Polytope of Type {836}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {836}*1672
Also Known As : 836-gon, {836}. if this polytope has another name.
Group : SmallGroup(1672,24)
Rank : 2
Schlafli Type : {836}
Number of vertices, edges, etc : 836, 836
Order of s0s1 : 836
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 : {418}*836
4-fold quotients : {209}*418
11-fold quotients : {76}*152
19-fold quotients : {44}*88
22-fold quotients : {38}*76
38-fold quotients : {22}*44
44-fold quotients : {19}*38
76-fold quotients : {11}*22
209-fold quotients : {4}*8
418-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 19)( 3, 18)( 4, 17)( 5, 16)( 6, 15)( 7, 14)( 8, 13)( 9, 12)
( 10, 11)( 20,191)( 21,209)( 22,208)( 23,207)( 24,206)( 25,205)( 26,204)
( 27,203)( 28,202)( 29,201)( 30,200)( 31,199)( 32,198)( 33,197)( 34,196)
( 35,195)( 36,194)( 37,193)( 38,192)( 39,172)( 40,190)( 41,189)( 42,188)
( 43,187)( 44,186)( 45,185)( 46,184)( 47,183)( 48,182)( 49,181)( 50,180)
( 51,179)( 52,178)( 53,177)( 54,176)( 55,175)( 56,174)( 57,173)( 58,153)
( 59,171)( 60,170)( 61,169)( 62,168)( 63,167)( 64,166)( 65,165)( 66,164)
( 67,163)( 68,162)( 69,161)( 70,160)( 71,159)( 72,158)( 73,157)( 74,156)
( 75,155)( 76,154)( 77,134)( 78,152)( 79,151)( 80,150)( 81,149)( 82,148)
( 83,147)( 84,146)( 85,145)( 86,144)( 87,143)( 88,142)( 89,141)( 90,140)
( 91,139)( 92,138)( 93,137)( 94,136)( 95,135)( 96,115)( 97,133)( 98,132)
( 99,131)(100,130)(101,129)(102,128)(103,127)(104,126)(105,125)(106,124)
(107,123)(108,122)(109,121)(110,120)(111,119)(112,118)(113,117)(114,116)
(211,228)(212,227)(213,226)(214,225)(215,224)(216,223)(217,222)(218,221)
(219,220)(229,400)(230,418)(231,417)(232,416)(233,415)(234,414)(235,413)
(236,412)(237,411)(238,410)(239,409)(240,408)(241,407)(242,406)(243,405)
(244,404)(245,403)(246,402)(247,401)(248,381)(249,399)(250,398)(251,397)
(252,396)(253,395)(254,394)(255,393)(256,392)(257,391)(258,390)(259,389)
(260,388)(261,387)(262,386)(263,385)(264,384)(265,383)(266,382)(267,362)
(268,380)(269,379)(270,378)(271,377)(272,376)(273,375)(274,374)(275,373)
(276,372)(277,371)(278,370)(279,369)(280,368)(281,367)(282,366)(283,365)
(284,364)(285,363)(286,343)(287,361)(288,360)(289,359)(290,358)(291,357)
(292,356)(293,355)(294,354)(295,353)(296,352)(297,351)(298,350)(299,349)
(300,348)(301,347)(302,346)(303,345)(304,344)(305,324)(306,342)(307,341)
(308,340)(309,339)(310,338)(311,337)(312,336)(313,335)(314,334)(315,333)
(316,332)(317,331)(318,330)(319,329)(320,328)(321,327)(322,326)(323,325)
(419,628)(420,646)(421,645)(422,644)(423,643)(424,642)(425,641)(426,640)
(427,639)(428,638)(429,637)(430,636)(431,635)(432,634)(433,633)(434,632)
(435,631)(436,630)(437,629)(438,818)(439,836)(440,835)(441,834)(442,833)
(443,832)(444,831)(445,830)(446,829)(447,828)(448,827)(449,826)(450,825)
(451,824)(452,823)(453,822)(454,821)(455,820)(456,819)(457,799)(458,817)
(459,816)(460,815)(461,814)(462,813)(463,812)(464,811)(465,810)(466,809)
(467,808)(468,807)(469,806)(470,805)(471,804)(472,803)(473,802)(474,801)
(475,800)(476,780)(477,798)(478,797)(479,796)(480,795)(481,794)(482,793)
(483,792)(484,791)(485,790)(486,789)(487,788)(488,787)(489,786)(490,785)
(491,784)(492,783)(493,782)(494,781)(495,761)(496,779)(497,778)(498,777)
(499,776)(500,775)(501,774)(502,773)(503,772)(504,771)(505,770)(506,769)
(507,768)(508,767)(509,766)(510,765)(511,764)(512,763)(513,762)(514,742)
(515,760)(516,759)(517,758)(518,757)(519,756)(520,755)(521,754)(522,753)
(523,752)(524,751)(525,750)(526,749)(527,748)(528,747)(529,746)(530,745)
(531,744)(532,743)(533,723)(534,741)(535,740)(536,739)(537,738)(538,737)
(539,736)(540,735)(541,734)(542,733)(543,732)(544,731)(545,730)(546,729)
(547,728)(548,727)(549,726)(550,725)(551,724)(552,704)(553,722)(554,721)
(555,720)(556,719)(557,718)(558,717)(559,716)(560,715)(561,714)(562,713)
(563,712)(564,711)(565,710)(566,709)(567,708)(568,707)(569,706)(570,705)
(571,685)(572,703)(573,702)(574,701)(575,700)(576,699)(577,698)(578,697)
(579,696)(580,695)(581,694)(582,693)(583,692)(584,691)(585,690)(586,689)
(587,688)(588,687)(589,686)(590,666)(591,684)(592,683)(593,682)(594,681)
(595,680)(596,679)(597,678)(598,677)(599,676)(600,675)(601,674)(602,673)
(603,672)(604,671)(605,670)(606,669)(607,668)(608,667)(609,647)(610,665)
(611,664)(612,663)(613,662)(614,661)(615,660)(616,659)(617,658)(618,657)
(619,656)(620,655)(621,654)(622,653)(623,652)(624,651)(625,650)(626,649)
(627,648);;
s1 := ( 1,439)( 2,438)( 3,456)( 4,455)( 5,454)( 6,453)( 7,452)( 8,451)
( 9,450)( 10,449)( 11,448)( 12,447)( 13,446)( 14,445)( 15,444)( 16,443)
( 17,442)( 18,441)( 19,440)( 20,420)( 21,419)( 22,437)( 23,436)( 24,435)
( 25,434)( 26,433)( 27,432)( 28,431)( 29,430)( 30,429)( 31,428)( 32,427)
( 33,426)( 34,425)( 35,424)( 36,423)( 37,422)( 38,421)( 39,610)( 40,609)
( 41,627)( 42,626)( 43,625)( 44,624)( 45,623)( 46,622)( 47,621)( 48,620)
( 49,619)( 50,618)( 51,617)( 52,616)( 53,615)( 54,614)( 55,613)( 56,612)
( 57,611)( 58,591)( 59,590)( 60,608)( 61,607)( 62,606)( 63,605)( 64,604)
( 65,603)( 66,602)( 67,601)( 68,600)( 69,599)( 70,598)( 71,597)( 72,596)
( 73,595)( 74,594)( 75,593)( 76,592)( 77,572)( 78,571)( 79,589)( 80,588)
( 81,587)( 82,586)( 83,585)( 84,584)( 85,583)( 86,582)( 87,581)( 88,580)
( 89,579)( 90,578)( 91,577)( 92,576)( 93,575)( 94,574)( 95,573)( 96,553)
( 97,552)( 98,570)( 99,569)(100,568)(101,567)(102,566)(103,565)(104,564)
(105,563)(106,562)(107,561)(108,560)(109,559)(110,558)(111,557)(112,556)
(113,555)(114,554)(115,534)(116,533)(117,551)(118,550)(119,549)(120,548)
(121,547)(122,546)(123,545)(124,544)(125,543)(126,542)(127,541)(128,540)
(129,539)(130,538)(131,537)(132,536)(133,535)(134,515)(135,514)(136,532)
(137,531)(138,530)(139,529)(140,528)(141,527)(142,526)(143,525)(144,524)
(145,523)(146,522)(147,521)(148,520)(149,519)(150,518)(151,517)(152,516)
(153,496)(154,495)(155,513)(156,512)(157,511)(158,510)(159,509)(160,508)
(161,507)(162,506)(163,505)(164,504)(165,503)(166,502)(167,501)(168,500)
(169,499)(170,498)(171,497)(172,477)(173,476)(174,494)(175,493)(176,492)
(177,491)(178,490)(179,489)(180,488)(181,487)(182,486)(183,485)(184,484)
(185,483)(186,482)(187,481)(188,480)(189,479)(190,478)(191,458)(192,457)
(193,475)(194,474)(195,473)(196,472)(197,471)(198,470)(199,469)(200,468)
(201,467)(202,466)(203,465)(204,464)(205,463)(206,462)(207,461)(208,460)
(209,459)(210,648)(211,647)(212,665)(213,664)(214,663)(215,662)(216,661)
(217,660)(218,659)(219,658)(220,657)(221,656)(222,655)(223,654)(224,653)
(225,652)(226,651)(227,650)(228,649)(229,629)(230,628)(231,646)(232,645)
(233,644)(234,643)(235,642)(236,641)(237,640)(238,639)(239,638)(240,637)
(241,636)(242,635)(243,634)(244,633)(245,632)(246,631)(247,630)(248,819)
(249,818)(250,836)(251,835)(252,834)(253,833)(254,832)(255,831)(256,830)
(257,829)(258,828)(259,827)(260,826)(261,825)(262,824)(263,823)(264,822)
(265,821)(266,820)(267,800)(268,799)(269,817)(270,816)(271,815)(272,814)
(273,813)(274,812)(275,811)(276,810)(277,809)(278,808)(279,807)(280,806)
(281,805)(282,804)(283,803)(284,802)(285,801)(286,781)(287,780)(288,798)
(289,797)(290,796)(291,795)(292,794)(293,793)(294,792)(295,791)(296,790)
(297,789)(298,788)(299,787)(300,786)(301,785)(302,784)(303,783)(304,782)
(305,762)(306,761)(307,779)(308,778)(309,777)(310,776)(311,775)(312,774)
(313,773)(314,772)(315,771)(316,770)(317,769)(318,768)(319,767)(320,766)
(321,765)(322,764)(323,763)(324,743)(325,742)(326,760)(327,759)(328,758)
(329,757)(330,756)(331,755)(332,754)(333,753)(334,752)(335,751)(336,750)
(337,749)(338,748)(339,747)(340,746)(341,745)(342,744)(343,724)(344,723)
(345,741)(346,740)(347,739)(348,738)(349,737)(350,736)(351,735)(352,734)
(353,733)(354,732)(355,731)(356,730)(357,729)(358,728)(359,727)(360,726)
(361,725)(362,705)(363,704)(364,722)(365,721)(366,720)(367,719)(368,718)
(369,717)(370,716)(371,715)(372,714)(373,713)(374,712)(375,711)(376,710)
(377,709)(378,708)(379,707)(380,706)(381,686)(382,685)(383,703)(384,702)
(385,701)(386,700)(387,699)(388,698)(389,697)(390,696)(391,695)(392,694)
(393,693)(394,692)(395,691)(396,690)(397,689)(398,688)(399,687)(400,667)
(401,666)(402,684)(403,683)(404,682)(405,681)(406,680)(407,679)(408,678)
(409,677)(410,676)(411,675)(412,674)(413,673)(414,672)(415,671)(416,670)
(417,669)(418,668);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(836)!( 2, 19)( 3, 18)( 4, 17)( 5, 16)( 6, 15)( 7, 14)( 8, 13)
( 9, 12)( 10, 11)( 20,191)( 21,209)( 22,208)( 23,207)( 24,206)( 25,205)
( 26,204)( 27,203)( 28,202)( 29,201)( 30,200)( 31,199)( 32,198)( 33,197)
( 34,196)( 35,195)( 36,194)( 37,193)( 38,192)( 39,172)( 40,190)( 41,189)
( 42,188)( 43,187)( 44,186)( 45,185)( 46,184)( 47,183)( 48,182)( 49,181)
( 50,180)( 51,179)( 52,178)( 53,177)( 54,176)( 55,175)( 56,174)( 57,173)
( 58,153)( 59,171)( 60,170)( 61,169)( 62,168)( 63,167)( 64,166)( 65,165)
( 66,164)( 67,163)( 68,162)( 69,161)( 70,160)( 71,159)( 72,158)( 73,157)
( 74,156)( 75,155)( 76,154)( 77,134)( 78,152)( 79,151)( 80,150)( 81,149)
( 82,148)( 83,147)( 84,146)( 85,145)( 86,144)( 87,143)( 88,142)( 89,141)
( 90,140)( 91,139)( 92,138)( 93,137)( 94,136)( 95,135)( 96,115)( 97,133)
( 98,132)( 99,131)(100,130)(101,129)(102,128)(103,127)(104,126)(105,125)
(106,124)(107,123)(108,122)(109,121)(110,120)(111,119)(112,118)(113,117)
(114,116)(211,228)(212,227)(213,226)(214,225)(215,224)(216,223)(217,222)
(218,221)(219,220)(229,400)(230,418)(231,417)(232,416)(233,415)(234,414)
(235,413)(236,412)(237,411)(238,410)(239,409)(240,408)(241,407)(242,406)
(243,405)(244,404)(245,403)(246,402)(247,401)(248,381)(249,399)(250,398)
(251,397)(252,396)(253,395)(254,394)(255,393)(256,392)(257,391)(258,390)
(259,389)(260,388)(261,387)(262,386)(263,385)(264,384)(265,383)(266,382)
(267,362)(268,380)(269,379)(270,378)(271,377)(272,376)(273,375)(274,374)
(275,373)(276,372)(277,371)(278,370)(279,369)(280,368)(281,367)(282,366)
(283,365)(284,364)(285,363)(286,343)(287,361)(288,360)(289,359)(290,358)
(291,357)(292,356)(293,355)(294,354)(295,353)(296,352)(297,351)(298,350)
(299,349)(300,348)(301,347)(302,346)(303,345)(304,344)(305,324)(306,342)
(307,341)(308,340)(309,339)(310,338)(311,337)(312,336)(313,335)(314,334)
(315,333)(316,332)(317,331)(318,330)(319,329)(320,328)(321,327)(322,326)
(323,325)(419,628)(420,646)(421,645)(422,644)(423,643)(424,642)(425,641)
(426,640)(427,639)(428,638)(429,637)(430,636)(431,635)(432,634)(433,633)
(434,632)(435,631)(436,630)(437,629)(438,818)(439,836)(440,835)(441,834)
(442,833)(443,832)(444,831)(445,830)(446,829)(447,828)(448,827)(449,826)
(450,825)(451,824)(452,823)(453,822)(454,821)(455,820)(456,819)(457,799)
(458,817)(459,816)(460,815)(461,814)(462,813)(463,812)(464,811)(465,810)
(466,809)(467,808)(468,807)(469,806)(470,805)(471,804)(472,803)(473,802)
(474,801)(475,800)(476,780)(477,798)(478,797)(479,796)(480,795)(481,794)
(482,793)(483,792)(484,791)(485,790)(486,789)(487,788)(488,787)(489,786)
(490,785)(491,784)(492,783)(493,782)(494,781)(495,761)(496,779)(497,778)
(498,777)(499,776)(500,775)(501,774)(502,773)(503,772)(504,771)(505,770)
(506,769)(507,768)(508,767)(509,766)(510,765)(511,764)(512,763)(513,762)
(514,742)(515,760)(516,759)(517,758)(518,757)(519,756)(520,755)(521,754)
(522,753)(523,752)(524,751)(525,750)(526,749)(527,748)(528,747)(529,746)
(530,745)(531,744)(532,743)(533,723)(534,741)(535,740)(536,739)(537,738)
(538,737)(539,736)(540,735)(541,734)(542,733)(543,732)(544,731)(545,730)
(546,729)(547,728)(548,727)(549,726)(550,725)(551,724)(552,704)(553,722)
(554,721)(555,720)(556,719)(557,718)(558,717)(559,716)(560,715)(561,714)
(562,713)(563,712)(564,711)(565,710)(566,709)(567,708)(568,707)(569,706)
(570,705)(571,685)(572,703)(573,702)(574,701)(575,700)(576,699)(577,698)
(578,697)(579,696)(580,695)(581,694)(582,693)(583,692)(584,691)(585,690)
(586,689)(587,688)(588,687)(589,686)(590,666)(591,684)(592,683)(593,682)
(594,681)(595,680)(596,679)(597,678)(598,677)(599,676)(600,675)(601,674)
(602,673)(603,672)(604,671)(605,670)(606,669)(607,668)(608,667)(609,647)
(610,665)(611,664)(612,663)(613,662)(614,661)(615,660)(616,659)(617,658)
(618,657)(619,656)(620,655)(621,654)(622,653)(623,652)(624,651)(625,650)
(626,649)(627,648);
s1 := Sym(836)!( 1,439)( 2,438)( 3,456)( 4,455)( 5,454)( 6,453)( 7,452)
( 8,451)( 9,450)( 10,449)( 11,448)( 12,447)( 13,446)( 14,445)( 15,444)
( 16,443)( 17,442)( 18,441)( 19,440)( 20,420)( 21,419)( 22,437)( 23,436)
( 24,435)( 25,434)( 26,433)( 27,432)( 28,431)( 29,430)( 30,429)( 31,428)
( 32,427)( 33,426)( 34,425)( 35,424)( 36,423)( 37,422)( 38,421)( 39,610)
( 40,609)( 41,627)( 42,626)( 43,625)( 44,624)( 45,623)( 46,622)( 47,621)
( 48,620)( 49,619)( 50,618)( 51,617)( 52,616)( 53,615)( 54,614)( 55,613)
( 56,612)( 57,611)( 58,591)( 59,590)( 60,608)( 61,607)( 62,606)( 63,605)
( 64,604)( 65,603)( 66,602)( 67,601)( 68,600)( 69,599)( 70,598)( 71,597)
( 72,596)( 73,595)( 74,594)( 75,593)( 76,592)( 77,572)( 78,571)( 79,589)
( 80,588)( 81,587)( 82,586)( 83,585)( 84,584)( 85,583)( 86,582)( 87,581)
( 88,580)( 89,579)( 90,578)( 91,577)( 92,576)( 93,575)( 94,574)( 95,573)
( 96,553)( 97,552)( 98,570)( 99,569)(100,568)(101,567)(102,566)(103,565)
(104,564)(105,563)(106,562)(107,561)(108,560)(109,559)(110,558)(111,557)
(112,556)(113,555)(114,554)(115,534)(116,533)(117,551)(118,550)(119,549)
(120,548)(121,547)(122,546)(123,545)(124,544)(125,543)(126,542)(127,541)
(128,540)(129,539)(130,538)(131,537)(132,536)(133,535)(134,515)(135,514)
(136,532)(137,531)(138,530)(139,529)(140,528)(141,527)(142,526)(143,525)
(144,524)(145,523)(146,522)(147,521)(148,520)(149,519)(150,518)(151,517)
(152,516)(153,496)(154,495)(155,513)(156,512)(157,511)(158,510)(159,509)
(160,508)(161,507)(162,506)(163,505)(164,504)(165,503)(166,502)(167,501)
(168,500)(169,499)(170,498)(171,497)(172,477)(173,476)(174,494)(175,493)
(176,492)(177,491)(178,490)(179,489)(180,488)(181,487)(182,486)(183,485)
(184,484)(185,483)(186,482)(187,481)(188,480)(189,479)(190,478)(191,458)
(192,457)(193,475)(194,474)(195,473)(196,472)(197,471)(198,470)(199,469)
(200,468)(201,467)(202,466)(203,465)(204,464)(205,463)(206,462)(207,461)
(208,460)(209,459)(210,648)(211,647)(212,665)(213,664)(214,663)(215,662)
(216,661)(217,660)(218,659)(219,658)(220,657)(221,656)(222,655)(223,654)
(224,653)(225,652)(226,651)(227,650)(228,649)(229,629)(230,628)(231,646)
(232,645)(233,644)(234,643)(235,642)(236,641)(237,640)(238,639)(239,638)
(240,637)(241,636)(242,635)(243,634)(244,633)(245,632)(246,631)(247,630)
(248,819)(249,818)(250,836)(251,835)(252,834)(253,833)(254,832)(255,831)
(256,830)(257,829)(258,828)(259,827)(260,826)(261,825)(262,824)(263,823)
(264,822)(265,821)(266,820)(267,800)(268,799)(269,817)(270,816)(271,815)
(272,814)(273,813)(274,812)(275,811)(276,810)(277,809)(278,808)(279,807)
(280,806)(281,805)(282,804)(283,803)(284,802)(285,801)(286,781)(287,780)
(288,798)(289,797)(290,796)(291,795)(292,794)(293,793)(294,792)(295,791)
(296,790)(297,789)(298,788)(299,787)(300,786)(301,785)(302,784)(303,783)
(304,782)(305,762)(306,761)(307,779)(308,778)(309,777)(310,776)(311,775)
(312,774)(313,773)(314,772)(315,771)(316,770)(317,769)(318,768)(319,767)
(320,766)(321,765)(322,764)(323,763)(324,743)(325,742)(326,760)(327,759)
(328,758)(329,757)(330,756)(331,755)(332,754)(333,753)(334,752)(335,751)
(336,750)(337,749)(338,748)(339,747)(340,746)(341,745)(342,744)(343,724)
(344,723)(345,741)(346,740)(347,739)(348,738)(349,737)(350,736)(351,735)
(352,734)(353,733)(354,732)(355,731)(356,730)(357,729)(358,728)(359,727)
(360,726)(361,725)(362,705)(363,704)(364,722)(365,721)(366,720)(367,719)
(368,718)(369,717)(370,716)(371,715)(372,714)(373,713)(374,712)(375,711)
(376,710)(377,709)(378,708)(379,707)(380,706)(381,686)(382,685)(383,703)
(384,702)(385,701)(386,700)(387,699)(388,698)(389,697)(390,696)(391,695)
(392,694)(393,693)(394,692)(395,691)(396,690)(397,689)(398,688)(399,687)
(400,667)(401,666)(402,684)(403,683)(404,682)(405,681)(406,680)(407,679)
(408,678)(409,677)(410,676)(411,675)(412,674)(413,673)(414,672)(415,671)
(416,670)(417,669)(418,668);
poly := sub<Sym(836)|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 >;
References : None.
to this polytope