735)
(376,734)(377,733)(378,732)(379,731)(380,730)(381,729)(382,728)(383,727)
(384,726)(385,725)(386,724)(387,723)(388,722)(389,721)(390,720)(391,719)
(392,718)(393,717)(394,716)(395,715)(396,714)(397,713)(398,712)(399,711)
(400,710)(401,709)(402,708)(403,707)(404,706)(405,705)(406,704)(407,703)
(408,702)(409,701)(410,700);
poly := sub<Sym(820)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope