Polytope of Type {824}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {824}*1648
Also Known As : 824-gon, {824}. if this polytope has another name.
Group : SmallGroup(1648,26)
Rank : 2
Schlafli Type : {824}
Number of vertices, edges, etc : 824, 824
Order of s0s1 : 824
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 : {412}*824
4-fold quotients : {206}*412
8-fold quotients : {103}*206
103-fold quotients : {8}*16
206-fold quotients : {4}*8
412-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2,103)( 3,102)( 4,101)( 5,100)( 6, 99)( 7, 98)( 8, 97)( 9, 96)
( 10, 95)( 11, 94)( 12, 93)( 13, 92)( 14, 91)( 15, 90)( 16, 89)( 17, 88)
( 18, 87)( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 82)( 24, 81)( 25, 80)
( 26, 79)( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31, 74)( 32, 73)( 33, 72)
( 34, 71)( 35, 70)( 36, 69)( 37, 68)( 38, 67)( 39, 66)( 40, 65)( 41, 64)
( 42, 63)( 43, 62)( 44, 61)( 45, 60)( 46, 59)( 47, 58)( 48, 57)( 49, 56)
( 50, 55)( 51, 54)( 52, 53)(105,206)(106,205)(107,204)(108,203)(109,202)
(110,201)(111,200)(112,199)(113,198)(114,197)(115,196)(116,195)(117,194)
(118,193)(119,192)(120,191)(121,190)(122,189)(123,188)(124,187)(125,186)
(126,185)(127,184)(128,183)(129,182)(130,181)(131,180)(132,179)(133,178)
(134,177)(135,176)(136,175)(137,174)(138,173)(139,172)(140,171)(141,170)
(142,169)(143,168)(144,167)(145,166)(146,165)(147,164)(148,163)(149,162)
(150,161)(151,160)(152,159)(153,158)(154,157)(155,156)(207,310)(208,412)
(209,411)(210,410)(211,409)(212,408)(213,407)(214,406)(215,405)(216,404)
(217,403)(218,402)(219,401)(220,400)(221,399)(222,398)(223,397)(224,396)
(225,395)(226,394)(227,393)(228,392)(229,391)(230,390)(231,389)(232,388)
(233,387)(234,386)(235,385)(236,384)(237,383)(238,382)(239,381)(240,380)
(241,379)(242,378)(243,377)(244,376)(245,375)(246,374)(247,373)(248,372)
(249,371)(250,370)(251,369)(252,368)(253,367)(254,366)(255,365)(256,364)
(257,363)(258,362)(259,361)(260,360)(261,359)(262,358)(263,357)(264,356)
(265,355)(266,354)(267,353)(268,352)(269,351)(270,350)(271,349)(272,348)
(273,347)(274,346)(275,345)(276,344)(277,343)(278,342)(279,341)(280,340)
(281,339)(282,338)(283,337)(284,336)(285,335)(286,334)(287,333)(288,332)
(289,331)(290,330)(291,329)(292,328)(293,327)(294,326)(295,325)(296,324)
(297,323)(298,322)(299,321)(300,320)(301,319)(302,318)(303,317)(304,316)
(305,315)(306,314)(307,313)(308,312)(309,311)(413,619)(414,721)(415,720)
(416,719)(417,718)(418,717)(419,716)(420,715)(421,714)(422,713)(423,712)
(424,711)(425,710)(426,709)(427,708)(428,707)(429,706)(430,705)(431,704)
(432,703)(433,702)(434,701)(435,700)(436,699)(437,698)(438,697)(439,696)
(440,695)(441,694)(442,693)(443,692)(444,691)(445,690)(446,689)(447,688)
(448,687)(449,686)(450,685)(451,684)(452,683)(453,682)(454,681)(455,680)
(456,679)(457,678)(458,677)(459,676)(460,675)(461,674)(462,673)(463,672)
(464,671)(465,670)(466,669)(467,668)(468,667)(469,666)(470,665)(471,664)
(472,663)(473,662)(474,661)(475,660)(476,659)(477,658)(478,657)(479,656)
(480,655)(481,654)(482,653)(483,652)(484,651)(485,650)(486,649)(487,648)
(488,647)(489,646)(490,645)(491,644)(492,643)(493,642)(494,641)(495,640)
(496,639)(497,638)(498,637)(499,636)(500,635)(501,634)(502,633)(503,632)
(504,631)(505,630)(506,629)(507,628)(508,627)(509,626)(510,625)(511,624)
(512,623)(513,622)(514,621)(515,620)(516,722)(517,824)(518,823)(519,822)
(520,821)(521,820)(522,819)(523,818)(524,817)(525,816)(526,815)(527,814)
(528,813)(529,812)(530,811)(531,810)(532,809)(533,808)(534,807)(535,806)
(536,805)(537,804)(538,803)(539,802)(540,801)(541,800)(542,799)(543,798)
(544,797)(545,796)(546,795)(547,794)(548,793)(549,792)(550,791)(551,790)
(552,789)(553,788)(554,787)(555,786)(556,785)(557,784)(558,783)(559,782)
(560,781)(561,780)(562,779)(563,778)(564,777)(565,776)(566,775)(567,774)
(568,773)(569,772)(570,771)(571,770)(572,769)(573,768)(574,767)(575,766)
(576,765)(577,764)(578,763)(579,762)(580,761)(581,760)(582,759)(583,758)
(584,757)(585,756)(586,755)(587,754)(588,753)(589,752)(590,751)(591,750)
(592,749)(593,748)(594,747)(595,746)(596,745)(597,744)(598,743)(599,742)
(600,741)(601,740)(602,739)(603,738)(604,737)(605,736)(606,735)(607,734)
(608,733)(609,732)(610,731)(611,730)(612,729)(613,728)(614,727)(615,726)
(616,725)(617,724)(618,723);;
s1 := ( 1,414)( 2,413)( 3,515)( 4,514)( 5,513)( 6,512)( 7,511)( 8,510)
( 9,509)( 10,508)( 11,507)( 12,506)( 13,505)( 14,504)( 15,503)( 16,502)
( 17,501)( 18,500)( 19,499)( 20,498)( 21,497)( 22,496)( 23,495)( 24,494)
( 25,493)( 26,492)( 27,491)( 28,490)( 29,489)( 30,488)( 31,487)( 32,486)
( 33,485)( 34,484)( 35,483)( 36,482)( 37,481)( 38,480)( 39,479)( 40,478)
( 41,477)( 42,476)( 43,475)( 44,474)( 45,473)( 46,472)( 47,471)( 48,470)
( 49,469)( 50,468)( 51,467)( 52,466)( 53,465)( 54,464)( 55,463)( 56,462)
( 57,461)( 58,460)( 59,459)( 60,458)( 61,457)( 62,456)( 63,455)( 64,454)
( 65,453)( 66,452)( 67,451)( 68,450)( 69,449)( 70,448)( 71,447)( 72,446)
( 73,445)( 74,444)( 75,443)( 76,442)( 77,441)( 78,440)( 79,439)( 80,438)
( 81,437)( 82,436)( 83,435)( 84,434)( 85,433)( 86,432)( 87,431)( 88,430)
( 89,429)( 90,428)( 91,427)( 92,426)( 93,425)( 94,424)( 95,423)( 96,422)
( 97,421)( 98,420)( 99,419)(100,418)(101,417)(102,416)(103,415)(104,517)
(105,516)(106,618)(107,617)(108,616)(109,615)(110,614)(111,613)(112,612)
(113,611)(114,610)(115,609)(116,608)(117,607)(118,606)(119,605)(120,604)
(121,603)(122,602)(123,601)(124,600)(125,599)(126,598)(127,597)(128,596)
(129,595)(130,594)(131,593)(132,592)(133,591)(134,590)(135,589)(136,588)
(137,587)(138,586)(139,585)(140,584)(141,583)(142,582)(143,581)(144,580)
(145,579)(146,578)(147,577)(148,576)(149,575)(150,574)(151,573)(152,572)
(153,571)(154,570)(155,569)(156,568)(157,567)(158,566)(159,565)(160,564)
(161,563)(162,562)(163,561)(164,560)(165,559)(166,558)(167,557)(168,556)
(169,555)(170,554)(171,553)(172,552)(173,551)(174,550)(175,549)(176,548)
(177,547)(178,546)(179,545)(180,544)(181,543)(182,542)(183,541)(184,540)
(185,539)(186,538)(187,537)(188,536)(189,535)(190,534)(191,533)(192,532)
(193,531)(194,530)(195,529)(196,528)(197,527)(198,526)(199,525)(200,524)
(201,523)(202,522)(203,521)(204,520)(205,519)(206,518)(207,723)(208,722)
(209,824)(210,823)(211,822)(212,821)(213,820)(214,819)(215,818)(216,817)
(217,816)(218,815)(219,814)(220,813)(221,812)(222,811)(223,810)(224,809)
(225,808)(226,807)(227,806)(228,805)(229,804)(230,803)(231,802)(232,801)
(233,800)(234,799)(235,798)(236,797)(237,796)(238,795)(239,794)(240,793)
(241,792)(242,791)(243,790)(244,789)(245,788)(246,787)(247,786)(248,785)
(249,784)(250,783)(251,782)(252,781)(253,780)(254,779)(255,778)(256,777)
(257,776)(258,775)(259,774)(260,773)(261,772)(262,771)(263,770)(264,769)
(265,768)(266,767)(267,766)(268,765)(269,764)(270,763)(271,762)(272,761)
(273,760)(274,759)(275,758)(276,757)(277,756)(278,755)(279,754)(280,753)
(281,752)(282,751)(283,750)(284,749)(285,748)(286,747)(287,746)(288,745)
(289,744)(290,743)(291,742)(292,741)(293,740)(294,739)(295,738)(296,737)
(297,736)(298,735)(299,734)(300,733)(301,732)(302,731)(303,730)(304,729)
(305,728)(306,727)(307,726)(308,725)(309,724)(310,620)(311,619)(312,721)
(313,720)(314,719)(315,718)(316,717)(317,716)(318,715)(319,714)(320,713)
(321,712)(322,711)(323,710)(324,709)(325,708)(326,707)(327,706)(328,705)
(329,704)(330,703)(331,702)(332,701)(333,700)(334,699)(335,698)(336,697)
(337,696)(338,695)(339,694)(340,693)(341,692)(342,691)(343,690)(344,689)
(345,688)(346,687)(347,686)(348,685)(349,684)(350,683)(351,682)(352,681)
(353,680)(354,679)(355,678)(356,677)(357,676)(358,675)(359,674)(360,673)
(361,672)(362,671)(363,670)(364,669)(365,668)(366,667)(367,666)(368,665)
(369,664)(370,663)(371,662)(372,661)(373,660)(374,659)(375,658)(376,657)
(377,656)(378,655)(379,654)(380,653)(381,652)(382,651)(383,650)(384,649)
(385,648)(386,647)(387,646)(388,645)(389,644)(390,643)(391,642)(392,641)
(393,640)(394,639)(395,638)(396,637)(397,636)(398,635)(399,634)(400,633)
(401,632)(402,631)(403,630)(404,629)(405,628)(406,627)(407,626)(408,625)
(409,624)(410,623)(411,622)(412,621);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(824)!( 2,103)( 3,102)( 4,101)( 5,100)( 6, 99)( 7, 98)( 8, 97)
( 9, 96)( 10, 95)( 11, 94)( 12, 93)( 13, 92)( 14, 91)( 15, 90)( 16, 89)
( 17, 88)( 18, 87)( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 82)( 24, 81)
( 25, 80)( 26, 79)( 27, 78)( 28, 77)( 29, 76)( 30, 75)( 31, 74)( 32, 73)
( 33, 72)( 34, 71)( 35, 70)( 36, 69)( 37, 68)( 38, 67)( 39, 66)( 40, 65)
( 41, 64)( 42, 63)( 43, 62)( 44, 61)( 45, 60)( 46, 59)( 47, 58)( 48, 57)
( 49, 56)( 50, 55)( 51, 54)( 52, 53)(105,206)(106,205)(107,204)(108,203)
(109,202)(110,201)(111,200)(112,199)(113,198)(114,197)(115,196)(116,195)
(117,194)(118,193)(119,192)(120,191)(121,190)(122,189)(123,188)(124,187)
(125,186)(126,185)(127,184)(128,183)(129,182)(130,181)(131,180)(132,179)
(133,178)(134,177)(135,176)(136,175)(137,174)(138,173)(139,172)(140,171)
(141,170)(142,169)(143,168)(144,167)(145,166)(146,165)(147,164)(148,163)
(149,162)(150,161)(151,160)(152,159)(153,158)(154,157)(155,156)(207,310)
(208,412)(209,411)(210,410)(211,409)(212,408)(213,407)(214,406)(215,405)
(216,404)(217,403)(218,402)(219,401)(220,400)(221,399)(222,398)(223,397)
(224,396)(225,395)(226,394)(227,393)(228,392)(229,391)(230,390)(231,389)
(232,388)(233,387)(234,386)(235,385)(236,384)(237,383)(238,382)(239,381)
(240,380)(241,379)(242,378)(243,377)(244,376)(245,375)(246,374)(247,373)
(248,372)(249,371)(250,370)(251,369)(252,368)(253,367)(254,366)(255,365)
(256,364)(257,363)(258,362)(259,361)(260,360)(261,359)(262,358)(263,357)
(264,356)(265,355)(266,354)(267,353)(268,352)(269,351)(270,350)(271,349)
(272,348)(273,347)(274,346)(275,345)(276,344)(277,343)(278,342)(279,341)
(280,340)(281,339)(282,338)(283,337)(284,336)(285,335)(286,334)(287,333)
(288,332)(289,331)(290,330)(291,329)(292,328)(293,327)(294,326)(295,325)
(296,324)(297,323)(298,322)(299,321)(300,320)(301,319)(302,318)(303,317)
(304,316)(305,315)(306,314)(307,313)(308,312)(309,311)(413,619)(414,721)
(415,720)(416,719)(417,718)(418,717)(419,716)(420,715)(421,714)(422,713)
(423,712)(424,711)(425,710)(426,709)(427,708)(428,707)(429,706)(430,705)
(431,704)(432,703)(433,702)(434,701)(435,700)(436,699)(437,698)(438,697)
(439,696)(440,695)(441,694)(442,693)(443,692)(444,691)(445,690)(446,689)
(447,688)(448,687)(449,686)(450,685)(451,684)(452,683)(453,682)(454,681)
(455,680)(456,679)(457,678)(458,677)(459,676)(460,675)(461,674)(462,673)
(463,672)(464,671)(465,670)(466,669)(467,668)(468,667)(469,666)(470,665)
(471,664)(472,663)(473,662)(474,661)(475,660)(476,659)(477,658)(478,657)
(479,656)(480,655)(481,654)(482,653)(483,652)(484,651)(485,650)(486,649)
(487,648)(488,647)(489,646)(490,645)(491,644)(492,643)(493,642)(494,641)
(495,640)(496,639)(497,638)(498,637)(499,636)(500,635)(501,634)(502,633)
(503,632)(504,631)(505,630)(506,629)(507,628)(508,627)(509,626)(510,625)
(511,624)(512,623)(513,622)(514,621)(515,620)(516,722)(517,824)(518,823)
(519,822)(520,821)(521,820)(522,819)(523,818)(524,817)(525,816)(526,815)
(527,814)(528,813)(529,812)(530,811)(531,810)(532,809)(533,808)(534,807)
(535,806)(536,805)(537,804)(538,803)(539,802)(540,801)(541,800)(542,799)
(543,798)(544,797)(545,796)(546,795)(547,794)(548,793)(549,792)(550,791)
(551,790)(552,789)(553,788)(554,787)(555,786)(556,785)(557,784)(558,783)
(559,782)(560,781)(561,780)(562,779)(563,778)(564,777)(565,776)(566,775)
(567,774)(568,773)(569,772)(570,771)(571,770)(572,769)(573,768)(574,767)
(575,766)(576,765)(577,764)(578,763)(579,762)(580,761)(581,760)(582,759)
(583,758)(584,757)(585,756)(586,755)(587,754)(588,753)(589,752)(590,751)
(591,750)(592,749)(593,748)(594,747)(595,746)(596,745)(597,744)(598,743)
(599,742)(600,741)(601,740)(602,739)(603,738)(604,737)(605,736)(606,735)
(607,734)(608,733)(609,732)(610,731)(611,730)(612,729)(613,728)(614,727)
(615,726)(616,725)(617,724)(618,723);
s1 := Sym(824)!( 1,414)( 2,413)( 3,515)( 4,514)( 5,513)( 6,512)( 7,511)
( 8,510)( 9,509)( 10,508)( 11,507)( 12,506)( 13,505)( 14,504)( 15,503)
( 16,502)( 17,501)( 18,500)( 19,499)( 20,498)( 21,497)( 22,496)( 23,495)
( 24,494)( 25,493)( 26,492)( 27,491)( 28,490)( 29,489)( 30,488)( 31,487)
( 32,486)( 33,485)( 34,484)( 35,483)( 36,482)( 37,481)( 38,480)( 39,479)
( 40,478)( 41,477)( 42,476)( 43,475)( 44,474)( 45,473)( 46,472)( 47,471)
( 48,470)( 49,469)( 50,468)( 51,467)( 52,466)( 53,465)( 54,464)( 55,463)
( 56,462)( 57,461)( 58,460)( 59,459)( 60,458)( 61,457)( 62,456)( 63,455)
( 64,454)( 65,453)( 66,452)( 67,451)( 68,450)( 69,449)( 70,448)( 71,447)
( 72,446)( 73,445)( 74,444)( 75,443)( 76,442)( 77,441)( 78,440)( 79,439)
( 80,438)( 81,437)( 82,436)( 83,435)( 84,434)( 85,433)( 86,432)( 87,431)
( 88,430)( 89,429)( 90,428)( 91,427)( 92,426)( 93,425)( 94,424)( 95,423)
( 96,422)( 97,421)( 98,420)( 99,419)(100,418)(101,417)(102,416)(103,415)
(104,517)(105,516)(106,618)(107,617)(108,616)(109,615)(110,614)(111,613)
(112,612)(113,611)(114,610)(115,609)(116,608)(117,607)(118,606)(119,605)
(120,604)(121,603)(122,602)(123,601)(124,600)(125,599)(126,598)(127,597)
(128,596)(129,595)(130,594)(131,593)(132,592)(133,591)(134,590)(135,589)
(136,588)(137,587)(138,586)(139,585)(140,584)(141,583)(142,582)(143,581)
(144,580)(145,579)(146,578)(147,577)(148,576)(149,575)(150,574)(151,573)
(152,572)(153,571)(154,570)(155,569)(156,568)(157,567)(158,566)(159,565)
(160,564)(161,563)(162,562)(163,561)(164,560)(165,559)(166,558)(167,557)
(168,556)(169,555)(170,554)(171,553)(172,552)(173,551)(174,550)(175,549)
(176,548)(177,547)(178,546)(179,545)(180,544)(181,543)(182,542)(183,541)
(184,540)(185,539)(186,538)(187,537)(188,536)(189,535)(190,534)(191,533)
(192,532)(193,531)(194,530)(195,529)(196,528)(197,527)(198,526)(199,525)
(200,524)(201,523)(202,522)(203,521)(204,520)(205,519)(206,518)(207,723)
(208,722)(209,824)(210,823)(211,822)(212,821)(213,820)(214,819)(215,818)
(216,817)(217,816)(218,815)(219,814)(220,813)(221,812)(222,811)(223,810)
(224,809)(225,808)(226,807)(227,806)(228,805)(229,804)(230,803)(231,802)
(232,801)(233,800)(234,799)(235,798)(236,797)(237,796)(238,795)(239,794)
(240,793)(241,792)(242,791)(243,790)(244,789)(245,788)(246,787)(247,786)
(248,785)(249,784)(250,783)(251,782)(252,781)(253,780)(254,779)(255,778)
(256,777)(257,776)(258,775)(259,774)(260,773)(261,772)(262,771)(263,770)
(264,769)(265,768)(266,767)(267,766)(268,765)(269,764)(270,763)(271,762)
(272,761)(273,760)(274,759)(275,758)(276,757)(277,756)(278,755)(279,754)
(280,753)(281,752)(282,751)(283,750)(284,749)(285,748)(286,747)(287,746)
(288,745)(289,744)(290,743)(291,742)(292,741)(293,740)(294,739)(295,738)
(296,737)(297,736)(298,735)(299,734)(300,733)(301,732)(302,731)(303,730)
(304,729)(305,728)(306,727)(307,726)(308,725)(309,724)(310,620)(311,619)
(312,721)(313,720)(314,719)(315,718)(316,717)(317,716)(318,715)(319,714)
(320,713)(321,712)(322,711)(323,710)(324,709)(325,708)(326,707)(327,706)
(328,705)(329,704)(330,703)(331,702)(332,701)(333,700)(334,699)(335,698)
(336,697)(337,696)(338,695)(339,694)(340,693)(341,692)(342,691)(343,690)
(344,689)(345,688)(346,687)(347,686)(348,685)(349,684)(350,683)(351,682)
(352,681)(353,680)(354,679)(355,678)(356,677)(357,676)(358,675)(359,674)
(360,673)(361,672)(362,671)(363,670)(364,669)(365,668)(366,667)(367,666)
(368,665)(369,664)(370,663)(371,662)(372,661)(373,660)(374,659)(375,658)
(376,657)(377,656)(378,655)(379,654)(380,653)(381,652)(382,651)(383,650)
(384,649)(385,648)(386,647)(387,646)(388,645)(389,644)(390,643)(391,642)
(392,641)(393,640)(394,639)(395,638)(396,637)(397,636)(398,635)(399,634)
(400,633)(401,632)(402,631)(403,630)(404,629)(405,628)(406,627)(407,626)
(408,625)(409,624)(410,623)(411,622)(412,621);
poly := sub<Sym(824)|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 >;
References : None.
to this polytope