Polytope of Type {832}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {832}*1664
Also Known As : 832-gon, {832}. if this polytope has another name.
Group : SmallGroup(1664,2723)
Rank : 2
Schlafli Type : {832}
Number of vertices, edges, etc : 832, 832
Order of s0s1 : 832
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 : {416}*832
4-fold quotients : {208}*416
8-fold quotients : {104}*208
13-fold quotients : {64}*128
16-fold quotients : {52}*104
26-fold quotients : {32}*64
32-fold quotients : {26}*52
52-fold quotients : {16}*32
64-fold quotients : {13}*26
104-fold quotients : {8}*16
208-fold quotients : {4}*8
416-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)
( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 27, 40)( 28, 52)( 29, 51)( 30, 50)
( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)( 38, 42)
( 39, 41)( 53, 79)( 54, 91)( 55, 90)( 56, 89)( 57, 88)( 58, 87)( 59, 86)
( 60, 85)( 61, 84)( 62, 83)( 63, 82)( 64, 81)( 65, 80)( 66, 92)( 67,104)
( 68,103)( 69,102)( 70,101)( 71,100)( 72, 99)( 73, 98)( 74, 97)( 75, 96)
( 76, 95)( 77, 94)( 78, 93)(105,157)(106,169)(107,168)(108,167)(109,166)
(110,165)(111,164)(112,163)(113,162)(114,161)(115,160)(116,159)(117,158)
(118,170)(119,182)(120,181)(121,180)(122,179)(123,178)(124,177)(125,176)
(126,175)(127,174)(128,173)(129,172)(130,171)(131,196)(132,208)(133,207)
(134,206)(135,205)(136,204)(137,203)(138,202)(139,201)(140,200)(141,199)
(142,198)(143,197)(144,183)(145,195)(146,194)(147,193)(148,192)(149,191)
(150,190)(151,189)(152,188)(153,187)(154,186)(155,185)(156,184)(209,313)
(210,325)(211,324)(212,323)(213,322)(214,321)(215,320)(216,319)(217,318)
(218,317)(219,316)(220,315)(221,314)(222,326)(223,338)(224,337)(225,336)
(226,335)(227,334)(228,333)(229,332)(230,331)(231,330)(232,329)(233,328)
(234,327)(235,352)(236,364)(237,363)(238,362)(239,361)(240,360)(241,359)
(242,358)(243,357)(244,356)(245,355)(246,354)(247,353)(248,339)(249,351)
(250,350)(251,349)(252,348)(253,347)(254,346)(255,345)(256,344)(257,343)
(258,342)(259,341)(260,340)(261,391)(262,403)(263,402)(264,401)(265,400)
(266,399)(267,398)(268,397)(269,396)(270,395)(271,394)(272,393)(273,392)
(274,404)(275,416)(276,415)(277,414)(278,413)(279,412)(280,411)(281,410)
(282,409)(283,408)(284,407)(285,406)(286,405)(287,365)(288,377)(289,376)
(290,375)(291,374)(292,373)(293,372)(294,371)(295,370)(296,369)(297,368)
(298,367)(299,366)(300,378)(301,390)(302,389)(303,388)(304,387)(305,386)
(306,385)(307,384)(308,383)(309,382)(310,381)(311,380)(312,379)(417,625)
(418,637)(419,636)(420,635)(421,634)(422,633)(423,632)(424,631)(425,630)
(426,629)(427,628)(428,627)(429,626)(430,638)(431,650)(432,649)(433,648)
(434,647)(435,646)(436,645)(437,644)(438,643)(439,642)(440,641)(441,640)
(442,639)(443,664)(444,676)(445,675)(446,674)(447,673)(448,672)(449,671)
(450,670)(451,669)(452,668)(453,667)(454,666)(455,665)(456,651)(457,663)
(458,662)(459,661)(460,660)(461,659)(462,658)(463,657)(464,656)(465,655)
(466,654)(467,653)(468,652)(469,703)(470,715)(471,714)(472,713)(473,712)
(474,711)(475,710)(476,709)(477,708)(478,707)(479,706)(480,705)(481,704)
(482,716)(483,728)(484,727)(485,726)(486,725)(487,724)(488,723)(489,722)
(490,721)(491,720)(492,719)(493,718)(494,717)(495,677)(496,689)(497,688)
(498,687)(499,686)(500,685)(501,684)(502,683)(503,682)(504,681)(505,680)
(506,679)(507,678)(508,690)(509,702)(510,701)(511,700)(512,699)(513,698)
(514,697)(515,696)(516,695)(517,694)(518,693)(519,692)(520,691)(521,781)
(522,793)(523,792)(524,791)(525,790)(526,789)(527,788)(528,787)(529,786)
(530,785)(531,784)(532,783)(533,782)(534,794)(535,806)(536,805)(537,804)
(538,803)(539,802)(540,801)(541,800)(542,799)(543,798)(544,797)(545,796)
(546,795)(547,820)(548,832)(549,831)(550,830)(551,829)(552,828)(553,827)
(554,826)(555,825)(556,824)(557,823)(558,822)(559,821)(560,807)(561,819)
(562,818)(563,817)(564,816)(565,815)(566,814)(567,813)(568,812)(569,811)
(570,810)(571,809)(572,808)(573,729)(574,741)(575,740)(576,739)(577,738)
(578,737)(579,736)(580,735)(581,734)(582,733)(583,732)(584,731)(585,730)
(586,742)(587,754)(588,753)(589,752)(590,751)(591,750)(592,749)(593,748)
(594,747)(595,746)(596,745)(597,744)(598,743)(599,768)(600,780)(601,779)
(602,778)(603,777)(604,776)(605,775)(606,774)(607,773)(608,772)(609,771)
(610,770)(611,769)(612,755)(613,767)(614,766)(615,765)(616,764)(617,763)
(618,762)(619,761)(620,760)(621,759)(622,758)(623,757)(624,756);;
s1 := ( 1,418)( 2,417)( 3,429)( 4,428)( 5,427)( 6,426)( 7,425)( 8,424)
( 9,423)( 10,422)( 11,421)( 12,420)( 13,419)( 14,431)( 15,430)( 16,442)
( 17,441)( 18,440)( 19,439)( 20,438)( 21,437)( 22,436)( 23,435)( 24,434)
( 25,433)( 26,432)( 27,457)( 28,456)( 29,468)( 30,467)( 31,466)( 32,465)
( 33,464)( 34,463)( 35,462)( 36,461)( 37,460)( 38,459)( 39,458)( 40,444)
( 41,443)( 42,455)( 43,454)( 44,453)( 45,452)( 46,451)( 47,450)( 48,449)
( 49,448)( 50,447)( 51,446)( 52,445)( 53,496)( 54,495)( 55,507)( 56,506)
( 57,505)( 58,504)( 59,503)( 60,502)( 61,501)( 62,500)( 63,499)( 64,498)
( 65,497)( 66,509)( 67,508)( 68,520)( 69,519)( 70,518)( 71,517)( 72,516)
( 73,515)( 74,514)( 75,513)( 76,512)( 77,511)( 78,510)( 79,470)( 80,469)
( 81,481)( 82,480)( 83,479)( 84,478)( 85,477)( 86,476)( 87,475)( 88,474)
( 89,473)( 90,472)( 91,471)( 92,483)( 93,482)( 94,494)( 95,493)( 96,492)
( 97,491)( 98,490)( 99,489)(100,488)(101,487)(102,486)(103,485)(104,484)
(105,574)(106,573)(107,585)(108,584)(109,583)(110,582)(111,581)(112,580)
(113,579)(114,578)(115,577)(116,576)(117,575)(118,587)(119,586)(120,598)
(121,597)(122,596)(123,595)(124,594)(125,593)(126,592)(127,591)(128,590)
(129,589)(130,588)(131,613)(132,612)(133,624)(134,623)(135,622)(136,621)
(137,620)(138,619)(139,618)(140,617)(141,616)(142,615)(143,614)(144,600)
(145,599)(146,611)(147,610)(148,609)(149,608)(150,607)(151,606)(152,605)
(153,604)(154,603)(155,602)(156,601)(157,522)(158,521)(159,533)(160,532)
(161,531)(162,530)(163,529)(164,528)(165,527)(166,526)(167,525)(168,524)
(169,523)(170,535)(171,534)(172,546)(173,545)(174,544)(175,543)(176,542)
(177,541)(178,540)(179,539)(180,538)(181,537)(182,536)(183,561)(184,560)
(185,572)(186,571)(187,570)(188,569)(189,568)(190,567)(191,566)(192,565)
(193,564)(194,563)(195,562)(196,548)(197,547)(198,559)(199,558)(200,557)
(201,556)(202,555)(203,554)(204,553)(205,552)(206,551)(207,550)(208,549)
(209,730)(210,729)(211,741)(212,740)(213,739)(214,738)(215,737)(216,736)
(217,735)(218,734)(219,733)(220,732)(221,731)(222,743)(223,742)(224,754)
(225,753)(226,752)(227,751)(228,750)(229,749)(230,748)(231,747)(232,746)
(233,745)(234,744)(235,769)(236,768)(237,780)(238,779)(239,778)(240,777)
(241,776)(242,775)(243,774)(244,773)(245,772)(246,771)(247,770)(248,756)
(249,755)(250,767)(251,766)(252,765)(253,764)(254,763)(255,762)(256,761)
(257,760)(258,759)(259,758)(260,757)(261,808)(262,807)(263,819)(264,818)
(265,817)(266,816)(267,815)(268,814)(269,813)(270,812)(271,811)(272,810)
(273,809)(274,821)(275,820)(276,832)(277,831)(278,830)(279,829)(280,828)
(281,827)(282,826)(283,825)(284,824)(285,823)(286,822)(287,782)(288,781)
(289,793)(290,792)(291,791)(292,790)(293,789)(294,788)(295,787)(296,786)
(297,785)(298,784)(299,783)(300,795)(301,794)(302,806)(303,805)(304,804)
(305,803)(306,802)(307,801)(308,800)(309,799)(310,798)(311,797)(312,796)
(313,626)(314,625)(315,637)(316,636)(317,635)(318,634)(319,633)(320,632)
(321,631)(322,630)(323,629)(324,628)(325,627)(326,639)(327,638)(328,650)
(329,649)(330,648)(331,647)(332,646)(333,645)(334,644)(335,643)(336,642)
(337,641)(338,640)(339,665)(340,664)(341,676)(342,675)(343,674)(344,673)
(345,672)(346,671)(347,670)(348,669)(349,668)(350,667)(351,666)(352,652)
(353,651)(354,663)(355,662)(356,661)(357,660)(358,659)(359,658)(360,657)
(361,656)(362,655)(363,654)(364,653)(365,704)(366,703)(367,715)(368,714)
(369,713)(370,712)(371,711)(372,710)(373,709)(374,708)(375,707)(376,706)
(377,705)(378,717)(379,716)(380,728)(381,727)(382,726)(383,725)(384,724)
(385,723)(386,722)(387,721)(388,720)(389,719)(390,718)(391,678)(392,677)
(393,689)(394,688)(395,687)(396,686)(397,685)(398,684)(399,683)(400,682)
(401,681)(402,680)(403,679)(404,691)(405,690)(406,702)(407,701)(408,700)
(409,699)(410,698)(411,697)(412,696)(413,695)(414,694)(415,693)(416,692);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(832)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)
( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 27, 40)( 28, 52)( 29, 51)
( 30, 50)( 31, 49)( 32, 48)( 33, 47)( 34, 46)( 35, 45)( 36, 44)( 37, 43)
( 38, 42)( 39, 41)( 53, 79)( 54, 91)( 55, 90)( 56, 89)( 57, 88)( 58, 87)
( 59, 86)( 60, 85)( 61, 84)( 62, 83)( 63, 82)( 64, 81)( 65, 80)( 66, 92)
( 67,104)( 68,103)( 69,102)( 70,101)( 71,100)( 72, 99)( 73, 98)( 74, 97)
( 75, 96)( 76, 95)( 77, 94)( 78, 93)(105,157)(106,169)(107,168)(108,167)
(109,166)(110,165)(111,164)(112,163)(113,162)(114,161)(115,160)(116,159)
(117,158)(118,170)(119,182)(120,181)(121,180)(122,179)(123,178)(124,177)
(125,176)(126,175)(127,174)(128,173)(129,172)(130,171)(131,196)(132,208)
(133,207)(134,206)(135,205)(136,204)(137,203)(138,202)(139,201)(140,200)
(141,199)(142,198)(143,197)(144,183)(145,195)(146,194)(147,193)(148,192)
(149,191)(150,190)(151,189)(152,188)(153,187)(154,186)(155,185)(156,184)
(209,313)(210,325)(211,324)(212,323)(213,322)(214,321)(215,320)(216,319)
(217,318)(218,317)(219,316)(220,315)(221,314)(222,326)(223,338)(224,337)
(225,336)(226,335)(227,334)(228,333)(229,332)(230,331)(231,330)(232,329)
(233,328)(234,327)(235,352)(236,364)(237,363)(238,362)(239,361)(240,360)
(241,359)(242,358)(243,357)(244,356)(245,355)(246,354)(247,353)(248,339)
(249,351)(250,350)(251,349)(252,348)(253,347)(254,346)(255,345)(256,344)
(257,343)(258,342)(259,341)(260,340)(261,391)(262,403)(263,402)(264,401)
(265,400)(266,399)(267,398)(268,397)(269,396)(270,395)(271,394)(272,393)
(273,392)(274,404)(275,416)(276,415)(277,414)(278,413)(279,412)(280,411)
(281,410)(282,409)(283,408)(284,407)(285,406)(286,405)(287,365)(288,377)
(289,376)(290,375)(291,374)(292,373)(293,372)(294,371)(295,370)(296,369)
(297,368)(298,367)(299,366)(300,378)(301,390)(302,389)(303,388)(304,387)
(305,386)(306,385)(307,384)(308,383)(309,382)(310,381)(311,380)(312,379)
(417,625)(418,637)(419,636)(420,635)(421,634)(422,633)(423,632)(424,631)
(425,630)(426,629)(427,628)(428,627)(429,626)(430,638)(431,650)(432,649)
(433,648)(434,647)(435,646)(436,645)(437,644)(438,643)(439,642)(440,641)
(441,640)(442,639)(443,664)(444,676)(445,675)(446,674)(447,673)(448,672)
(449,671)(450,670)(451,669)(452,668)(453,667)(454,666)(455,665)(456,651)
(457,663)(458,662)(459,661)(460,660)(461,659)(462,658)(463,657)(464,656)
(465,655)(466,654)(467,653)(468,652)(469,703)(470,715)(471,714)(472,713)
(473,712)(474,711)(475,710)(476,709)(477,708)(478,707)(479,706)(480,705)
(481,704)(482,716)(483,728)(484,727)(485,726)(486,725)(487,724)(488,723)
(489,722)(490,721)(491,720)(492,719)(493,718)(494,717)(495,677)(496,689)
(497,688)(498,687)(499,686)(500,685)(501,684)(502,683)(503,682)(504,681)
(505,680)(506,679)(507,678)(508,690)(509,702)(510,701)(511,700)(512,699)
(513,698)(514,697)(515,696)(516,695)(517,694)(518,693)(519,692)(520,691)
(521,781)(522,793)(523,792)(524,791)(525,790)(526,789)(527,788)(528,787)
(529,786)(530,785)(531,784)(532,783)(533,782)(534,794)(535,806)(536,805)
(537,804)(538,803)(539,802)(540,801)(541,800)(542,799)(543,798)(544,797)
(545,796)(546,795)(547,820)(548,832)(549,831)(550,830)(551,829)(552,828)
(553,827)(554,826)(555,825)(556,824)(557,823)(558,822)(559,821)(560,807)
(561,819)(562,818)(563,817)(564,816)(565,815)(566,814)(567,813)(568,812)
(569,811)(570,810)(571,809)(572,808)(573,729)(574,741)(575,740)(576,739)
(577,738)(578,737)(579,736)(580,735)(581,734)(582,733)(583,732)(584,731)
(585,730)(586,742)(587,754)(588,753)(589,752)(590,751)(591,750)(592,749)
(593,748)(594,747)(595,746)(596,745)(597,744)(598,743)(599,768)(600,780)
(601,779)(602,778)(603,777)(604,776)(605,775)(606,774)(607,773)(608,772)
(609,771)(610,770)(611,769)(612,755)(613,767)(614,766)(615,765)(616,764)
(617,763)(618,762)(619,761)(620,760)(621,759)(622,758)(623,757)(624,756);
s1 := Sym(832)!( 1,418)( 2,417)( 3,429)( 4,428)( 5,427)( 6,426)( 7,425)
( 8,424)( 9,423)( 10,422)( 11,421)( 12,420)( 13,419)( 14,431)( 15,430)
( 16,442)( 17,441)( 18,440)( 19,439)( 20,438)( 21,437)( 22,436)( 23,435)
( 24,434)( 25,433)( 26,432)( 27,457)( 28,456)( 29,468)( 30,467)( 31,466)
( 32,465)( 33,464)( 34,463)( 35,462)( 36,461)( 37,460)( 38,459)( 39,458)
( 40,444)( 41,443)( 42,455)( 43,454)( 44,453)( 45,452)( 46,451)( 47,450)
( 48,449)( 49,448)( 50,447)( 51,446)( 52,445)( 53,496)( 54,495)( 55,507)
( 56,506)( 57,505)( 58,504)( 59,503)( 60,502)( 61,501)( 62,500)( 63,499)
( 64,498)( 65,497)( 66,509)( 67,508)( 68,520)( 69,519)( 70,518)( 71,517)
( 72,516)( 73,515)( 74,514)( 75,513)( 76,512)( 77,511)( 78,510)( 79,470)
( 80,469)( 81,481)( 82,480)( 83,479)( 84,478)( 85,477)( 86,476)( 87,475)
( 88,474)( 89,473)( 90,472)( 91,471)( 92,483)( 93,482)( 94,494)( 95,493)
( 96,492)( 97,491)( 98,490)( 99,489)(100,488)(101,487)(102,486)(103,485)
(104,484)(105,574)(106,573)(107,585)(108,584)(109,583)(110,582)(111,581)
(112,580)(113,579)(114,578)(115,577)(116,576)(117,575)(118,587)(119,586)
(120,598)(121,597)(122,596)(123,595)(124,594)(125,593)(126,592)(127,591)
(128,590)(129,589)(130,588)(131,613)(132,612)(133,624)(134,623)(135,622)
(136,621)(137,620)(138,619)(139,618)(140,617)(141,616)(142,615)(143,614)
(144,600)(145,599)(146,611)(147,610)(148,609)(149,608)(150,607)(151,606)
(152,605)(153,604)(154,603)(155,602)(156,601)(157,522)(158,521)(159,533)
(160,532)(161,531)(162,530)(163,529)(164,528)(165,527)(166,526)(167,525)
(168,524)(169,523)(170,535)(171,534)(172,546)(173,545)(174,544)(175,543)
(176,542)(177,541)(178,540)(179,539)(180,538)(181,537)(182,536)(183,561)
(184,560)(185,572)(186,571)(187,570)(188,569)(189,568)(190,567)(191,566)
(192,565)(193,564)(194,563)(195,562)(196,548)(197,547)(198,559)(199,558)
(200,557)(201,556)(202,555)(203,554)(204,553)(205,552)(206,551)(207,550)
(208,549)(209,730)(210,729)(211,741)(212,740)(213,739)(214,738)(215,737)
(216,736)(217,735)(218,734)(219,733)(220,732)(221,731)(222,743)(223,742)
(224,754)(225,753)(226,752)(227,751)(228,750)(229,749)(230,748)(231,747)
(232,746)(233,745)(234,744)(235,769)(236,768)(237,780)(238,779)(239,778)
(240,777)(241,776)(242,775)(243,774)(244,773)(245,772)(246,771)(247,770)
(248,756)(249,755)(250,767)(251,766)(252,765)(253,764)(254,763)(255,762)
(256,761)(257,760)(258,759)(259,758)(260,757)(261,808)(262,807)(263,819)
(264,818)(265,817)(266,816)(267,815)(268,814)(269,813)(270,812)(271,811)
(272,810)(273,809)(274,821)(275,820)(276,832)(277,831)(278,830)(279,829)
(280,828)(281,827)(282,826)(283,825)(284,824)(285,823)(286,822)(287,782)
(288,781)(289,793)(290,792)(291,791)(292,790)(293,789)(294,788)(295,787)
(296,786)(297,785)(298,784)(299,783)(300,795)(301,794)(302,806)(303,805)
(304,804)(305,803)(306,802)(307,801)(308,800)(309,799)(310,798)(311,797)
(312,796)(313,626)(314,625)(315,637)(316,636)(317,635)(318,634)(319,633)
(320,632)(321,631)(322,630)(323,629)(324,628)(325,627)(326,639)(327,638)
(328,650)(329,649)(330,648)(331,647)(332,646)(333,645)(334,644)(335,643)
(336,642)(337,641)(338,640)(339,665)(340,664)(341,676)(342,675)(343,674)
(344,673)(345,672)(346,671)(347,670)(348,669)(349,668)(350,667)(351,666)
(352,652)(353,651)(354,663)(355,662)(356,661)(357,660)(358,659)(359,658)
(360,657)(361,656)(362,655)(363,654)(364,653)(365,704)(366,703)(367,715)
(368,714)(369,713)(370,712)(371,711)(372,710)(373,709)(374,708)(375,707)
(376,706)(377,705)(378,717)(379,716)(380,728)(381,727)(382,726)(383,725)
(384,724)(385,723)(386,722)(387,721)(388,720)(389,719)(390,718)(391,678)
(392,677)(393,689)(394,688)(395,687)(396,686)(397,685)(398,684)(399,683)
(400,682)(401,681)(402,680)(403,679)(404,691)(405,690)(406,702)(407,701)
(408,700)(409,699)(410,698)(411,697)(412,696)(413,695)(414,694)(415,693)
(416,692);
poly := sub<Sym(832)|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 >;
References : None.
to this polytope