Polytope of Type {860}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {860}*1720
Also Known As : 860-gon, {860}. if this polytope has another name.
Group : SmallGroup(1720,26)
Rank : 2
Schlafli Type : {860}
Number of vertices, edges, etc : 860, 860
Order of s0s1 : 860
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 : {430}*860
4-fold quotients : {215}*430
5-fold quotients : {172}*344
10-fold quotients : {86}*172
20-fold quotients : {43}*86
43-fold quotients : {20}*40
86-fold quotients : {10}*20
172-fold quotients : {5}*10
215-fold quotients : {4}*8
430-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 43)( 3, 42)( 4, 41)( 5, 40)( 6, 39)( 7, 38)( 8, 37)( 9, 36)
( 10, 35)( 11, 34)( 12, 33)( 13, 32)( 14, 31)( 15, 30)( 16, 29)( 17, 28)
( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 44,173)( 45,215)( 46,214)
( 47,213)( 48,212)( 49,211)( 50,210)( 51,209)( 52,208)( 53,207)( 54,206)
( 55,205)( 56,204)( 57,203)( 58,202)( 59,201)( 60,200)( 61,199)( 62,198)
( 63,197)( 64,196)( 65,195)( 66,194)( 67,193)( 68,192)( 69,191)( 70,190)
( 71,189)( 72,188)( 73,187)( 74,186)( 75,185)( 76,184)( 77,183)( 78,182)
( 79,181)( 80,180)( 81,179)( 82,178)( 83,177)( 84,176)( 85,175)( 86,174)
( 87,130)( 88,172)( 89,171)( 90,170)( 91,169)( 92,168)( 93,167)( 94,166)
( 95,165)( 96,164)( 97,163)( 98,162)( 99,161)(100,160)(101,159)(102,158)
(103,157)(104,156)(105,155)(106,154)(107,153)(108,152)(109,151)(110,150)
(111,149)(112,148)(113,147)(114,146)(115,145)(116,144)(117,143)(118,142)
(119,141)(120,140)(121,139)(122,138)(123,137)(124,136)(125,135)(126,134)
(127,133)(128,132)(129,131)(217,258)(218,257)(219,256)(220,255)(221,254)
(222,253)(223,252)(224,251)(225,250)(226,249)(227,248)(228,247)(229,246)
(230,245)(231,244)(232,243)(233,242)(234,241)(235,240)(236,239)(237,238)
(259,388)(260,430)(261,429)(262,428)(263,427)(264,426)(265,425)(266,424)
(267,423)(268,422)(269,421)(270,420)(271,419)(272,418)(273,417)(274,416)
(275,415)(276,414)(277,413)(278,412)(279,411)(280,410)(281,409)(282,408)
(283,407)(284,406)(285,405)(286,404)(287,403)(288,402)(289,401)(290,400)
(291,399)(292,398)(293,397)(294,396)(295,395)(296,394)(297,393)(298,392)
(299,391)(300,390)(301,389)(302,345)(303,387)(304,386)(305,385)(306,384)
(307,383)(308,382)(309,381)(310,380)(311,379)(312,378)(313,377)(314,376)
(315,375)(316,374)(317,373)(318,372)(319,371)(320,370)(321,369)(322,368)
(323,367)(324,366)(325,365)(326,364)(327,363)(328,362)(329,361)(330,360)
(331,359)(332,358)(333,357)(334,356)(335,355)(336,354)(337,353)(338,352)
(339,351)(340,350)(341,349)(342,348)(343,347)(344,346)(431,646)(432,688)
(433,687)(434,686)(435,685)(436,684)(437,683)(438,682)(439,681)(440,680)
(441,679)(442,678)(443,677)(444,676)(445,675)(446,674)(447,673)(448,672)
(449,671)(450,670)(451,669)(452,668)(453,667)(454,666)(455,665)(456,664)
(457,663)(458,662)(459,661)(460,660)(461,659)(462,658)(463,657)(464,656)
(465,655)(466,654)(467,653)(468,652)(469,651)(470,650)(471,649)(472,648)
(473,647)(474,818)(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)
(497,838)(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)(517,775)(518,817)(519,816)(520,815)
(521,814)(522,813)(523,812)(524,811)(525,810)(526,809)(527,808)(528,807)
(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)(559,776)(560,732)
(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)(590,745)(591,744)(592,743)
(593,742)(594,741)(595,740)(596,739)(597,738)(598,737)(599,736)(600,735)
(601,734)(602,733)(603,689)(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)(621,714)(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);;
s1 := ( 1,475)( 2,474)( 3,516)( 4,515)( 5,514)( 6,513)( 7,512)( 8,511)
( 9,510)( 10,509)( 11,508)( 12,507)( 13,506)( 14,505)( 15,504)( 16,503)
( 17,502)( 18,501)( 19,500)( 20,499)( 21,498)( 22,497)( 23,496)( 24,495)
( 25,494)( 26,493)( 27,492)( 28,491)( 29,490)( 30,489)( 31,488)( 32,487)
( 33,486)( 34,485)( 35,484)( 36,483)( 37,482)( 38,481)( 39,480)( 40,479)
( 41,478)( 42,477)( 43,476)( 44,432)( 45,431)( 46,473)( 47,472)( 48,471)
( 49,470)( 50,469)( 51,468)( 52,467)( 53,466)( 54,465)( 55,464)( 56,463)
( 57,462)( 58,461)( 59,460)( 60,459)( 61,458)( 62,457)( 63,456)( 64,455)
( 65,454)( 66,453)( 67,452)( 68,451)( 69,450)( 70,449)( 71,448)( 72,447)
( 73,446)( 74,445)( 75,444)( 76,443)( 77,442)( 78,441)( 79,440)( 80,439)
( 81,438)( 82,437)( 83,436)( 84,435)( 85,434)( 86,433)( 87,604)( 88,603)
( 89,645)( 90,644)( 91,643)( 92,642)( 93,641)( 94,640)( 95,639)( 96,638)
( 97,637)( 98,636)( 99,635)(100,634)(101,633)(102,632)(103,631)(104,630)
(105,629)(106,628)(107,627)(108,626)(109,625)(110,624)(111,623)(112,622)
(113,621)(114,620)(115,619)(116,618)(117,617)(118,616)(119,615)(120,614)
(121,613)(122,612)(123,611)(124,610)(125,609)(126,608)(127,607)(128,606)
(129,605)(130,561)(131,560)(132,602)(133,601)(134,600)(135,599)(136,598)
(137,597)(138,596)(139,595)(140,594)(141,593)(142,592)(143,591)(144,590)
(145,589)(146,588)(147,587)(148,586)(149,585)(150,584)(151,583)(152,582)
(153,581)(154,580)(155,579)(156,578)(157,577)(158,576)(159,575)(160,574)
(161,573)(162,572)(163,571)(164,570)(165,569)(166,568)(167,567)(168,566)
(169,565)(170,564)(171,563)(172,562)(173,518)(174,517)(175,559)(176,558)
(177,557)(178,556)(179,555)(180,554)(181,553)(182,552)(183,551)(184,550)
(185,549)(186,548)(187,547)(188,546)(189,545)(190,544)(191,543)(192,542)
(193,541)(194,540)(195,539)(196,538)(197,537)(198,536)(199,535)(200,534)
(201,533)(202,532)(203,531)(204,530)(205,529)(206,528)(207,527)(208,526)
(209,525)(210,524)(211,523)(212,522)(213,521)(214,520)(215,519)(216,690)
(217,689)(218,731)(219,730)(220,729)(221,728)(222,727)(223,726)(224,725)
(225,724)(226,723)(227,722)(228,721)(229,720)(230,719)(231,718)(232,717)
(233,716)(234,715)(235,714)(236,713)(237,712)(238,711)(239,710)(240,709)
(241,708)(242,707)(243,706)(244,705)(245,704)(246,703)(247,702)(248,701)
(249,700)(250,699)(251,698)(252,697)(253,696)(254,695)(255,694)(256,693)
(257,692)(258,691)(259,647)(260,646)(261,688)(262,687)(263,686)(264,685)
(265,684)(266,683)(267,682)(268,681)(269,680)(270,679)(271,678)(272,677)
(273,676)(274,675)(275,674)(276,673)(277,672)(278,671)(279,670)(280,669)
(281,668)(282,667)(283,666)(284,665)(285,664)(286,663)(287,662)(288,661)
(289,660)(290,659)(291,658)(292,657)(293,656)(294,655)(295,654)(296,653)
(297,652)(298,651)(299,650)(300,649)(301,648)(302,819)(303,818)(304,860)
(305,859)(306,858)(307,857)(308,856)(309,855)(310,854)(311,853)(312,852)
(313,851)(314,850)(315,849)(316,848)(317,847)(318,846)(319,845)(320,844)
(321,843)(322,842)(323,841)(324,840)(325,839)(326,838)(327,837)(328,836)
(329,835)(330,834)(331,833)(332,832)(333,831)(334,830)(335,829)(336,828)
(337,827)(338,826)(339,825)(340,824)(341,823)(342,822)(343,821)(344,820)
(345,776)(346,775)(347,817)(348,816)(349,815)(350,814)(351,813)(352,812)
(353,811)(354,810)(355,809)(356,808)(357,807)(358,806)(359,805)(360,804)
(361,803)(362,802)(363,801)(364,800)(365,799)(366,798)(367,797)(368,796)
(369,795)(370,794)(371,793)(372,792)(373,791)(374,790)(375,789)(376,788)
(377,787)(378,786)(379,785)(380,784)(381,783)(382,782)(383,781)(384,780)
(385,779)(386,778)(387,777)(388,733)(389,732)(390,774)(391,773)(392,772)
(393,771)(394,770)(395,769)(396,768)(397,767)(398,766)(399,765)(400,764)
(401,763)(402,762)(403,761)(404,760)(405,759)(406,758)(407,757)(408,756)
(409,755)(410,754)(411,753)(412,752)(413,751)(414,750)(415,749)(416,748)
(417,747)(418,746)(419,745)(420,744)(421,743)(422,742)(423,741)(424,740)
(425,739)(426,738)(427,737)(428,736)(429,735)(430,734);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(860)!( 2, 43)( 3, 42)( 4, 41)( 5, 40)( 6, 39)( 7, 38)( 8, 37)
( 9, 36)( 10, 35)( 11, 34)( 12, 33)( 13, 32)( 14, 31)( 15, 30)( 16, 29)
( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 44,173)( 45,215)
( 46,214)( 47,213)( 48,212)( 49,211)( 50,210)( 51,209)( 52,208)( 53,207)
( 54,206)( 55,205)( 56,204)( 57,203)( 58,202)( 59,201)( 60,200)( 61,199)
( 62,198)( 63,197)( 64,196)( 65,195)( 66,194)( 67,193)( 68,192)( 69,191)
( 70,190)( 71,189)( 72,188)( 73,187)( 74,186)( 75,185)( 76,184)( 77,183)
( 78,182)( 79,181)( 80,180)( 81,179)( 82,178)( 83,177)( 84,176)( 85,175)
( 86,174)( 87,130)( 88,172)( 89,171)( 90,170)( 91,169)( 92,168)( 93,167)
( 94,166)( 95,165)( 96,164)( 97,163)( 98,162)( 99,161)(100,160)(101,159)
(102,158)(103,157)(104,156)(105,155)(106,154)(107,153)(108,152)(109,151)
(110,150)(111,149)(112,148)(113,147)(114,146)(115,145)(116,144)(117,143)
(118,142)(119,141)(120,140)(121,139)(122,138)(123,137)(124,136)(125,135)
(126,134)(127,133)(128,132)(129,131)(217,258)(218,257)(219,256)(220,255)
(221,254)(222,253)(223,252)(224,251)(225,250)(226,249)(227,248)(228,247)
(229,246)(230,245)(231,244)(232,243)(233,242)(234,241)(235,240)(236,239)
(237,238)(259,388)(260,430)(261,429)(262,428)(263,427)(264,426)(265,425)
(266,424)(267,423)(268,422)(269,421)(270,420)(271,419)(272,418)(273,417)
(274,416)(275,415)(276,414)(277,413)(278,412)(279,411)(280,410)(281,409)
(282,408)(283,407)(284,406)(285,405)(286,404)(287,403)(288,402)(289,401)
(290,400)(291,399)(292,398)(293,397)(294,396)(295,395)(296,394)(297,393)
(298,392)(299,391)(300,390)(301,389)(302,345)(303,387)(304,386)(305,385)
(306,384)(307,383)(308,382)(309,381)(310,380)(311,379)(312,378)(313,377)
(314,376)(315,375)(316,374)(317,373)(318,372)(319,371)(320,370)(321,369)
(322,368)(323,367)(324,366)(325,365)(326,364)(327,363)(328,362)(329,361)
(330,360)(331,359)(332,358)(333,357)(334,356)(335,355)(336,354)(337,353)
(338,352)(339,351)(340,350)(341,349)(342,348)(343,347)(344,346)(431,646)
(432,688)(433,687)(434,686)(435,685)(436,684)(437,683)(438,682)(439,681)
(440,680)(441,679)(442,678)(443,677)(444,676)(445,675)(446,674)(447,673)
(448,672)(449,671)(450,670)(451,669)(452,668)(453,667)(454,666)(455,665)
(456,664)(457,663)(458,662)(459,661)(460,660)(461,659)(462,658)(463,657)
(464,656)(465,655)(466,654)(467,653)(468,652)(469,651)(470,650)(471,649)
(472,648)(473,647)(474,818)(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)(497,838)(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)(517,775)(518,817)(519,816)
(520,815)(521,814)(522,813)(523,812)(524,811)(525,810)(526,809)(527,808)
(528,807)(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)(559,776)
(560,732)(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)(590,745)(591,744)
(592,743)(593,742)(594,741)(595,740)(596,739)(597,738)(598,737)(599,736)
(600,735)(601,734)(602,733)(603,689)(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)(621,714)(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);
s1 := Sym(860)!( 1,475)( 2,474)( 3,516)( 4,515)( 5,514)( 6,513)( 7,512)
( 8,511)( 9,510)( 10,509)( 11,508)( 12,507)( 13,506)( 14,505)( 15,504)
( 16,503)( 17,502)( 18,501)( 19,500)( 20,499)( 21,498)( 22,497)( 23,496)
( 24,495)( 25,494)( 26,493)( 27,492)( 28,491)( 29,490)( 30,489)( 31,488)
( 32,487)( 33,486)( 34,485)( 35,484)( 36,483)( 37,482)( 38,481)( 39,480)
( 40,479)( 41,478)( 42,477)( 43,476)( 44,432)( 45,431)( 46,473)( 47,472)
( 48,471)( 49,470)( 50,469)( 51,468)( 52,467)( 53,466)( 54,465)( 55,464)
( 56,463)( 57,462)( 58,461)( 59,460)( 60,459)( 61,458)( 62,457)( 63,456)
( 64,455)( 65,454)( 66,453)( 67,452)( 68,451)( 69,450)( 70,449)( 71,448)
( 72,447)( 73,446)( 74,445)( 75,444)( 76,443)( 77,442)( 78,441)( 79,440)
( 80,439)( 81,438)( 82,437)( 83,436)( 84,435)( 85,434)( 86,433)( 87,604)
( 88,603)( 89,645)( 90,644)( 91,643)( 92,642)( 93,641)( 94,640)( 95,639)
( 96,638)( 97,637)( 98,636)( 99,635)(100,634)(101,633)(102,632)(103,631)
(104,630)(105,629)(106,628)(107,627)(108,626)(109,625)(110,624)(111,623)
(112,622)(113,621)(114,620)(115,619)(116,618)(117,617)(118,616)(119,615)
(120,614)(121,613)(122,612)(123,611)(124,610)(125,609)(126,608)(127,607)
(128,606)(129,605)(130,561)(131,560)(132,602)(133,601)(134,600)(135,599)
(136,598)(137,597)(138,596)(139,595)(140,594)(141,593)(142,592)(143,591)
(144,590)(145,589)(146,588)(147,587)(148,586)(149,585)(150,584)(151,583)
(152,582)(153,581)(154,580)(155,579)(156,578)(157,577)(158,576)(159,575)
(160,574)(161,573)(162,572)(163,571)(164,570)(165,569)(166,568)(167,567)
(168,566)(169,565)(170,564)(171,563)(172,562)(173,518)(174,517)(175,559)
(176,558)(177,557)(178,556)(179,555)(180,554)(181,553)(182,552)(183,551)
(184,550)(185,549)(186,548)(187,547)(188,546)(189,545)(190,544)(191,543)
(192,542)(193,541)(194,540)(195,539)(196,538)(197,537)(198,536)(199,535)
(200,534)(201,533)(202,532)(203,531)(204,530)(205,529)(206,528)(207,527)
(208,526)(209,525)(210,524)(211,523)(212,522)(213,521)(214,520)(215,519)
(216,690)(217,689)(218,731)(219,730)(220,729)(221,728)(222,727)(223,726)
(224,725)(225,724)(226,723)(227,722)(228,721)(229,720)(230,719)(231,718)
(232,717)(233,716)(234,715)(235,714)(236,713)(237,712)(238,711)(239,710)
(240,709)(241,708)(242,707)(243,706)(244,705)(245,704)(246,703)(247,702)
(248,701)(249,700)(250,699)(251,698)(252,697)(253,696)(254,695)(255,694)
(256,693)(257,692)(258,691)(259,647)(260,646)(261,688)(262,687)(263,686)
(264,685)(265,684)(266,683)(267,682)(268,681)(269,680)(270,679)(271,678)
(272,677)(273,676)(274,675)(275,674)(276,673)(277,672)(278,671)(279,670)
(280,669)(281,668)(282,667)(283,666)(284,665)(285,664)(286,663)(287,662)
(288,661)(289,660)(290,659)(291,658)(292,657)(293,656)(294,655)(295,654)
(296,653)(297,652)(298,651)(299,650)(300,649)(301,648)(302,819)(303,818)
(304,860)(305,859)(306,858)(307,857)(308,856)(309,855)(310,854)(311,853)
(312,852)(313,851)(314,850)(315,849)(316,848)(317,847)(318,846)(319,845)
(320,844)(321,843)(322,842)(323,841)(324,840)(325,839)(326,838)(327,837)
(328,836)(329,835)(330,834)(331,833)(332,832)(333,831)(334,830)(335,829)
(336,828)(337,827)(338,826)(339,825)(340,824)(341,823)(342,822)(343,821)
(344,820)(345,776)(346,775)(347,817)(348,816)(349,815)(350,814)(351,813)
(352,812)(353,811)(354,810)(355,809)(356,808)(357,807)(358,806)(359,805)
(360,804)(361,803)(362,802)(363,801)(364,800)(365,799)(366,798)(367,797)
(368,796)(369,795)(370,794)(371,793)(372,792)(373,791)(374,790)(375,789)
(376,788)(377,787)(378,786)(379,785)(380,784)(381,783)(382,782)(383,781)
(384,780)(385,779)(386,778)(387,777)(388,733)(389,732)(390,774)(391,773)
(392,772)(393,771)(394,770)(395,769)(396,768)(397,767)(398,766)(399,765)
(400,764)(401,763)(402,762)(403,761)(404,760)(405,759)(406,758)(407,757)
(408,756)(409,755)(410,754)(411,753)(412,752)(413,751)(414,750)(415,749)
(416,748)(417,747)(418,746)(419,745)(420,744)(421,743)(422,742)(423,741)
(424,740)(425,739)(426,738)(427,737)(428,736)(429,735)(430,734);
poly := sub<Sym(860)|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 >;
References : None.
to this polytope