Polytope of Type {826}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {826}*1652
Also Known As : 826-gon, {826}. if this polytope has another name.
Group : SmallGroup(1652,8)
Rank : 2
Schlafli Type : {826}
Number of vertices, edges, etc : 826, 826
Order of s₀s₁ : 826
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 : {413}*826
   7-fold quotients : {118}*236
   14-fold quotients : {59}*118
   59-fold quotients : {14}*28
   118-fold quotients : {7}*14
   413-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope