Polytope of Type {848}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {848}*1696
Also Known As : 848-gon, {848}. if this polytope has another name.
Group : SmallGroup(1696,88)
Rank : 2
Schlafli Type : {848}
Number of vertices, edges, etc : 848, 848
Order of s0s1 : 848
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 : {424}*848
4-fold quotients : {212}*424
8-fold quotients : {106}*212
16-fold quotients : {53}*106
53-fold quotients : {16}*32
106-fold quotients : {8}*16
212-fold quotients : {4}*8
424-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 53)( 3, 52)( 4, 51)( 5, 50)( 6, 49)( 7, 48)( 8, 47)( 9, 46)
( 10, 45)( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)( 16, 39)( 17, 38)
( 18, 37)( 19, 36)( 20, 35)( 21, 34)( 22, 33)( 23, 32)( 24, 31)( 25, 30)
( 26, 29)( 27, 28)( 55,106)( 56,105)( 57,104)( 58,103)( 59,102)( 60,101)
( 61,100)( 62, 99)( 63, 98)( 64, 97)( 65, 96)( 66, 95)( 67, 94)( 68, 93)
( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)( 76, 85)
( 77, 84)( 78, 83)( 79, 82)( 80, 81)(107,160)(108,212)(109,211)(110,210)
(111,209)(112,208)(113,207)(114,206)(115,205)(116,204)(117,203)(118,202)
(119,201)(120,200)(121,199)(122,198)(123,197)(124,196)(125,195)(126,194)
(127,193)(128,192)(129,191)(130,190)(131,189)(132,188)(133,187)(134,186)
(135,185)(136,184)(137,183)(138,182)(139,181)(140,180)(141,179)(142,178)
(143,177)(144,176)(145,175)(146,174)(147,173)(148,172)(149,171)(150,170)
(151,169)(152,168)(153,167)(154,166)(155,165)(156,164)(157,163)(158,162)
(159,161)(213,319)(214,371)(215,370)(216,369)(217,368)(218,367)(219,366)
(220,365)(221,364)(222,363)(223,362)(224,361)(225,360)(226,359)(227,358)
(228,357)(229,356)(230,355)(231,354)(232,353)(233,352)(234,351)(235,350)
(236,349)(237,348)(238,347)(239,346)(240,345)(241,344)(242,343)(243,342)
(244,341)(245,340)(246,339)(247,338)(248,337)(249,336)(250,335)(251,334)
(252,333)(253,332)(254,331)(255,330)(256,329)(257,328)(258,327)(259,326)
(260,325)(261,324)(262,323)(263,322)(264,321)(265,320)(266,372)(267,424)
(268,423)(269,422)(270,421)(271,420)(272,419)(273,418)(274,417)(275,416)
(276,415)(277,414)(278,413)(279,412)(280,411)(281,410)(282,409)(283,408)
(284,407)(285,406)(286,405)(287,404)(288,403)(289,402)(290,401)(291,400)
(292,399)(293,398)(294,397)(295,396)(296,395)(297,394)(298,393)(299,392)
(300,391)(301,390)(302,389)(303,388)(304,387)(305,386)(306,385)(307,384)
(308,383)(309,382)(310,381)(311,380)(312,379)(313,378)(314,377)(315,376)
(316,375)(317,374)(318,373)(425,637)(426,689)(427,688)(428,687)(429,686)
(430,685)(431,684)(432,683)(433,682)(434,681)(435,680)(436,679)(437,678)
(438,677)(439,676)(440,675)(441,674)(442,673)(443,672)(444,671)(445,670)
(446,669)(447,668)(448,667)(449,666)(450,665)(451,664)(452,663)(453,662)
(454,661)(455,660)(456,659)(457,658)(458,657)(459,656)(460,655)(461,654)
(462,653)(463,652)(464,651)(465,650)(466,649)(467,648)(468,647)(469,646)
(470,645)(471,644)(472,643)(473,642)(474,641)(475,640)(476,639)(477,638)
(478,690)(479,742)(480,741)(481,740)(482,739)(483,738)(484,737)(485,736)
(486,735)(487,734)(488,733)(489,732)(490,731)(491,730)(492,729)(493,728)
(494,727)(495,726)(496,725)(497,724)(498,723)(499,722)(500,721)(501,720)
(502,719)(503,718)(504,717)(505,716)(506,715)(507,714)(508,713)(509,712)
(510,711)(511,710)(512,709)(513,708)(514,707)(515,706)(516,705)(517,704)
(518,703)(519,702)(520,701)(521,700)(522,699)(523,698)(524,697)(525,696)
(526,695)(527,694)(528,693)(529,692)(530,691)(531,796)(532,848)(533,847)
(534,846)(535,845)(536,844)(537,843)(538,842)(539,841)(540,840)(541,839)
(542,838)(543,837)(544,836)(545,835)(546,834)(547,833)(548,832)(549,831)
(550,830)(551,829)(552,828)(553,827)(554,826)(555,825)(556,824)(557,823)
(558,822)(559,821)(560,820)(561,819)(562,818)(563,817)(564,816)(565,815)
(566,814)(567,813)(568,812)(569,811)(570,810)(571,809)(572,808)(573,807)
(574,806)(575,805)(576,804)(577,803)(578,802)(579,801)(580,800)(581,799)
(582,798)(583,797)(584,743)(585,795)(586,794)(587,793)(588,792)(589,791)
(590,790)(591,789)(592,788)(593,787)(594,786)(595,785)(596,784)(597,783)
(598,782)(599,781)(600,780)(601,779)(602,778)(603,777)(604,776)(605,775)
(606,774)(607,773)(608,772)(609,771)(610,770)(611,769)(612,768)(613,767)
(614,766)(615,765)(616,764)(617,763)(618,762)(619,761)(620,760)(621,759)
(622,758)(623,757)(624,756)(625,755)(626,754)(627,753)(628,752)(629,751)
(630,750)(631,749)(632,748)(633,747)(634,746)(635,745)(636,744);;
s1 := ( 1,426)( 2,425)( 3,477)( 4,476)( 5,475)( 6,474)( 7,473)( 8,472)
( 9,471)( 10,470)( 11,469)( 12,468)( 13,467)( 14,466)( 15,465)( 16,464)
( 17,463)( 18,462)( 19,461)( 20,460)( 21,459)( 22,458)( 23,457)( 24,456)
( 25,455)( 26,454)( 27,453)( 28,452)( 29,451)( 30,450)( 31,449)( 32,448)
( 33,447)( 34,446)( 35,445)( 36,444)( 37,443)( 38,442)( 39,441)( 40,440)
( 41,439)( 42,438)( 43,437)( 44,436)( 45,435)( 46,434)( 47,433)( 48,432)
( 49,431)( 50,430)( 51,429)( 52,428)( 53,427)( 54,479)( 55,478)( 56,530)
( 57,529)( 58,528)( 59,527)( 60,526)( 61,525)( 62,524)( 63,523)( 64,522)
( 65,521)( 66,520)( 67,519)( 68,518)( 69,517)( 70,516)( 71,515)( 72,514)
( 73,513)( 74,512)( 75,511)( 76,510)( 77,509)( 78,508)( 79,507)( 80,506)
( 81,505)( 82,504)( 83,503)( 84,502)( 85,501)( 86,500)( 87,499)( 88,498)
( 89,497)( 90,496)( 91,495)( 92,494)( 93,493)( 94,492)( 95,491)( 96,490)
( 97,489)( 98,488)( 99,487)(100,486)(101,485)(102,484)(103,483)(104,482)
(105,481)(106,480)(107,585)(108,584)(109,636)(110,635)(111,634)(112,633)
(113,632)(114,631)(115,630)(116,629)(117,628)(118,627)(119,626)(120,625)
(121,624)(122,623)(123,622)(124,621)(125,620)(126,619)(127,618)(128,617)
(129,616)(130,615)(131,614)(132,613)(133,612)(134,611)(135,610)(136,609)
(137,608)(138,607)(139,606)(140,605)(141,604)(142,603)(143,602)(144,601)
(145,600)(146,599)(147,598)(148,597)(149,596)(150,595)(151,594)(152,593)
(153,592)(154,591)(155,590)(156,589)(157,588)(158,587)(159,586)(160,532)
(161,531)(162,583)(163,582)(164,581)(165,580)(166,579)(167,578)(168,577)
(169,576)(170,575)(171,574)(172,573)(173,572)(174,571)(175,570)(176,569)
(177,568)(178,567)(179,566)(180,565)(181,564)(182,563)(183,562)(184,561)
(185,560)(186,559)(187,558)(188,557)(189,556)(190,555)(191,554)(192,553)
(193,552)(194,551)(195,550)(196,549)(197,548)(198,547)(199,546)(200,545)
(201,544)(202,543)(203,542)(204,541)(205,540)(206,539)(207,538)(208,537)
(209,536)(210,535)(211,534)(212,533)(213,744)(214,743)(215,795)(216,794)
(217,793)(218,792)(219,791)(220,790)(221,789)(222,788)(223,787)(224,786)
(225,785)(226,784)(227,783)(228,782)(229,781)(230,780)(231,779)(232,778)
(233,777)(234,776)(235,775)(236,774)(237,773)(238,772)(239,771)(240,770)
(241,769)(242,768)(243,767)(244,766)(245,765)(246,764)(247,763)(248,762)
(249,761)(250,760)(251,759)(252,758)(253,757)(254,756)(255,755)(256,754)
(257,753)(258,752)(259,751)(260,750)(261,749)(262,748)(263,747)(264,746)
(265,745)(266,797)(267,796)(268,848)(269,847)(270,846)(271,845)(272,844)
(273,843)(274,842)(275,841)(276,840)(277,839)(278,838)(279,837)(280,836)
(281,835)(282,834)(283,833)(284,832)(285,831)(286,830)(287,829)(288,828)
(289,827)(290,826)(291,825)(292,824)(293,823)(294,822)(295,821)(296,820)
(297,819)(298,818)(299,817)(300,816)(301,815)(302,814)(303,813)(304,812)
(305,811)(306,810)(307,809)(308,808)(309,807)(310,806)(311,805)(312,804)
(313,803)(314,802)(315,801)(316,800)(317,799)(318,798)(319,638)(320,637)
(321,689)(322,688)(323,687)(324,686)(325,685)(326,684)(327,683)(328,682)
(329,681)(330,680)(331,679)(332,678)(333,677)(334,676)(335,675)(336,674)
(337,673)(338,672)(339,671)(340,670)(341,669)(342,668)(343,667)(344,666)
(345,665)(346,664)(347,663)(348,662)(349,661)(350,660)(351,659)(352,658)
(353,657)(354,656)(355,655)(356,654)(357,653)(358,652)(359,651)(360,650)
(361,649)(362,648)(363,647)(364,646)(365,645)(366,644)(367,643)(368,642)
(369,641)(370,640)(371,639)(372,691)(373,690)(374,742)(375,741)(376,740)
(377,739)(378,738)(379,737)(380,736)(381,735)(382,734)(383,733)(384,732)
(385,731)(386,730)(387,729)(388,728)(389,727)(390,726)(391,725)(392,724)
(393,723)(394,722)(395,721)(396,720)(397,719)(398,718)(399,717)(400,716)
(401,715)(402,714)(403,713)(404,712)(405,711)(406,710)(407,709)(408,708)
(409,707)(410,706)(411,705)(412,704)(413,703)(414,702)(415,701)(416,700)
(417,699)(418,698)(419,697)(420,696)(421,695)(422,694)(423,693)(424,692);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(848)!( 2, 53)( 3, 52)( 4, 51)( 5, 50)( 6, 49)( 7, 48)( 8, 47)
( 9, 46)( 10, 45)( 11, 44)( 12, 43)( 13, 42)( 14, 41)( 15, 40)( 16, 39)
( 17, 38)( 18, 37)( 19, 36)( 20, 35)( 21, 34)( 22, 33)( 23, 32)( 24, 31)
( 25, 30)( 26, 29)( 27, 28)( 55,106)( 56,105)( 57,104)( 58,103)( 59,102)
( 60,101)( 61,100)( 62, 99)( 63, 98)( 64, 97)( 65, 96)( 66, 95)( 67, 94)
( 68, 93)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)
( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 80, 81)(107,160)(108,212)(109,211)
(110,210)(111,209)(112,208)(113,207)(114,206)(115,205)(116,204)(117,203)
(118,202)(119,201)(120,200)(121,199)(122,198)(123,197)(124,196)(125,195)
(126,194)(127,193)(128,192)(129,191)(130,190)(131,189)(132,188)(133,187)
(134,186)(135,185)(136,184)(137,183)(138,182)(139,181)(140,180)(141,179)
(142,178)(143,177)(144,176)(145,175)(146,174)(147,173)(148,172)(149,171)
(150,170)(151,169)(152,168)(153,167)(154,166)(155,165)(156,164)(157,163)
(158,162)(159,161)(213,319)(214,371)(215,370)(216,369)(217,368)(218,367)
(219,366)(220,365)(221,364)(222,363)(223,362)(224,361)(225,360)(226,359)
(227,358)(228,357)(229,356)(230,355)(231,354)(232,353)(233,352)(234,351)
(235,350)(236,349)(237,348)(238,347)(239,346)(240,345)(241,344)(242,343)
(243,342)(244,341)(245,340)(246,339)(247,338)(248,337)(249,336)(250,335)
(251,334)(252,333)(253,332)(254,331)(255,330)(256,329)(257,328)(258,327)
(259,326)(260,325)(261,324)(262,323)(263,322)(264,321)(265,320)(266,372)
(267,424)(268,423)(269,422)(270,421)(271,420)(272,419)(273,418)(274,417)
(275,416)(276,415)(277,414)(278,413)(279,412)(280,411)(281,410)(282,409)
(283,408)(284,407)(285,406)(286,405)(287,404)(288,403)(289,402)(290,401)
(291,400)(292,399)(293,398)(294,397)(295,396)(296,395)(297,394)(298,393)
(299,392)(300,391)(301,390)(302,389)(303,388)(304,387)(305,386)(306,385)
(307,384)(308,383)(309,382)(310,381)(311,380)(312,379)(313,378)(314,377)
(315,376)(316,375)(317,374)(318,373)(425,637)(426,689)(427,688)(428,687)
(429,686)(430,685)(431,684)(432,683)(433,682)(434,681)(435,680)(436,679)
(437,678)(438,677)(439,676)(440,675)(441,674)(442,673)(443,672)(444,671)
(445,670)(446,669)(447,668)(448,667)(449,666)(450,665)(451,664)(452,663)
(453,662)(454,661)(455,660)(456,659)(457,658)(458,657)(459,656)(460,655)
(461,654)(462,653)(463,652)(464,651)(465,650)(466,649)(467,648)(468,647)
(469,646)(470,645)(471,644)(472,643)(473,642)(474,641)(475,640)(476,639)
(477,638)(478,690)(479,742)(480,741)(481,740)(482,739)(483,738)(484,737)
(485,736)(486,735)(487,734)(488,733)(489,732)(490,731)(491,730)(492,729)
(493,728)(494,727)(495,726)(496,725)(497,724)(498,723)(499,722)(500,721)
(501,720)(502,719)(503,718)(504,717)(505,716)(506,715)(507,714)(508,713)
(509,712)(510,711)(511,710)(512,709)(513,708)(514,707)(515,706)(516,705)
(517,704)(518,703)(519,702)(520,701)(521,700)(522,699)(523,698)(524,697)
(525,696)(526,695)(527,694)(528,693)(529,692)(530,691)(531,796)(532,848)
(533,847)(534,846)(535,845)(536,844)(537,843)(538,842)(539,841)(540,840)
(541,839)(542,838)(543,837)(544,836)(545,835)(546,834)(547,833)(548,832)
(549,831)(550,830)(551,829)(552,828)(553,827)(554,826)(555,825)(556,824)
(557,823)(558,822)(559,821)(560,820)(561,819)(562,818)(563,817)(564,816)
(565,815)(566,814)(567,813)(568,812)(569,811)(570,810)(571,809)(572,808)
(573,807)(574,806)(575,805)(576,804)(577,803)(578,802)(579,801)(580,800)
(581,799)(582,798)(583,797)(584,743)(585,795)(586,794)(587,793)(588,792)
(589,791)(590,790)(591,789)(592,788)(593,787)(594,786)(595,785)(596,784)
(597,783)(598,782)(599,781)(600,780)(601,779)(602,778)(603,777)(604,776)
(605,775)(606,774)(607,773)(608,772)(609,771)(610,770)(611,769)(612,768)
(613,767)(614,766)(615,765)(616,764)(617,763)(618,762)(619,761)(620,760)
(621,759)(622,758)(623,757)(624,756)(625,755)(626,754)(627,753)(628,752)
(629,751)(630,750)(631,749)(632,748)(633,747)(634,746)(635,745)(636,744);
s1 := Sym(848)!( 1,426)( 2,425)( 3,477)( 4,476)( 5,475)( 6,474)( 7,473)
( 8,472)( 9,471)( 10,470)( 11,469)( 12,468)( 13,467)( 14,466)( 15,465)
( 16,464)( 17,463)( 18,462)( 19,461)( 20,460)( 21,459)( 22,458)( 23,457)
( 24,456)( 25,455)( 26,454)( 27,453)( 28,452)( 29,451)( 30,450)( 31,449)
( 32,448)( 33,447)( 34,446)( 35,445)( 36,444)( 37,443)( 38,442)( 39,441)
( 40,440)( 41,439)( 42,438)( 43,437)( 44,436)( 45,435)( 46,434)( 47,433)
( 48,432)( 49,431)( 50,430)( 51,429)( 52,428)( 53,427)( 54,479)( 55,478)
( 56,530)( 57,529)( 58,528)( 59,527)( 60,526)( 61,525)( 62,524)( 63,523)
( 64,522)( 65,521)( 66,520)( 67,519)( 68,518)( 69,517)( 70,516)( 71,515)
( 72,514)( 73,513)( 74,512)( 75,511)( 76,510)( 77,509)( 78,508)( 79,507)
( 80,506)( 81,505)( 82,504)( 83,503)( 84,502)( 85,501)( 86,500)( 87,499)
( 88,498)( 89,497)( 90,496)( 91,495)( 92,494)( 93,493)( 94,492)( 95,491)
( 96,490)( 97,489)( 98,488)( 99,487)(100,486)(101,485)(102,484)(103,483)
(104,482)(105,481)(106,480)(107,585)(108,584)(109,636)(110,635)(111,634)
(112,633)(113,632)(114,631)(115,630)(116,629)(117,628)(118,627)(119,626)
(120,625)(121,624)(122,623)(123,622)(124,621)(125,620)(126,619)(127,618)
(128,617)(129,616)(130,615)(131,614)(132,613)(133,612)(134,611)(135,610)
(136,609)(137,608)(138,607)(139,606)(140,605)(141,604)(142,603)(143,602)
(144,601)(145,600)(146,599)(147,598)(148,597)(149,596)(150,595)(151,594)
(152,593)(153,592)(154,591)(155,590)(156,589)(157,588)(158,587)(159,586)
(160,532)(161,531)(162,583)(163,582)(164,581)(165,580)(166,579)(167,578)
(168,577)(169,576)(170,575)(171,574)(172,573)(173,572)(174,571)(175,570)
(176,569)(177,568)(178,567)(179,566)(180,565)(181,564)(182,563)(183,562)
(184,561)(185,560)(186,559)(187,558)(188,557)(189,556)(190,555)(191,554)
(192,553)(193,552)(194,551)(195,550)(196,549)(197,548)(198,547)(199,546)
(200,545)(201,544)(202,543)(203,542)(204,541)(205,540)(206,539)(207,538)
(208,537)(209,536)(210,535)(211,534)(212,533)(213,744)(214,743)(215,795)
(216,794)(217,793)(218,792)(219,791)(220,790)(221,789)(222,788)(223,787)
(224,786)(225,785)(226,784)(227,783)(228,782)(229,781)(230,780)(231,779)
(232,778)(233,777)(234,776)(235,775)(236,774)(237,773)(238,772)(239,771)
(240,770)(241,769)(242,768)(243,767)(244,766)(245,765)(246,764)(247,763)
(248,762)(249,761)(250,760)(251,759)(252,758)(253,757)(254,756)(255,755)
(256,754)(257,753)(258,752)(259,751)(260,750)(261,749)(262,748)(263,747)
(264,746)(265,745)(266,797)(267,796)(268,848)(269,847)(270,846)(271,845)
(272,844)(273,843)(274,842)(275,841)(276,840)(277,839)(278,838)(279,837)
(280,836)(281,835)(282,834)(283,833)(284,832)(285,831)(286,830)(287,829)
(288,828)(289,827)(290,826)(291,825)(292,824)(293,823)(294,822)(295,821)
(296,820)(297,819)(298,818)(299,817)(300,816)(301,815)(302,814)(303,813)
(304,812)(305,811)(306,810)(307,809)(308,808)(309,807)(310,806)(311,805)
(312,804)(313,803)(314,802)(315,801)(316,800)(317,799)(318,798)(319,638)
(320,637)(321,689)(322,688)(323,687)(324,686)(325,685)(326,684)(327,683)
(328,682)(329,681)(330,680)(331,679)(332,678)(333,677)(334,676)(335,675)
(336,674)(337,673)(338,672)(339,671)(340,670)(341,669)(342,668)(343,667)
(344,666)(345,665)(346,664)(347,663)(348,662)(349,661)(350,660)(351,659)
(352,658)(353,657)(354,656)(355,655)(356,654)(357,653)(358,652)(359,651)
(360,650)(361,649)(362,648)(363,647)(364,646)(365,645)(366,644)(367,643)
(368,642)(369,641)(370,640)(371,639)(372,691)(373,690)(374,742)(375,741)
(376,740)(377,739)(378,738)(379,737)(380,736)(381,735)(382,734)(383,733)
(384,732)(385,731)(386,730)(387,729)(388,728)(389,727)(390,726)(391,725)
(392,724)(393,723)(394,722)(395,721)(396,720)(397,719)(398,718)(399,717)
(400,716)(401,715)(402,714)(403,713)(404,712)(405,711)(406,710)(407,709)
(408,708)(409,707)(410,706)(411,705)(412,704)(413,703)(414,702)(415,701)
(416,700)(417,699)(418,698)(419,697)(420,696)(421,695)(422,694)(423,693)
(424,692);
poly := sub<Sym(848)|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 >;
References : None.
to this polytope