Polytope of Type {828}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {828}*1656
Also Known As : 828-gon, {828}. if this polytope has another name.
Group : SmallGroup(1656,25)
Rank : 2
Schlafli Type : {828}
Number of vertices, edges, etc : 828, 828
Order of s₀s₁ : 828
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 : {414}*828
   3-fold quotients : {276}*552
   4-fold quotients : {207}*414
   6-fold quotients : {138}*276
   9-fold quotients : {92}*184
   12-fold quotients : {69}*138
   18-fold quotients : {46}*92
   23-fold quotients : {36}*72
   36-fold quotients : {23}*46
   46-fold quotients : {18}*36
   69-fold quotients : {12}*24
   92-fold quotients : {9}*18
   138-fold quotients : {6}*12
   207-fold quotients : {4}*8
   276-fold quotients : {3}*6
   414-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope