Polytope of Type {868}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {868}*1736
Also Known As : 868-gon, {868}. if this polytope has another name.
Group : SmallGroup(1736,24)
Rank : 2
Schlafli Type : {868}
Number of vertices, edges, etc : 868, 868
Order of s0s1 : 868
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 : {434}*868
4-fold quotients : {217}*434
7-fold quotients : {124}*248
14-fold quotients : {62}*124
28-fold quotients : {31}*62
31-fold quotients : {28}*56
62-fold quotients : {14}*28
124-fold quotients : {7}*14
217-fold quotients : {4}*8
434-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 31)( 3, 30)( 4, 29)( 5, 28)( 6, 27)( 7, 26)( 8, 25)( 9, 24)
( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)( 32,187)
( 33,217)( 34,216)( 35,215)( 36,214)( 37,213)( 38,212)( 39,211)( 40,210)
( 41,209)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)( 48,202)
( 49,201)( 50,200)( 51,199)( 52,198)( 53,197)( 54,196)( 55,195)( 56,194)
( 57,193)( 58,192)( 59,191)( 60,190)( 61,189)( 62,188)( 63,156)( 64,186)
( 65,185)( 66,184)( 67,183)( 68,182)( 69,181)( 70,180)( 71,179)( 72,178)
( 73,177)( 74,176)( 75,175)( 76,174)( 77,173)( 78,172)( 79,171)( 80,170)
( 81,169)( 82,168)( 83,167)( 84,166)( 85,165)( 86,164)( 87,163)( 88,162)
( 89,161)( 90,160)( 91,159)( 92,158)( 93,157)( 94,125)( 95,155)( 96,154)
( 97,153)( 98,152)( 99,151)(100,150)(101,149)(102,148)(103,147)(104,146)
(105,145)(106,144)(107,143)(108,142)(109,141)(110,140)(111,139)(112,138)
(113,137)(114,136)(115,135)(116,134)(117,133)(118,132)(119,131)(120,130)
(121,129)(122,128)(123,127)(124,126)(219,248)(220,247)(221,246)(222,245)
(223,244)(224,243)(225,242)(226,241)(227,240)(228,239)(229,238)(230,237)
(231,236)(232,235)(233,234)(249,404)(250,434)(251,433)(252,432)(253,431)
(254,430)(255,429)(256,428)(257,427)(258,426)(259,425)(260,424)(261,423)
(262,422)(263,421)(264,420)(265,419)(266,418)(267,417)(268,416)(269,415)
(270,414)(271,413)(272,412)(273,411)(274,410)(275,409)(276,408)(277,407)
(278,406)(279,405)(280,373)(281,403)(282,402)(283,401)(284,400)(285,399)
(286,398)(287,397)(288,396)(289,395)(290,394)(291,393)(292,392)(293,391)
(294,390)(295,389)(296,388)(297,387)(298,386)(299,385)(300,384)(301,383)
(302,382)(303,381)(304,380)(305,379)(306,378)(307,377)(308,376)(309,375)
(310,374)(311,342)(312,372)(313,371)(314,370)(315,369)(316,368)(317,367)
(318,366)(319,365)(320,364)(321,363)(322,362)(323,361)(324,360)(325,359)
(326,358)(327,357)(328,356)(329,355)(330,354)(331,353)(332,352)(333,351)
(334,350)(335,349)(336,348)(337,347)(338,346)(339,345)(340,344)(341,343)
(435,652)(436,682)(437,681)(438,680)(439,679)(440,678)(441,677)(442,676)
(443,675)(444,674)(445,673)(446,672)(447,671)(448,670)(449,669)(450,668)
(451,667)(452,666)(453,665)(454,664)(455,663)(456,662)(457,661)(458,660)
(459,659)(460,658)(461,657)(462,656)(463,655)(464,654)(465,653)(466,838)
(467,868)(468,867)(469,866)(470,865)(471,864)(472,863)(473,862)(474,861)
(475,860)(476,859)(477,858)(478,857)(479,856)(480,855)(481,854)(482,853)
(483,852)(484,851)(485,850)(486,849)(487,848)(488,847)(489,846)(490,845)
(491,844)(492,843)(493,842)(494,841)(495,840)(496,839)(497,807)(498,837)
(499,836)(500,835)(501,834)(502,833)(503,832)(504,831)(505,830)(506,829)
(507,828)(508,827)(509,826)(510,825)(511,824)(512,823)(513,822)(514,821)
(515,820)(516,819)(517,818)(518,817)(519,816)(520,815)(521,814)(522,813)
(523,812)(524,811)(525,810)(526,809)(527,808)(528,776)(529,806)(530,805)
(531,804)(532,803)(533,802)(534,801)(535,800)(536,799)(537,798)(538,797)
(539,796)(540,795)(541,794)(542,793)(543,792)(544,791)(545,790)(546,789)
(547,788)(548,787)(549,786)(550,785)(551,784)(552,783)(553,782)(554,781)
(555,780)(556,779)(557,778)(558,777)(559,745)(560,775)(561,774)(562,773)
(563,772)(564,771)(565,770)(566,769)(567,768)(568,767)(569,766)(570,765)
(571,764)(572,763)(573,762)(574,761)(575,760)(576,759)(577,758)(578,757)
(579,756)(580,755)(581,754)(582,753)(583,752)(584,751)(585,750)(586,749)
(587,748)(588,747)(589,746)(590,714)(591,744)(592,743)(593,742)(594,741)
(595,740)(596,739)(597,738)(598,737)(599,736)(600,735)(601,734)(602,733)
(603,732)(604,731)(605,730)(606,729)(607,728)(608,727)(609,726)(610,725)
(611,724)(612,723)(613,722)(614,721)(615,720)(616,719)(617,718)(618,717)
(619,716)(620,715)(621,683)(622,713)(623,712)(624,711)(625,710)(626,709)
(627,708)(628,707)(629,706)(630,705)(631,704)(632,703)(633,702)(634,701)
(635,700)(636,699)(637,698)(638,697)(639,696)(640,695)(641,694)(642,693)
(643,692)(644,691)(645,690)(646,689)(647,688)(648,687)(649,686)(650,685)
(651,684);;
s1 := ( 1,467)( 2,466)( 3,496)( 4,495)( 5,494)( 6,493)( 7,492)( 8,491)
( 9,490)( 10,489)( 11,488)( 12,487)( 13,486)( 14,485)( 15,484)( 16,483)
( 17,482)( 18,481)( 19,480)( 20,479)( 21,478)( 22,477)( 23,476)( 24,475)
( 25,474)( 26,473)( 27,472)( 28,471)( 29,470)( 30,469)( 31,468)( 32,436)
( 33,435)( 34,465)( 35,464)( 36,463)( 37,462)( 38,461)( 39,460)( 40,459)
( 41,458)( 42,457)( 43,456)( 44,455)( 45,454)( 46,453)( 47,452)( 48,451)
( 49,450)( 50,449)( 51,448)( 52,447)( 53,446)( 54,445)( 55,444)( 56,443)
( 57,442)( 58,441)( 59,440)( 60,439)( 61,438)( 62,437)( 63,622)( 64,621)
( 65,651)( 66,650)( 67,649)( 68,648)( 69,647)( 70,646)( 71,645)( 72,644)
( 73,643)( 74,642)( 75,641)( 76,640)( 77,639)( 78,638)( 79,637)( 80,636)
( 81,635)( 82,634)( 83,633)( 84,632)( 85,631)( 86,630)( 87,629)( 88,628)
( 89,627)( 90,626)( 91,625)( 92,624)( 93,623)( 94,591)( 95,590)( 96,620)
( 97,619)( 98,618)( 99,617)(100,616)(101,615)(102,614)(103,613)(104,612)
(105,611)(106,610)(107,609)(108,608)(109,607)(110,606)(111,605)(112,604)
(113,603)(114,602)(115,601)(116,600)(117,599)(118,598)(119,597)(120,596)
(121,595)(122,594)(123,593)(124,592)(125,560)(126,559)(127,589)(128,588)
(129,587)(130,586)(131,585)(132,584)(133,583)(134,582)(135,581)(136,580)
(137,579)(138,578)(139,577)(140,576)(141,575)(142,574)(143,573)(144,572)
(145,571)(146,570)(147,569)(148,568)(149,567)(150,566)(151,565)(152,564)
(153,563)(154,562)(155,561)(156,529)(157,528)(158,558)(159,557)(160,556)
(161,555)(162,554)(163,553)(164,552)(165,551)(166,550)(167,549)(168,548)
(169,547)(170,546)(171,545)(172,544)(173,543)(174,542)(175,541)(176,540)
(177,539)(178,538)(179,537)(180,536)(181,535)(182,534)(183,533)(184,532)
(185,531)(186,530)(187,498)(188,497)(189,527)(190,526)(191,525)(192,524)
(193,523)(194,522)(195,521)(196,520)(197,519)(198,518)(199,517)(200,516)
(201,515)(202,514)(203,513)(204,512)(205,511)(206,510)(207,509)(208,508)
(209,507)(210,506)(211,505)(212,504)(213,503)(214,502)(215,501)(216,500)
(217,499)(218,684)(219,683)(220,713)(221,712)(222,711)(223,710)(224,709)
(225,708)(226,707)(227,706)(228,705)(229,704)(230,703)(231,702)(232,701)
(233,700)(234,699)(235,698)(236,697)(237,696)(238,695)(239,694)(240,693)
(241,692)(242,691)(243,690)(244,689)(245,688)(246,687)(247,686)(248,685)
(249,653)(250,652)(251,682)(252,681)(253,680)(254,679)(255,678)(256,677)
(257,676)(258,675)(259,674)(260,673)(261,672)(262,671)(263,670)(264,669)
(265,668)(266,667)(267,666)(268,665)(269,664)(270,663)(271,662)(272,661)
(273,660)(274,659)(275,658)(276,657)(277,656)(278,655)(279,654)(280,839)
(281,838)(282,868)(283,867)(284,866)(285,865)(286,864)(287,863)(288,862)
(289,861)(290,860)(291,859)(292,858)(293,857)(294,856)(295,855)(296,854)
(297,853)(298,852)(299,851)(300,850)(301,849)(302,848)(303,847)(304,846)
(305,845)(306,844)(307,843)(308,842)(309,841)(310,840)(311,808)(312,807)
(313,837)(314,836)(315,835)(316,834)(317,833)(318,832)(319,831)(320,830)
(321,829)(322,828)(323,827)(324,826)(325,825)(326,824)(327,823)(328,822)
(329,821)(330,820)(331,819)(332,818)(333,817)(334,816)(335,815)(336,814)
(337,813)(338,812)(339,811)(340,810)(341,809)(342,777)(343,776)(344,806)
(345,805)(346,804)(347,803)(348,802)(349,801)(350,800)(351,799)(352,798)
(353,797)(354,796)(355,795)(356,794)(357,793)(358,792)(359,791)(360,790)
(361,789)(362,788)(363,787)(364,786)(365,785)(366,784)(367,783)(368,782)
(369,781)(370,780)(371,779)(372,778)(373,746)(374,745)(375,775)(376,774)
(377,773)(378,772)(379,771)(380,770)(381,769)(382,768)(383,767)(384,766)
(385,765)(386,764)(387,763)(388,762)(389,761)(390,760)(391,759)(392,758)
(393,757)(394,756)(395,755)(396,754)(397,753)(398,752)(399,751)(400,750)
(401,749)(402,748)(403,747)(404,715)(405,714)(406,744)(407,743)(408,742)
(409,741)(410,740)(411,739)(412,738)(413,737)(414,736)(415,735)(416,734)
(417,733)(418,732)(419,731)(420,730)(421,729)(422,728)(423,727)(424,726)
(425,725)(426,724)(427,723)(428,722)(429,721)(430,720)(431,719)(432,718)
(433,717)(434,716);;
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*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(868)!( 2, 31)( 3, 30)( 4, 29)( 5, 28)( 6, 27)( 7, 26)( 8, 25)
( 9, 24)( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)
( 32,187)( 33,217)( 34,216)( 35,215)( 36,214)( 37,213)( 38,212)( 39,211)
( 40,210)( 41,209)( 42,208)( 43,207)( 44,206)( 45,205)( 46,204)( 47,203)
( 48,202)( 49,201)( 50,200)( 51,199)( 52,198)( 53,197)( 54,196)( 55,195)
( 56,194)( 57,193)( 58,192)( 59,191)( 60,190)( 61,189)( 62,188)( 63,156)
( 64,186)( 65,185)( 66,184)( 67,183)( 68,182)( 69,181)( 70,180)( 71,179)
( 72,178)( 73,177)( 74,176)( 75,175)( 76,174)( 77,173)( 78,172)( 79,171)
( 80,170)( 81,169)( 82,168)( 83,167)( 84,166)( 85,165)( 86,164)( 87,163)
( 88,162)( 89,161)( 90,160)( 91,159)( 92,158)( 93,157)( 94,125)( 95,155)
( 96,154)( 97,153)( 98,152)( 99,151)(100,150)(101,149)(102,148)(103,147)
(104,146)(105,145)(106,144)(107,143)(108,142)(109,141)(110,140)(111,139)
(112,138)(113,137)(114,136)(115,135)(116,134)(117,133)(118,132)(119,131)
(120,130)(121,129)(122,128)(123,127)(124,126)(219,248)(220,247)(221,246)
(222,245)(223,244)(224,243)(225,242)(226,241)(227,240)(228,239)(229,238)
(230,237)(231,236)(232,235)(233,234)(249,404)(250,434)(251,433)(252,432)
(253,431)(254,430)(255,429)(256,428)(257,427)(258,426)(259,425)(260,424)
(261,423)(262,422)(263,421)(264,420)(265,419)(266,418)(267,417)(268,416)
(269,415)(270,414)(271,413)(272,412)(273,411)(274,410)(275,409)(276,408)
(277,407)(278,406)(279,405)(280,373)(281,403)(282,402)(283,401)(284,400)
(285,399)(286,398)(287,397)(288,396)(289,395)(290,394)(291,393)(292,392)
(293,391)(294,390)(295,389)(296,388)(297,387)(298,386)(299,385)(300,384)
(301,383)(302,382)(303,381)(304,380)(305,379)(306,378)(307,377)(308,376)
(309,375)(310,374)(311,342)(312,372)(313,371)(314,370)(315,369)(316,368)
(317,367)(318,366)(319,365)(320,364)(321,363)(322,362)(323,361)(324,360)
(325,359)(326,358)(327,357)(328,356)(329,355)(330,354)(331,353)(332,352)
(333,351)(334,350)(335,349)(336,348)(337,347)(338,346)(339,345)(340,344)
(341,343)(435,652)(436,682)(437,681)(438,680)(439,679)(440,678)(441,677)
(442,676)(443,675)(444,674)(445,673)(446,672)(447,671)(448,670)(449,669)
(450,668)(451,667)(452,666)(453,665)(454,664)(455,663)(456,662)(457,661)
(458,660)(459,659)(460,658)(461,657)(462,656)(463,655)(464,654)(465,653)
(466,838)(467,868)(468,867)(469,866)(470,865)(471,864)(472,863)(473,862)
(474,861)(475,860)(476,859)(477,858)(478,857)(479,856)(480,855)(481,854)
(482,853)(483,852)(484,851)(485,850)(486,849)(487,848)(488,847)(489,846)
(490,845)(491,844)(492,843)(493,842)(494,841)(495,840)(496,839)(497,807)
(498,837)(499,836)(500,835)(501,834)(502,833)(503,832)(504,831)(505,830)
(506,829)(507,828)(508,827)(509,826)(510,825)(511,824)(512,823)(513,822)
(514,821)(515,820)(516,819)(517,818)(518,817)(519,816)(520,815)(521,814)
(522,813)(523,812)(524,811)(525,810)(526,809)(527,808)(528,776)(529,806)
(530,805)(531,804)(532,803)(533,802)(534,801)(535,800)(536,799)(537,798)
(538,797)(539,796)(540,795)(541,794)(542,793)(543,792)(544,791)(545,790)
(546,789)(547,788)(548,787)(549,786)(550,785)(551,784)(552,783)(553,782)
(554,781)(555,780)(556,779)(557,778)(558,777)(559,745)(560,775)(561,774)
(562,773)(563,772)(564,771)(565,770)(566,769)(567,768)(568,767)(569,766)
(570,765)(571,764)(572,763)(573,762)(574,761)(575,760)(576,759)(577,758)
(578,757)(579,756)(580,755)(581,754)(582,753)(583,752)(584,751)(585,750)
(586,749)(587,748)(588,747)(589,746)(590,714)(591,744)(592,743)(593,742)
(594,741)(595,740)(596,739)(597,738)(598,737)(599,736)(600,735)(601,734)
(602,733)(603,732)(604,731)(605,730)(606,729)(607,728)(608,727)(609,726)
(610,725)(611,724)(612,723)(613,722)(614,721)(615,720)(616,719)(617,718)
(618,717)(619,716)(620,715)(621,683)(622,713)(623,712)(624,711)(625,710)
(626,709)(627,708)(628,707)(629,706)(630,705)(631,704)(632,703)(633,702)
(634,701)(635,700)(636,699)(637,698)(638,697)(639,696)(640,695)(641,694)
(642,693)(643,692)(644,691)(645,690)(646,689)(647,688)(648,687)(649,686)
(650,685)(651,684);
s1 := Sym(868)!( 1,467)( 2,466)( 3,496)( 4,495)( 5,494)( 6,493)( 7,492)
( 8,491)( 9,490)( 10,489)( 11,488)( 12,487)( 13,486)( 14,485)( 15,484)
( 16,483)( 17,482)( 18,481)( 19,480)( 20,479)( 21,478)( 22,477)( 23,476)
( 24,475)( 25,474)( 26,473)( 27,472)( 28,471)( 29,470)( 30,469)( 31,468)
( 32,436)( 33,435)( 34,465)( 35,464)( 36,463)( 37,462)( 38,461)( 39,460)
( 40,459)( 41,458)( 42,457)( 43,456)( 44,455)( 45,454)( 46,453)( 47,452)
( 48,451)( 49,450)( 50,449)( 51,448)( 52,447)( 53,446)( 54,445)( 55,444)
( 56,443)( 57,442)( 58,441)( 59,440)( 60,439)( 61,438)( 62,437)( 63,622)
( 64,621)( 65,651)( 66,650)( 67,649)( 68,648)( 69,647)( 70,646)( 71,645)
( 72,644)( 73,643)( 74,642)( 75,641)( 76,640)( 77,639)( 78,638)( 79,637)
( 80,636)( 81,635)( 82,634)( 83,633)( 84,632)( 85,631)( 86,630)( 87,629)
( 88,628)( 89,627)( 90,626)( 91,625)( 92,624)( 93,623)( 94,591)( 95,590)
( 96,620)( 97,619)( 98,618)( 99,617)(100,616)(101,615)(102,614)(103,613)
(104,612)(105,611)(106,610)(107,609)(108,608)(109,607)(110,606)(111,605)
(112,604)(113,603)(114,602)(115,601)(116,600)(117,599)(118,598)(119,597)
(120,596)(121,595)(122,594)(123,593)(124,592)(125,560)(126,559)(127,589)
(128,588)(129,587)(130,586)(131,585)(132,584)(133,583)(134,582)(135,581)
(136,580)(137,579)(138,578)(139,577)(140,576)(141,575)(142,574)(143,573)
(144,572)(145,571)(146,570)(147,569)(148,568)(149,567)(150,566)(151,565)
(152,564)(153,563)(154,562)(155,561)(156,529)(157,528)(158,558)(159,557)
(160,556)(161,555)(162,554)(163,553)(164,552)(165,551)(166,550)(167,549)
(168,548)(169,547)(170,546)(171,545)(172,544)(173,543)(174,542)(175,541)
(176,540)(177,539)(178,538)(179,537)(180,536)(181,535)(182,534)(183,533)
(184,532)(185,531)(186,530)(187,498)(188,497)(189,527)(190,526)(191,525)
(192,524)(193,523)(194,522)(195,521)(196,520)(197,519)(198,518)(199,517)
(200,516)(201,515)(202,514)(203,513)(204,512)(205,511)(206,510)(207,509)
(208,508)(209,507)(210,506)(211,505)(212,504)(213,503)(214,502)(215,501)
(216,500)(217,499)(218,684)(219,683)(220,713)(221,712)(222,711)(223,710)
(224,709)(225,708)(226,707)(227,706)(228,705)(229,704)(230,703)(231,702)
(232,701)(233,700)(234,699)(235,698)(236,697)(237,696)(238,695)(239,694)
(240,693)(241,692)(242,691)(243,690)(244,689)(245,688)(246,687)(247,686)
(248,685)(249,653)(250,652)(251,682)(252,681)(253,680)(254,679)(255,678)
(256,677)(257,676)(258,675)(259,674)(260,673)(261,672)(262,671)(263,670)
(264,669)(265,668)(266,667)(267,666)(268,665)(269,664)(270,663)(271,662)
(272,661)(273,660)(274,659)(275,658)(276,657)(277,656)(278,655)(279,654)
(280,839)(281,838)(282,868)(283,867)(284,866)(285,865)(286,864)(287,863)
(288,862)(289,861)(290,860)(291,859)(292,858)(293,857)(294,856)(295,855)
(296,854)(297,853)(298,852)(299,851)(300,850)(301,849)(302,848)(303,847)
(304,846)(305,845)(306,844)(307,843)(308,842)(309,841)(310,840)(311,808)
(312,807)(313,837)(314,836)(315,835)(316,834)(317,833)(318,832)(319,831)
(320,830)(321,829)(322,828)(323,827)(324,826)(325,825)(326,824)(327,823)
(328,822)(329,821)(330,820)(331,819)(332,818)(333,817)(334,816)(335,815)
(336,814)(337,813)(338,812)(339,811)(340,810)(341,809)(342,777)(343,776)
(344,806)(345,805)(346,804)(347,803)(348,802)(349,801)(350,800)(351,799)
(352,798)(353,797)(354,796)(355,795)(356,794)(357,793)(358,792)(359,791)
(360,790)(361,789)(362,788)(363,787)(364,786)(365,785)(366,784)(367,783)
(368,782)(369,781)(370,780)(371,779)(372,778)(373,746)(374,745)(375,775)
(376,774)(377,773)(378,772)(379,771)(380,770)(381,769)(382,768)(383,767)
(384,766)(385,765)(386,764)(387,763)(388,762)(389,761)(390,760)(391,759)
(392,758)(393,757)(394,756)(395,755)(396,754)(397,753)(398,752)(399,751)
(400,750)(401,749)(402,748)(403,747)(404,715)(405,714)(406,744)(407,743)
(408,742)(409,741)(410,740)(411,739)(412,738)(413,737)(414,736)(415,735)
(416,734)(417,733)(418,732)(419,731)(420,730)(421,729)(422,728)(423,727)
(424,726)(425,725)(426,724)(427,723)(428,722)(429,721)(430,720)(431,719)
(432,718)(433,717)(434,716);
poly := sub<Sym(868)|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*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