Polytope of Type {856}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {856}*1712
Also Known As : 856-gon, {856}. if this polytope has another name.
Group : SmallGroup(1712,26)
Rank : 2
Schlafli Type : {856}
Number of vertices, edges, etc : 856, 856
Order of s₀s₁ : 856
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 : {428}*856
   4-fold quotients : {214}*428
   8-fold quotients : {107}*214
   107-fold quotients : {8}*16
   214-fold quotients : {4}*8
   428-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,107)(  3,106)(  4,105)(  5,104)(  6,103)(  7,102)(  8,101)(  9,100)
( 10, 99)( 11, 98)( 12, 97)( 13, 96)( 14, 95)( 15, 94)( 16, 93)( 17, 92)
( 18, 91)( 19, 90)( 20, 89)( 21, 88)( 22, 87)( 23, 86)( 24, 85)( 25, 84)
( 26, 83)( 27, 82)( 28, 81)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 76)
( 34, 75)( 35, 74)( 36, 73)( 37, 72)( 38, 71)( 39, 70)( 40, 69)( 41, 68)
( 42, 67)( 43, 66)( 44, 65)( 45, 64)( 46, 63)( 47, 62)( 48, 61)( 49, 60)
( 50, 59)( 51, 58)( 52, 57)( 53, 56)( 54, 55)(109,214)(110,213)(111,212)
(112,211)(113,210)(114,209)(115,208)(116,207)(117,206)(118,205)(119,204)
(120,203)(121,202)(122,201)(123,200)(124,199)(125,198)(126,197)(127,196)
(128,195)(129,194)(130,193)(131,192)(132,191)(133,190)(134,189)(135,188)
(136,187)(137,186)(138,185)(139,184)(140,183)(141,182)(142,181)(143,180)
(144,179)(145,178)(146,177)(147,176)(148,175)(149,174)(150,173)(151,172)
(152,171)(153,170)(154,169)(155,168)(156,167)(157,166)(158,165)(159,164)
(160,163)(161,162)(215,322)(216,428)(217,427)(218,426)(219,425)(220,424)
(221,423)(222,422)(223,421)(224,420)(225,419)(226,418)(227,417)(228,416)
(229,415)(230,414)(231,413)(232,412)(233,411)(234,410)(235,409)(236,408)
(237,407)(238,406)(239,405)(240,404)(241,403)(242,402)(243,401)(244,400)
(245,399)(246,398)(247,397)(248,396)(249,395)(250,394)(251,393)(252,392)
(253,391)(254,390)(255,389)(256,388)(257,387)(258,386)(259,385)(260,384)
(261,383)(262,382)(263,381)(264,380)(265,379)(266,378)(267,377)(268,376)
(269,375)(270,374)(271,373)(272,372)(273,371)(274,370)(275,369)(276,368)
(277,367)(278,366)(279,365)(280,364)(281,363)(282,362)(283,361)(284,360)
(285,359)(286,358)(287,357)(288,356)(289,355)(290,354)(291,353)(292,352)
(293,351)(294,350)(295,349)(296,348)(297,347)(298,346)(299,345)(300,344)
(301,343)(302,342)(303,341)(304,340)(305,339)(306,338)(307,337)(308,336)
(309,335)(310,334)(311,333)(312,332)(313,331)(314,330)(315,329)(316,328)
(317,327)(318,326)(319,325)(320,324)(321,323)(429,643)(430,749)(431,748)
(432,747)(433,746)(434,745)(435,744)(436,743)(437,742)(438,741)(439,740)
(440,739)(441,738)(442,737)(443,736)(444,735)(445,734)(446,733)(447,732)
(448,731)(449,730)(450,729)(451,728)(452,727)(453,726)(454,725)(455,724)
(456,723)(457,722)(458,721)(459,720)(460,719)(461,718)(462,717)(463,716)
(464,715)(465,714)(466,713)(467,712)(468,711)(469,710)(470,709)(471,708)
(472,707)(473,706)(474,705)(475,704)(476,703)(477,702)(478,701)(479,700)
(480,699)(481,698)(482,697)(483,696)(484,695)(485,694)(486,693)(487,692)
(488,691)(489,690)(490,689)(491,688)(492,687)(493,686)(494,685)(495,684)
(496,683)(497,682)(498,681)(499,680)(500,679)(501,678)(502,677)(503,676)
(504,675)(505,674)(506,673)(507,672)(508,671)(509,670)(510,669)(511,668)
(512,667)(513,666)(514,665)(515,664)(516,663)(517,662)(518,661)(519,660)
(520,659)(521,658)(522,657)(523,656)(524,655)(525,654)(526,653)(527,652)
(528,651)(529,650)(530,649)(531,648)(532,647)(533,646)(534,645)(535,644)
(536,750)(537,856)(538,855)(539,854)(540,853)(541,852)(542,851)(543,850)
(544,849)(545,848)(546,847)(547,846)(548,845)(549,844)(550,843)(551,842)
(552,841)(553,840)(554,839)(555,838)(556,837)(557,836)(558,835)(559,834)
(560,833)(561,832)(562,831)(563,830)(564,829)(565,828)(566,827)(567,826)
(568,825)(569,824)(570,823)(571,822)(572,821)(573,820)(574,819)(575,818)
(576,817)(577,816)(578,815)(579,814)(580,813)(581,812)(582,811)(583,810)
(584,809)(585,808)(586,807)(587,806)(588,805)(589,804)(590,803)(591,802)
(592,801)(593,800)(594,799)(595,798)(596,797)(597,796)(598,795)(599,794)
(600,793)(601,792)(602,791)(603,790)(604,789)(605,788)(606,787)(607,786)
(608,785)(609,784)(610,783)(611,782)(612,781)(613,780)(614,779)(615,778)
(616,777)(617,776)(618,775)(619,774)(620,773)(621,772)(622,771)(623,770)
(624,769)(625,768)(626,767)(627,766)(628,765)(629,764)(630,763)(631,762)
(632,761)(633,760)(634,759)(635,758)(636,757)(637,756)(638,755)(639,754)
(640,753)(641,752)(642,751);;
s1 := (  1,430)(  2,429)(  3,535)(  4,534)(  5,533)(  6,532)(  7,531)(  8,530)
(  9,529)( 10,528)( 11,527)( 12,526)( 13,525)( 14,524)( 15,523)( 16,522)
( 17,521)( 18,520)( 19,519)( 20,518)( 21,517)( 22,516)( 23,515)( 24,514)
( 25,513)( 26,512)( 27,511)( 28,510)( 29,509)( 30,508)( 31,507)( 32,506)
( 33,505)( 34,504)( 35,503)( 36,502)( 37,501)( 38,500)( 39,499)( 40,498)
( 41,497)( 42,496)( 43,495)( 44,494)( 45,493)( 46,492)( 47,491)( 48,490)
( 49,489)( 50,488)( 51,487)( 52,486)( 53,485)( 54,484)( 55,483)( 56,482)
( 57,481)( 58,480)( 59,479)( 60,478)( 61,477)( 62,476)( 63,475)( 64,474)
( 65,473)( 66,472)( 67,471)( 68,470)( 69,469)( 70,468)( 71,467)( 72,466)
( 73,465)( 74,464)( 75,463)( 76,462)( 77,461)( 78,460)( 79,459)( 80,458)
( 81,457)( 82,456)( 83,455)( 84,454)( 85,453)( 86,452)( 87,451)( 88,450)
( 89,449)( 90,448)( 91,447)( 92,446)( 93,445)( 94,444)( 95,443)( 96,442)
( 97,441)( 98,440)( 99,439)(100,438)(101,437)(102,436)(103,435)(104,434)
(105,433)(106,432)(107,431)(108,537)(109,536)(110,642)(111,641)(112,640)
(113,639)(114,638)(115,637)(116,636)(117,635)(118,634)(119,633)(120,632)
(121,631)(122,630)(123,629)(124,628)(125,627)(126,626)(127,625)(128,624)
(129,623)(130,622)(131,621)(132,620)(133,619)(134,618)(135,617)(136,616)
(137,615)(138,614)(139,613)(140,612)(141,611)(142,610)(143,609)(144,608)
(145,607)(146,606)(147,605)(148,604)(149,603)(150,602)(151,601)(152,600)
(153,599)(154,598)(155,597)(156,596)(157,595)(158,594)(159,593)(160,592)
(161,591)(162,590)(163,589)(164,588)(165,587)(166,586)(167,585)(168,584)
(169,583)(170,582)(171,581)(172,580)(173,579)(174,578)(175,577)(176,576)
(177,575)(178,574)(179,573)(180,572)(181,571)(182,570)(183,569)(184,568)
(185,567)(186,566)(187,565)(188,564)(189,563)(190,562)(191,561)(192,560)
(193,559)(194,558)(195,557)(196,556)(197,555)(198,554)(199,553)(200,552)
(201,551)(202,550)(203,549)(204,548)(205,547)(206,546)(207,545)(208,544)
(209,543)(210,542)(211,541)(212,540)(213,539)(214,538)(215,751)(216,750)
(217,856)(218,855)(219,854)(220,853)(221,852)(222,851)(223,850)(224,849)
(225,848)(226,847)(227,846)(228,845)(229,844)(230,843)(231,842)(232,841)
(233,840)(234,839)(235,838)(236,837)(237,836)(238,835)(239,834)(240,833)
(241,832)(242,831)(243,830)(244,829)(245,828)(246,827)(247,826)(248,825)
(249,824)(250,823)(251,822)(252,821)(253,820)(254,819)(255,818)(256,817)
(257,816)(258,815)(259,814)(260,813)(261,812)(262,811)(263,810)(264,809)
(265,808)(266,807)(267,806)(268,805)(269,804)(270,803)(271,802)(272,801)
(273,800)(274,799)(275,798)(276,797)(277,796)(278,795)(279,794)(280,793)
(281,792)(282,791)(283,790)(284,789)(285,788)(286,787)(287,786)(288,785)
(289,784)(290,783)(291,782)(292,781)(293,780)(294,779)(295,778)(296,777)
(297,776)(298,775)(299,774)(300,773)(301,772)(302,771)(303,770)(304,769)
(305,768)(306,767)(307,766)(308,765)(309,764)(310,763)(311,762)(312,761)
(313,760)(314,759)(315,758)(316,757)(317,756)(318,755)(319,754)(320,753)
(321,752)(322,644)(323,643)(324,749)(325,748)(326,747)(327,746)(328,745)
(329,744)(330,743)(331,742)(332,741)(333,740)(334,739)(335,738)(336,737)
(337,736)(338,735)(339,734)(340,733)(341,732)(342,731)(343,730)(344,729)
(345,728)(346,727)(347,726)(348,725)(349,724)(350,723)(351,722)(352,721)
(353,720)(354,719)(355,718)(356,717)(357,716)(358,715)(359,714)(360,713)
(361,712)(362,711)(363,710)(364,709)(365,708)(366,707)(367,706)(368,705)
(369,704)(370,703)(371,702)(372,701)(373,700)(374,699)(375,698)(376,697)
(377,696)(378,695)(379,694)(380,693)(381,692)(382,691)(383,690)(384,689)
(385,688)(386,687)(387,686)(388,685)(389,684)(390,683)(391,682)(392,681)
(393,680)(394,679)(395,678)(396,677)(397,676)(398,675)(399,674)(400,673)
(401,672)(402,671)(403,670)(404,669)(405,668)(406,667)(407,666)(408,665)
(409,664)(410,663)(411,662)(412,661)(413,660)(414,659)(415,658)(416,657)
(417,656)(418,655)(419,654)(420,653)(421,652)(422,651)(423,650)(424,649)
(425,648)(426,647)(427,646)(428,645);;
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*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(856)!(  2,107)(  3,106)(  4,105)(  5,104)(  6,103)(  7,102)(  8,101)
(  9,100)( 10, 99)( 11, 98)( 12, 97)( 13, 96)( 14, 95)( 15, 94)( 16, 93)
( 17, 92)( 18, 91)( 19, 90)( 20, 89)( 21, 88)( 22, 87)( 23, 86)( 24, 85)
( 25, 84)( 26, 83)( 27, 82)( 28, 81)( 29, 80)( 30, 79)( 31, 78)( 32, 77)
( 33, 76)( 34, 75)( 35, 74)( 36, 73)( 37, 72)( 38, 71)( 39, 70)( 40, 69)
( 41, 68)( 42, 67)( 43, 66)( 44, 65)( 45, 64)( 46, 63)( 47, 62)( 48, 61)
( 49, 60)( 50, 59)( 51, 58)( 52, 57)( 53, 56)( 54, 55)(109,214)(110,213)
(111,212)(112,211)(113,210)(114,209)(115,208)(116,207)(117,206)(118,205)
(119,204)(120,203)(121,202)(122,201)(123,200)(124,199)(125,198)(126,197)
(127,196)(128,195)(129,194)(130,193)(131,192)(132,191)(133,190)(134,189)
(135,188)(136,187)(137,186)(138,185)(139,184)(140,183)(141,182)(142,181)
(143,180)(144,179)(145,178)(146,177)(147,176)(148,175)(149,174)(150,173)
(151,172)(152,171)(153,170)(154,169)(155,168)(156,167)(157,166)(158,165)
(159,164)(160,163)(161,162)(215,322)(216,428)(217,427)(218,426)(219,425)
(220,424)(221,423)(222,422)(223,421)(224,420)(225,419)(226,418)(227,417)
(228,416)(229,415)(230,414)(231,413)(232,412)(233,411)(234,410)(235,409)
(236,408)(237,407)(238,406)(239,405)(240,404)(241,403)(242,402)(243,401)
(244,400)(245,399)(246,398)(247,397)(248,396)(249,395)(250,394)(251,393)
(252,392)(253,391)(254,390)(255,389)(256,388)(257,387)(258,386)(259,385)
(260,384)(261,383)(262,382)(263,381)(264,380)(265,379)(266,378)(267,377)
(268,376)(269,375)(270,374)(271,373)(272,372)(273,371)(274,370)(275,369)
(276,368)(277,367)(278,366)(279,365)(280,364)(281,363)(282,362)(283,361)
(284,360)(285,359)(286,358)(287,357)(288,356)(289,355)(290,354)(291,353)
(292,352)(293,351)(294,350)(295,349)(296,348)(297,347)(298,346)(299,345)
(300,344)(301,343)(302,342)(303,341)(304,340)(305,339)(306,338)(307,337)
(308,336)(309,335)(310,334)(311,333)(312,332)(313,331)(314,330)(315,329)
(316,328)(317,327)(318,326)(319,325)(320,324)(321,323)(429,643)(430,749)
(431,748)(432,747)(433,746)(434,745)(435,744)(436,743)(437,742)(438,741)
(439,740)(440,739)(441,738)(442,737)(443,736)(444,735)(445,734)(446,733)
(447,732)(448,731)(449,730)(450,729)(451,728)(452,727)(453,726)(454,725)
(455,724)(456,723)(457,722)(458,721)(459,720)(460,719)(461,718)(462,717)
(463,716)(464,715)(465,714)(466,713)(467,712)(468,711)(469,710)(470,709)
(471,708)(472,707)(473,706)(474,705)(475,704)(476,703)(477,702)(478,701)
(479,700)(480,699)(481,698)(482,697)(483,696)(484,695)(485,694)(486,693)
(487,692)(488,691)(489,690)(490,689)(491,688)(492,687)(493,686)(494,685)
(495,684)(496,683)(497,682)(498,681)(499,680)(500,679)(501,678)(502,677)
(503,676)(504,675)(505,674)(506,673)(507,672)(508,671)(509,670)(510,669)
(511,668)(512,667)(513,666)(514,665)(515,664)(516,663)(517,662)(518,661)
(519,660)(520,659)(521,658)(522,657)(523,656)(524,655)(525,654)(526,653)
(527,652)(528,651)(529,650)(530,649)(531,648)(532,647)(533,646)(534,645)
(535,644)(536,750)(537,856)(538,855)(539,854)(540,853)(541,852)(542,851)
(543,850)(544,849)(545,848)(546,847)(547,846)(548,845)(549,844)(550,843)
(551,842)(552,841)(553,840)(554,839)(555,838)(556,837)(557,836)(558,835)
(559,834)(560,833)(561,832)(562,831)(563,830)(564,829)(565,828)(566,827)
(567,826)(568,825)(569,824)(570,823)(571,822)(572,821)(573,820)(574,819)
(575,818)(576,817)(577,816)(578,815)(579,814)(580,813)(581,812)(582,811)
(583,810)(584,809)(585,808)(586,807)(587,806)(588,805)(589,804)(590,803)
(591,802)(592,801)(593,800)(594,799)(595,798)(596,797)(597,796)(598,795)
(599,794)(600,793)(601,792)(602,791)(603,790)(604,789)(605,788)(606,787)
(607,786)(608,785)(609,784)(610,783)(611,782)(612,781)(613,780)(614,779)
(615,778)(616,777)(617,776)(618,775)(619,774)(620,773)(621,772)(622,771)
(623,770)(624,769)(625,768)(626,767)(627,766)(628,765)(629,764)(630,763)
(631,762)(632,761)(633,760)(634,759)(635,758)(636,757)(637,756)(638,755)
(639,754)(640,753)(641,752)(642,751);
s1 := Sym(856)!(  1,430)(  2,429)(  3,535)(  4,534)(  5,533)(  6,532)(  7,531)
(  8,530)(  9,529)( 10,528)( 11,527)( 12,526)( 13,525)( 14,524)( 15,523)
( 16,522)( 17,521)( 18,520)( 19,519)( 20,518)( 21,517)( 22,516)( 23,515)
( 24,514)( 25,513)( 26,512)( 27,511)( 28,510)( 29,509)( 30,508)( 31,507)
( 32,506)( 33,505)( 34,504)( 35,503)( 36,502)( 37,501)( 38,500)( 39,499)
( 40,498)( 41,497)( 42,496)( 43,495)( 44,494)( 45,493)( 46,492)( 47,491)
( 48,490)( 49,489)( 50,488)( 51,487)( 52,486)( 53,485)( 54,484)( 55,483)
( 56,482)( 57,481)( 58,480)( 59,479)( 60,478)( 61,477)( 62,476)( 63,475)
( 64,474)( 65,473)( 66,472)( 67,471)( 68,470)( 69,469)( 70,468)( 71,467)
( 72,466)( 73,465)( 74,464)( 75,463)( 76,462)( 77,461)( 78,460)( 79,459)
( 80,458)( 81,457)( 82,456)( 83,455)( 84,454)( 85,453)( 86,452)( 87,451)
( 88,450)( 89,449)( 90,448)( 91,447)( 92,446)( 93,445)( 94,444)( 95,443)
( 96,442)( 97,441)( 98,440)( 99,439)(100,438)(101,437)(102,436)(103,435)
(104,434)(105,433)(106,432)(107,431)(108,537)(109,536)(110,642)(111,641)
(112,640)(113,639)(114,638)(115,637)(116,636)(117,635)(118,634)(119,633)
(120,632)(121,631)(122,630)(123,629)(124,628)(125,627)(126,626)(127,625)
(128,624)(129,623)(130,622)(131,621)(132,620)(133,619)(134,618)(135,617)
(136,616)(137,615)(138,614)(139,613)(140,612)(141,611)(142,610)(143,609)
(144,608)(145,607)(146,606)(147,605)(148,604)(149,603)(150,602)(151,601)
(152,600)(153,599)(154,598)(155,597)(156,596)(157,595)(158,594)(159,593)
(160,592)(161,591)(162,590)(163,589)(164,588)(165,587)(166,586)(167,585)
(168,584)(169,583)(170,582)(171,581)(172,580)(173,579)(174,578)(175,577)
(176,576)(177,575)(178,574)(179,573)(180,572)(181,571)(182,570)(183,569)
(184,568)(185,567)(186,566)(187,565)(188,564)(189,563)(190,562)(191,561)
(192,560)(193,559)(194,558)(195,557)(196,556)(197,555)(198,554)(199,553)
(200,552)(201,551)(202,550)(203,549)(204,548)(205,547)(206,546)(207,545)
(208,544)(209,543)(210,542)(211,541)(212,540)(213,539)(214,538)(215,751)
(216,750)(217,856)(218,855)(219,854)(220,853)(221,852)(222,851)(223,850)
(224,849)(225,848)(226,847)(227,846)(228,845)(229,844)(230,843)(231,842)
(232,841)(233,840)(234,839)(235,838)(236,837)(237,836)(238,835)(239,834)
(240,833)(241,832)(242,831)(243,830)(244,829)(245,828)(246,827)(247,826)
(248,825)(249,824)(250,823)(251,822)(252,821)(253,820)(254,819)(255,818)
(256,817)(257,816)(258,815)(259,814)(260,813)(261,812)(262,811)(263,810)
(264,809)(265,808)(266,807)(267,806)(268,805)(269,804)(270,803)(271,802)
(272,801)(273,800)(274,799)(275,798)(276,797)(277,796)(278,795)(279,794)
(280,793)(281,792)(282,791)(283,790)(284,789)(285,788)(286,787)(287,786)
(288,785)(289,784)(290,783)(291,782)(292,781)(293,780)(294,779)(295,778)
(296,777)(297,776)(298,775)(299,774)(300,773)(301,772)(302,771)(303,770)
(304,769)(305,768)(306,767)(307,766)(308,765)(309,764)(310,763)(311,762)
(312,761)(313,760)(314,759)(315,758)(316,757)(317,756)(318,755)(319,754)
(320,753)(321,752)(322,644)(323,643)(324,749)(325,748)(326,747)(327,746)
(328,745)(329,744)(330,743)(331,742)(332,741)(333,740)(334,739)(335,738)
(336,737)(337,736)(338,735)(339,734)(340,733)(341,732)(342,731)(343,730)
(344,729)(345,728)(346,727)(347,726)(348,725)(349,724)(350,723)(351,722)
(352,721)(353,720)(354,719)(355,718)(356,717)(357,716)(358,715)(359,714)
(360,713)(361,712)(362,711)(363,710)(364,709)(365,708)(366,707)(367,706)
(368,705)(369,704)(370,703)(371,702)(372,701)(373,700)(374,699)(375,698)
(376,697)(377,696)(378,695)(379,694)(380,693)(381,692)(382,691)(383,690)
(384,689)(385,688)(386,687)(387,686)(388,685)(389,684)(390,683)(391,682)
(392,681)(393,680)(394,679)(395,678)(396,677)(397,676)(398,675)(399,674)
(400,673)(401,672)(402,671)(403,670)(404,669)(405,668)(406,667)(407,666)
(408,665)(409,664)(410,663)(411,662)(412,661)(413,660)(414,659)(415,658)
(416,657)(417,656)(418,655)(419,654)(420,653)(421,652)(422,651)(423,650)
(424,649)(425,648)(426,647)(427,646)(428,645);
poly := sub<Sym(856)|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*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