Polytope of Type {844}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {844}*1688
Also Known As : 844-gon, {844}. if this polytope has another name.
Group : SmallGroup(1688,10)
Rank : 2
Schlafli Type : {844}
Number of vertices, edges, etc : 844, 844
Order of s₀s₁ : 844
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 : {422}*844
   4-fold quotients : {211}*422
   211-fold quotients : {4}*8
   422-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,211)(  3,210)(  4,209)(  5,208)(  6,207)(  7,206)(  8,205)(  9,204)
( 10,203)( 11,202)( 12,201)( 13,200)( 14,199)( 15,198)( 16,197)( 17,196)
( 18,195)( 19,194)( 20,193)( 21,192)( 22,191)( 23,190)( 24,189)( 25,188)
( 26,187)( 27,186)( 28,185)( 29,184)( 30,183)( 31,182)( 32,181)( 33,180)
( 34,179)( 35,178)( 36,177)( 37,176)( 38,175)( 39,174)( 40,173)( 41,172)
( 42,171)( 43,170)( 44,169)( 45,168)( 46,167)( 47,166)( 48,165)( 49,164)
( 50,163)( 51,162)( 52,161)( 53,160)( 54,159)( 55,158)( 56,157)( 57,156)
( 58,155)( 59,154)( 60,153)( 61,152)( 62,151)( 63,150)( 64,149)( 65,148)
( 66,147)( 67,146)( 68,145)( 69,144)( 70,143)( 71,142)( 72,141)( 73,140)
( 74,139)( 75,138)( 76,137)( 77,136)( 78,135)( 79,134)( 80,133)( 81,132)
( 82,131)( 83,130)( 84,129)( 85,128)( 86,127)( 87,126)( 88,125)( 89,124)
( 90,123)( 91,122)( 92,121)( 93,120)( 94,119)( 95,118)( 96,117)( 97,116)
( 98,115)( 99,114)(100,113)(101,112)(102,111)(103,110)(104,109)(105,108)
(106,107)(213,422)(214,421)(215,420)(216,419)(217,418)(218,417)(219,416)
(220,415)(221,414)(222,413)(223,412)(224,411)(225,410)(226,409)(227,408)
(228,407)(229,406)(230,405)(231,404)(232,403)(233,402)(234,401)(235,400)
(236,399)(237,398)(238,397)(239,396)(240,395)(241,394)(242,393)(243,392)
(244,391)(245,390)(246,389)(247,388)(248,387)(249,386)(250,385)(251,384)
(252,383)(253,382)(254,381)(255,380)(256,379)(257,378)(258,377)(259,376)
(260,375)(261,374)(262,373)(263,372)(264,371)(265,370)(266,369)(267,368)
(268,367)(269,366)(270,365)(271,364)(272,363)(273,362)(274,361)(275,360)
(276,359)(277,358)(278,357)(279,356)(280,355)(281,354)(282,353)(283,352)
(284,351)(285,350)(286,349)(287,348)(288,347)(289,346)(290,345)(291,344)
(292,343)(293,342)(294,341)(295,340)(296,339)(297,338)(298,337)(299,336)
(300,335)(301,334)(302,333)(303,332)(304,331)(305,330)(306,329)(307,328)
(308,327)(309,326)(310,325)(311,324)(312,323)(313,322)(314,321)(315,320)
(316,319)(317,318)(423,634)(424,844)(425,843)(426,842)(427,841)(428,840)
(429,839)(430,838)(431,837)(432,836)(433,835)(434,834)(435,833)(436,832)
(437,831)(438,830)(439,829)(440,828)(441,827)(442,826)(443,825)(444,824)
(445,823)(446,822)(447,821)(448,820)(449,819)(450,818)(451,817)(452,816)
(453,815)(454,814)(455,813)(456,812)(457,811)(458,810)(459,809)(460,808)
(461,807)(462,806)(463,805)(464,804)(465,803)(466,802)(467,801)(468,800)
(469,799)(470,798)(471,797)(472,796)(473,795)(474,794)(475,793)(476,792)
(477,791)(478,790)(479,789)(480,788)(481,787)(482,786)(483,785)(484,784)
(485,783)(486,782)(487,781)(488,780)(489,779)(490,778)(491,777)(492,776)
(493,775)(494,774)(495,773)(496,772)(497,771)(498,770)(499,769)(500,768)
(501,767)(502,766)(503,765)(504,764)(505,763)(506,762)(507,761)(508,760)
(509,759)(510,758)(511,757)(512,756)(513,755)(514,754)(515,753)(516,752)
(517,751)(518,750)(519,749)(520,748)(521,747)(522,746)(523,745)(524,744)
(525,743)(526,742)(527,741)(528,740)(529,739)(530,738)(531,737)(532,736)
(533,735)(534,734)(535,733)(536,732)(537,731)(538,730)(539,729)(540,728)
(541,727)(542,726)(543,725)(544,724)(545,723)(546,722)(547,721)(548,720)
(549,719)(550,718)(551,717)(552,716)(553,715)(554,714)(555,713)(556,712)
(557,711)(558,710)(559,709)(560,708)(561,707)(562,706)(563,705)(564,704)
(565,703)(566,702)(567,701)(568,700)(569,699)(570,698)(571,697)(572,696)
(573,695)(574,694)(575,693)(576,692)(577,691)(578,690)(579,689)(580,688)
(581,687)(582,686)(583,685)(584,684)(585,683)(586,682)(587,681)(588,680)
(589,679)(590,678)(591,677)(592,676)(593,675)(594,674)(595,673)(596,672)
(597,671)(598,670)(599,669)(600,668)(601,667)(602,666)(603,665)(604,664)
(605,663)(606,662)(607,661)(608,660)(609,659)(610,658)(611,657)(612,656)
(613,655)(614,654)(615,653)(616,652)(617,651)(618,650)(619,649)(620,648)
(621,647)(622,646)(623,645)(624,644)(625,643)(626,642)(627,641)(628,640)
(629,639)(630,638)(631,637)(632,636)(633,635);;
s1 := (  1,424)(  2,423)(  3,633)(  4,632)(  5,631)(  6,630)(  7,629)(  8,628)
(  9,627)( 10,626)( 11,625)( 12,624)( 13,623)( 14,622)( 15,621)( 16,620)
( 17,619)( 18,618)( 19,617)( 20,616)( 21,615)( 22,614)( 23,613)( 24,612)
( 25,611)( 26,610)( 27,609)( 28,608)( 29,607)( 30,606)( 31,605)( 32,604)
( 33,603)( 34,602)( 35,601)( 36,600)( 37,599)( 38,598)( 39,597)( 40,596)
( 41,595)( 42,594)( 43,593)( 44,592)( 45,591)( 46,590)( 47,589)( 48,588)
( 49,587)( 50,586)( 51,585)( 52,584)( 53,583)( 54,582)( 55,581)( 56,580)
( 57,579)( 58,578)( 59,577)( 60,576)( 61,575)( 62,574)( 63,573)( 64,572)
( 65,571)( 66,570)( 67,569)( 68,568)( 69,567)( 70,566)( 71,565)( 72,564)
( 73,563)( 74,562)( 75,561)( 76,560)( 77,559)( 78,558)( 79,557)( 80,556)
( 81,555)( 82,554)( 83,553)( 84,552)( 85,551)( 86,550)( 87,549)( 88,548)
( 89,547)( 90,546)( 91,545)( 92,544)( 93,543)( 94,542)( 95,541)( 96,540)
( 97,539)( 98,538)( 99,537)(100,536)(101,535)(102,534)(103,533)(104,532)
(105,531)(106,530)(107,529)(108,528)(109,527)(110,526)(111,525)(112,524)
(113,523)(114,522)(115,521)(116,520)(117,519)(118,518)(119,517)(120,516)
(121,515)(122,514)(123,513)(124,512)(125,511)(126,510)(127,509)(128,508)
(129,507)(130,506)(131,505)(132,504)(133,503)(134,502)(135,501)(136,500)
(137,499)(138,498)(139,497)(140,496)(141,495)(142,494)(143,493)(144,492)
(145,491)(146,490)(147,489)(148,488)(149,487)(150,486)(151,485)(152,484)
(153,483)(154,482)(155,481)(156,480)(157,479)(158,478)(159,477)(160,476)
(161,475)(162,474)(163,473)(164,472)(165,471)(166,470)(167,469)(168,468)
(169,467)(170,466)(171,465)(172,464)(173,463)(174,462)(175,461)(176,460)
(177,459)(178,458)(179,457)(180,456)(181,455)(182,454)(183,453)(184,452)
(185,451)(186,450)(187,449)(188,448)(189,447)(190,446)(191,445)(192,444)
(193,443)(194,442)(195,441)(196,440)(197,439)(198,438)(199,437)(200,436)
(201,435)(202,434)(203,433)(204,432)(205,431)(206,430)(207,429)(208,428)
(209,427)(210,426)(211,425)(212,635)(213,634)(214,844)(215,843)(216,842)
(217,841)(218,840)(219,839)(220,838)(221,837)(222,836)(223,835)(224,834)
(225,833)(226,832)(227,831)(228,830)(229,829)(230,828)(231,827)(232,826)
(233,825)(234,824)(235,823)(236,822)(237,821)(238,820)(239,819)(240,818)
(241,817)(242,816)(243,815)(244,814)(245,813)(246,812)(247,811)(248,810)
(249,809)(250,808)(251,807)(252,806)(253,805)(254,804)(255,803)(256,802)
(257,801)(258,800)(259,799)(260,798)(261,797)(262,796)(263,795)(264,794)
(265,793)(266,792)(267,791)(268,790)(269,789)(270,788)(271,787)(272,786)
(273,785)(274,784)(275,783)(276,782)(277,781)(278,780)(279,779)(280,778)
(281,777)(282,776)(283,775)(284,774)(285,773)(286,772)(287,771)(288,770)
(289,769)(290,768)(291,767)(292,766)(293,765)(294,764)(295,763)(296,762)
(297,761)(298,760)(299,759)(300,758)(301,757)(302,756)(303,755)(304,754)
(305,753)(306,752)(307,751)(308,750)(309,749)(310,748)(311,747)(312,746)
(313,745)(314,744)(315,743)(316,742)(317,741)(318,740)(319,739)(320,738)
(321,737)(322,736)(323,735)(324,734)(325,733)(326,732)(327,731)(328,730)
(329,729)(330,728)(331,727)(332,726)(333,725)(334,724)(335,723)(336,722)
(337,721)(338,720)(339,719)(340,718)(341,717)(342,716)(343,715)(344,714)
(345,713)(346,712)(347,711)(348,710)(349,709)(350,708)(351,707)(352,706)
(353,705)(354,704)(355,703)(356,702)(357,701)(358,700)(359,699)(360,698)
(361,697)(362,696)(363,695)(364,694)(365,693)(366,692)(367,691)(368,690)
(369,689)(370,688)(371,687)(372,686)(373,685)(374,684)(375,683)(376,682)
(377,681)(378,680)(379,679)(380,678)(381,677)(382,676)(383,675)(384,674)
(385,673)(386,672)(387,671)(388,670)(389,669)(390,668)(391,667)(392,666)
(393,665)(394,664)(395,663)(396,662)(397,661)(398,660)(399,659)(400,658)
(401,657)(402,656)(403,655)(404,654)(405,653)(406,652)(407,651)(408,650)
(409,649)(410,648)(411,647)(412,646)(413,645)(414,644)(415,643)(416,642)
(417,641)(418,640)(419,639)(420,638)(421,637)(422,636);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(844)!(  2,211)(  3,210)(  4,209)(  5,208)(  6,207)(  7,206)(  8,205)
(  9,204)( 10,203)( 11,202)( 12,201)( 13,200)( 14,199)( 15,198)( 16,197)
( 17,196)( 18,195)( 19,194)( 20,193)( 21,192)( 22,191)( 23,190)( 24,189)
( 25,188)( 26,187)( 27,186)( 28,185)( 29,184)( 30,183)( 31,182)( 32,181)
( 33,180)( 34,179)( 35,178)( 36,177)( 37,176)( 38,175)( 39,174)( 40,173)
( 41,172)( 42,171)( 43,170)( 44,169)( 45,168)( 46,167)( 47,166)( 48,165)
( 49,164)( 50,163)( 51,162)( 52,161)( 53,160)( 54,159)( 55,158)( 56,157)
( 57,156)( 58,155)( 59,154)( 60,153)( 61,152)( 62,151)( 63,150)( 64,149)
( 65,148)( 66,147)( 67,146)( 68,145)( 69,144)( 70,143)( 71,142)( 72,141)
( 73,140)( 74,139)( 75,138)( 76,137)( 77,136)( 78,135)( 79,134)( 80,133)
( 81,132)( 82,131)( 83,130)( 84,129)( 85,128)( 86,127)( 87,126)( 88,125)
( 89,124)( 90,123)( 91,122)( 92,121)( 93,120)( 94,119)( 95,118)( 96,117)
( 97,116)( 98,115)( 99,114)(100,113)(101,112)(102,111)(103,110)(104,109)
(105,108)(106,107)(213,422)(214,421)(215,420)(216,419)(217,418)(218,417)
(219,416)(220,415)(221,414)(222,413)(223,412)(224,411)(225,410)(226,409)
(227,408)(228,407)(229,406)(230,405)(231,404)(232,403)(233,402)(234,401)
(235,400)(236,399)(237,398)(238,397)(239,396)(240,395)(241,394)(242,393)
(243,392)(244,391)(245,390)(246,389)(247,388)(248,387)(249,386)(250,385)
(251,384)(252,383)(253,382)(254,381)(255,380)(256,379)(257,378)(258,377)
(259,376)(260,375)(261,374)(262,373)(263,372)(264,371)(265,370)(266,369)
(267,368)(268,367)(269,366)(270,365)(271,364)(272,363)(273,362)(274,361)
(275,360)(276,359)(277,358)(278,357)(279,356)(280,355)(281,354)(282,353)
(283,352)(284,351)(285,350)(286,349)(287,348)(288,347)(289,346)(290,345)
(291,344)(292,343)(293,342)(294,341)(295,340)(296,339)(297,338)(298,337)
(299,336)(300,335)(301,334)(302,333)(303,332)(304,331)(305,330)(306,329)
(307,328)(308,327)(309,326)(310,325)(311,324)(312,323)(313,322)(314,321)
(315,320)(316,319)(317,318)(423,634)(424,844)(425,843)(426,842)(427,841)
(428,840)(429,839)(430,838)(431,837)(432,836)(433,835)(434,834)(435,833)
(436,832)(437,831)(438,830)(439,829)(440,828)(441,827)(442,826)(443,825)
(444,824)(445,823)(446,822)(447,821)(448,820)(449,819)(450,818)(451,817)
(452,816)(453,815)(454,814)(455,813)(456,812)(457,811)(458,810)(459,809)
(460,808)(461,807)(462,806)(463,805)(464,804)(465,803)(466,802)(467,801)
(468,800)(469,799)(470,798)(471,797)(472,796)(473,795)(474,794)(475,793)
(476,792)(477,791)(478,790)(479,789)(480,788)(481,787)(482,786)(483,785)
(484,784)(485,783)(486,782)(487,781)(488,780)(489,779)(490,778)(491,777)
(492,776)(493,775)(494,774)(495,773)(496,772)(497,771)(498,770)(499,769)
(500,768)(501,767)(502,766)(503,765)(504,764)(505,763)(506,762)(507,761)
(508,760)(509,759)(510,758)(511,757)(512,756)(513,755)(514,754)(515,753)
(516,752)(517,751)(518,750)(519,749)(520,748)(521,747)(522,746)(523,745)
(524,744)(525,743)(526,742)(527,741)(528,740)(529,739)(530,738)(531,737)
(532,736)(533,735)(534,734)(535,733)(536,732)(537,731)(538,730)(539,729)
(540,728)(541,727)(542,726)(543,725)(544,724)(545,723)(546,722)(547,721)
(548,720)(549,719)(550,718)(551,717)(552,716)(553,715)(554,714)(555,713)
(556,712)(557,711)(558,710)(559,709)(560,708)(561,707)(562,706)(563,705)
(564,704)(565,703)(566,702)(567,701)(568,700)(569,699)(570,698)(571,697)
(572,696)(573,695)(574,694)(575,693)(576,692)(577,691)(578,690)(579,689)
(580,688)(581,687)(582,686)(583,685)(584,684)(585,683)(586,682)(587,681)
(588,680)(589,679)(590,678)(591,677)(592,676)(593,675)(594,674)(595,673)
(596,672)(597,671)(598,670)(599,669)(600,668)(601,667)(602,666)(603,665)
(604,664)(605,663)(606,662)(607,661)(608,660)(609,659)(610,658)(611,657)
(612,656)(613,655)(614,654)(615,653)(616,652)(617,651)(618,650)(619,649)
(620,648)(621,647)(622,646)(623,645)(624,644)(625,643)(626,642)(627,641)
(628,640)(629,639)(630,638)(631,637)(632,636)(633,635);
s1 := Sym(844)!(  1,424)(  2,423)(  3,633)(  4,632)(  5,631)(  6,630)(  7,629)
(  8,628)(  9,627)( 10,626)( 11,625)( 12,624)( 13,623)( 14,622)( 15,621)
( 16,620)( 17,619)( 18,618)( 19,617)( 20,616)( 21,615)( 22,614)( 23,613)
( 24,612)( 25,611)( 26,610)( 27,609)( 28,608)( 29,607)( 30,606)( 31,605)
( 32,604)( 33,603)( 34,602)( 35,601)( 36,600)( 37,599)( 38,598)( 39,597)
( 40,596)( 41,595)( 42,594)( 43,593)( 44,592)( 45,591)( 46,590)( 47,589)
( 48,588)( 49,587)( 50,586)( 51,585)( 52,584)( 53,583)( 54,582)( 55,581)
( 56,580)( 57,579)( 58,578)( 59,577)( 60,576)( 61,575)( 62,574)( 63,573)
( 64,572)( 65,571)( 66,570)( 67,569)( 68,568)( 69,567)( 70,566)( 71,565)
( 72,564)( 73,563)( 74,562)( 75,561)( 76,560)( 77,559)( 78,558)( 79,557)
( 80,556)( 81,555)( 82,554)( 83,553)( 84,552)( 85,551)( 86,550)( 87,549)
( 88,548)( 89,547)( 90,546)( 91,545)( 92,544)( 93,543)( 94,542)( 95,541)
( 96,540)( 97,539)( 98,538)( 99,537)(100,536)(101,535)(102,534)(103,533)
(104,532)(105,531)(106,530)(107,529)(108,528)(109,527)(110,526)(111,525)
(112,524)(113,523)(114,522)(115,521)(116,520)(117,519)(118,518)(119,517)
(120,516)(121,515)(122,514)(123,513)(124,512)(125,511)(126,510)(127,509)
(128,508)(129,507)(130,506)(131,505)(132,504)(133,503)(134,502)(135,501)
(136,500)(137,499)(138,498)(139,497)(140,496)(141,495)(142,494)(143,493)
(144,492)(145,491)(146,490)(147,489)(148,488)(149,487)(150,486)(151,485)
(152,484)(153,483)(154,482)(155,481)(156,480)(157,479)(158,478)(159,477)
(160,476)(161,475)(162,474)(163,473)(164,472)(165,471)(166,470)(167,469)
(168,468)(169,467)(170,466)(171,465)(172,464)(173,463)(174,462)(175,461)
(176,460)(177,459)(178,458)(179,457)(180,456)(181,455)(182,454)(183,453)
(184,452)(185,451)(186,450)(187,449)(188,448)(189,447)(190,446)(191,445)
(192,444)(193,443)(194,442)(195,441)(196,440)(197,439)(198,438)(199,437)
(200,436)(201,435)(202,434)(203,433)(204,432)(205,431)(206,430)(207,429)
(208,428)(209,427)(210,426)(211,425)(212,635)(213,634)(214,844)(215,843)
(216,842)(217,841)(218,840)(219,839)(220,838)(221,837)(222,836)(223,835)
(224,834)(225,833)(226,832)(227,831)(228,830)(229,829)(230,828)(231,827)
(232,826)(233,825)(234,824)(235,823)(236,822)(237,821)(238,820)(239,819)
(240,818)(241,817)(242,816)(243,815)(244,814)(245,813)(246,812)(247,811)
(248,810)(249,809)(250,808)(251,807)(252,806)(253,805)(254,804)(255,803)
(256,802)(257,801)(258,800)(259,799)(260,798)(261,797)(262,796)(263,795)
(264,794)(265,793)(266,792)(267,791)(268,790)(269,789)(270,788)(271,787)
(272,786)(273,785)(274,784)(275,783)(276,782)(277,781)(278,780)(279,779)
(280,778)(281,777)(282,776)(283,775)(284,774)(285,773)(286,772)(287,771)
(288,770)(289,769)(290,768)(291,767)(292,766)(293,765)(294,764)(295,763)
(296,762)(297,761)(298,760)(299,759)(300,758)(301,757)(302,756)(303,755)
(304,754)(305,753)(306,752)(307,751)(308,750)(309,749)(310,748)(311,747)
(312,746)(313,745)(314,744)(315,743)(316,742)(317,741)(318,740)(319,739)
(320,738)(321,737)(322,736)(323,735)(324,734)(325,733)(326,732)(327,731)
(328,730)(329,729)(330,728)(331,727)(332,726)(333,725)(334,724)(335,723)
(336,722)(337,721)(338,720)(339,719)(340,718)(341,717)(342,716)(343,715)
(344,714)(345,713)(346,712)(347,711)(348,710)(349,709)(350,708)(351,707)
(352,706)(353,705)(354,704)(355,703)(356,702)(357,701)(358,700)(359,699)
(360,698)(361,697)(362,696)(363,695)(364,694)(365,693)(366,692)(367,691)
(368,690)(369,689)(370,688)(371,687)(372,686)(373,685)(374,684)(375,683)
(376,682)(377,681)(378,680)(379,679)(380,678)(381,677)(382,676)(383,675)
(384,674)(385,673)(386,672)(387,671)(388,670)(389,669)(390,668)(391,667)
(392,666)(393,665)(394,664)(395,663)(396,662)(397,661)(398,660)(399,659)
(400,658)(401,657)(402,656)(403,655)(404,654)(405,653)(406,652)(407,651)
(408,650)(409,649)(410,648)(411,647)(412,646)(413,645)(414,644)(415,643)
(416,642)(417,641)(418,640)(419,639)(420,638)(421,637)(422,636);
poly := sub<Sym(844)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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