Polytope of Type {858}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {858}*1716
Also Known As : 858-gon, {858}. if this polytope has another name.
Group : SmallGroup(1716,39)
Rank : 2
Schlafli Type : {858}
Number of vertices, edges, etc : 858, 858
Order of s0s1 : 858
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 : {429}*858
3-fold quotients : {286}*572
6-fold quotients : {143}*286
11-fold quotients : {78}*156
13-fold quotients : {66}*132
22-fold quotients : {39}*78
26-fold quotients : {33}*66
33-fold quotients : {26}*52
39-fold quotients : {22}*44
66-fold quotients : {13}*26
78-fold quotients : {11}*22
143-fold quotients : {6}*12
286-fold quotients : {3}*6
429-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 14,131)( 15,143)( 16,142)( 17,141)( 18,140)( 19,139)( 20,138)( 21,137)( 22,136)( 23,135)( 24,134)( 25,133)( 26,132)( 27,118)( 28,130)( 29,129)( 30,128)( 31,127)( 32,126)( 33,125)( 34,124)( 35,123)( 36,122)( 37,121)( 38,120)( 39,119)( 40,105)( 41,117)( 42,116)( 43,115)( 44,114)( 45,113)( 46,112)( 47,111)( 48,110)( 49,109)( 50,108)( 51,107)( 52,106)( 53, 92)( 54,104)( 55,103)( 56,102)( 57,101)( 58,100)( 59, 99)( 60, 98)( 61, 97)( 62, 96)( 63, 95)( 64, 94)( 65, 93)( 66, 79)( 67, 91)( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)( 74, 84)( 75, 83)( 76, 82)( 77, 81)( 78, 80)(144,287)(145,299)(146,298)(147,297)(148,296)(149,295)(150,294)(151,293)(152,292)(153,291)(154,290)(155,289)(156,288)(157,417)(158,429)(159,428)(160,427)(161,426)(162,425)(163,424)(164,423)(165,422)(166,421)(167,420)(168,419)(169,418)(170,404)(171,416)(172,415)(173,414)(174,413)(175,412)(176,411)(177,410)(178,409)(179,408)(180,407)(181,406)(182,405)(183,391)(184,403)(185,402)(186,401)(187,400)(188,399)(189,398)(190,397)(191,396)(192,395)(193,394)(194,393)(195,392)(196,378)(197,390)(198,389)(199,388)(200,387)(201,386)(202,385)(203,384)(204,383)(205,382)(206,381)(207,380)(208,379)(209,365)(210,377)(211,376)(212,375)(213,374)(214,373)(215,372)(216,371)(217,370)(218,369)(219,368)(220,367)(221,366)(222,352)(223,364)(224,363)(225,362)(226,361)(227,360)(228,359)(229,358)(230,357)(231,356)(232,355)(233,354)(234,353)(235,339)(236,351)(237,350)(238,349)(239,348)(240,347)(241,346)(242,345)(243,344)(244,343)(245,342)(246,341)(247,340)(248,326)(249,338)(250,337)(251,336)(252,335)(253,334)(254,333)(255,332)(256,331)(257,330)(258,329)(259,328)(260,327)(261,313)(262,325)(263,324)(264,323)(265,322)(266,321)(267,320)(268,319)(269,318)(270,317)(271,316)(272,315)(273,314)(274,300)(275,312)(276,311)(277,310)(278,309)(279,308)(280,307)(281,306)(282,305)(283,304)(284,303)(285,302)(286,301)(431,442)(432,441)(433,440)(434,439)(435,438)(436,437)(443,560)(444,572)(445,571)(446,570)(447,569)(448,568)(449,567)(450,566)(451,565)(452,564)(453,563)(454,562)(455,561)(456,547)(457,559)(458,558)(459,557)(460,556)(461,555)(462,554)(463,553)(464,552)(465,551)(466,550)(467,549)(468,548)(469,534)(470,546)(471,545)(472,544)(473,543)(474,542)(475,541)(476,540)(477,539)(478,538)(479,537)(480,536)(481,535)(482,521)(483,533)(484,532)(485,531)(486,530)(487,529)(488,528)(489,527)(490,526)(491,525)(492,524)(493,523)(494,522)(495,508)(496,520)(497,519)(498,518)(499,517)(500,516)(501,515)(502,514)(503,513)(504,512)(505,511)(506,510)(507,509)(573,716)(574,728)(575,727)(576,726)(577,725)(578,724)(579,723)(580,722)(581,721)(582,720)(583,719)(584,718)(585,717)(586,846)(587,858)(588,857)(589,856)(590,855)(591,854)(592,853)(593,852)(594,851)(595,850)(596,849)(597,848)(598,847)(599,833)(600,845)(601,844)(602,843)(603,842)(604,841)(605,840)(606,839)(607,838)(608,837)(609,836)(610,835)(611,834)(612,820)(613,832)(614,831)(615,830)(616,829)(617,828)(618,827)(619,826)(620,825)(621,824)(622,823)(623,822)(624,821)(625,807)(626,819)(627,818)(628,817)(629,816)(630,815)(631,814)(632,813)(633,812)(634,811)(635,810)(636,809)(637,808)(638,794)(639,806)(640,805)(641,804)(642,803)(643,802)(644,801)(645,800)(646,799)(647,798)(648,797)(649,796)(650,795)(651,781)(652,793)(653,792)(654,791)(655,790)(656,789)(657,788)(658,787)(659,786)(660,785)(661,784)(662,783)(663,782)(664,768)(665,780)(666,779)(667,778)(668,777)(669,776)(670,775)(671,774)(672,773)(673,772)(674,771)(675,770)(676,769)(677,755)(678,767)(679,766)(680,765)(681,764)(682,763)(683,762)(684,761)(685,760)(686,759)(687,758)(688,757)(689,756)(690,742)(691,754)(692,753)(693,752)(694,751)(695,750)(696,749)(697,748)(698,747)(699,746)(700,745)(701,744)(702,743)(703,729)(704,741)(705,740)(706,739)(707,738)(708,737)(709,736)(710,735)(711,734)(712,733)(713,732)(714,731)(715,730);;
s1 := ( 1,587)( 2,586)( 3,598)( 4,597)( 5,596)( 6,595)( 7,594)( 8,593)( 9,592)( 10,591)( 11,590)( 12,589)( 13,588)( 14,574)( 15,573)( 16,585)( 17,584)( 18,583)( 19,582)( 20,581)( 21,580)( 22,579)( 23,578)( 24,577)( 25,576)( 26,575)( 27,704)( 28,703)( 29,715)( 30,714)( 31,713)( 32,712)( 33,711)( 34,710)( 35,709)( 36,708)( 37,707)( 38,706)( 39,705)( 40,691)( 41,690)( 42,702)( 43,701)( 44,700)( 45,699)( 46,698)( 47,697)( 48,696)( 49,695)( 50,694)( 51,693)( 52,692)( 53,678)( 54,677)( 55,689)( 56,688)( 57,687)( 58,686)( 59,685)( 60,684)( 61,683)( 62,682)( 63,681)( 64,680)( 65,679)( 66,665)( 67,664)( 68,676)( 69,675)( 70,674)( 71,673)( 72,672)( 73,671)( 74,670)( 75,669)( 76,668)( 77,667)( 78,666)( 79,652)( 80,651)( 81,663)( 82,662)( 83,661)( 84,660)( 85,659)( 86,658)( 87,657)( 88,656)( 89,655)( 90,654)( 91,653)( 92,639)( 93,638)( 94,650)( 95,649)( 96,648)( 97,647)( 98,646)( 99,645)(100,644)(101,643)(102,642)(103,641)(104,640)(105,626)(106,625)(107,637)(108,636)(109,635)(110,634)(111,633)(112,632)(113,631)(114,630)(115,629)(116,628)(117,627)(118,613)(119,612)(120,624)(121,623)(122,622)(123,621)(124,620)(125,619)(126,618)(127,617)(128,616)(129,615)(130,614)(131,600)(132,599)(133,611)(134,610)(135,609)(136,608)(137,607)(138,606)(139,605)(140,604)(141,603)(142,602)(143,601)(144,444)(145,443)(146,455)(147,454)(148,453)(149,452)(150,451)(151,450)(152,449)(153,448)(154,447)(155,446)(156,445)(157,431)(158,430)(159,442)(160,441)(161,440)(162,439)(163,438)(164,437)(165,436)(166,435)(167,434)(168,433)(169,432)(170,561)(171,560)(172,572)(173,571)(174,570)(175,569)(176,568)(177,567)(178,566)(179,565)(180,564)(181,563)(182,562)(183,548)(184,547)(185,559)(186,558)(187,557)(188,556)(189,555)(190,554)(191,553)(192,552)(193,551)(194,550)(195,549)(196,535)(197,534)(198,546)(199,545)(200,544)(201,543)(202,542)(203,541)(204,540)(205,539)(206,538)(207,537)(208,536)(209,522)(210,521)(211,533)(212,532)(213,531)(214,530)(215,529)(216,528)(217,527)(218,526)(219,525)(220,524)(221,523)(222,509)(223,508)(224,520)(225,519)(226,518)(227,517)(228,516)(229,515)(230,514)(231,513)(232,512)(233,511)(234,510)(235,496)(236,495)(237,507)(238,506)(239,505)(240,504)(241,503)(242,502)(243,501)(244,500)(245,499)(246,498)(247,497)(248,483)(249,482)(250,494)(251,493)(252,492)(253,491)(254,490)(255,489)(256,488)(257,487)(258,486)(259,485)(260,484)(261,470)(262,469)(263,481)(264,480)(265,479)(266,478)(267,477)(268,476)(269,475)(270,474)(271,473)(272,472)(273,471)(274,457)(275,456)(276,468)(277,467)(278,466)(279,465)(280,464)(281,463)(282,462)(283,461)(284,460)(285,459)(286,458)(287,730)(288,729)(289,741)(290,740)(291,739)(292,738)(293,737)(294,736)(295,735)(296,734)(297,733)(298,732)(299,731)(300,717)(301,716)(302,728)(303,727)(304,726)(305,725)(306,724)(307,723)(308,722)(309,721)(310,720)(311,719)(312,718)(313,847)(314,846)(315,858)(316,857)(317,856)(318,855)(319,854)(320,853)(321,852)(322,851)(323,850)(324,849)(325,848)(326,834)(327,833)(328,845)(329,844)(330,843)(331,842)(332,841)(333,840)(334,839)(335,838)(336,837)(337,836)(338,835)(339,821)(340,820)(341,832)(342,831)(343,830)(344,829)(345,828)(346,827)(347,826)(348,825)(349,824)(350,823)(351,822)(352,808)(353,807)(354,819)(355,818)(356,817)(357,816)(358,815)(359,814)(360,813)(361,812)(362,811)(363,810)(364,809)(365,795)(366,794)(367,806)(368,805)(369,804)(370,803)(371,802)(372,801)(373,800)(374,799)(375,798)(376,797)(377,796)(378,782)(379,781)(380,793)(381,792)(382,791)(383,790)(384,789)(385,788)(386,787)(387,786)(388,785)(389,784)(390,783)(391,769)(392,768)(393,780)(394,779)(395,778)(396,777)(397,776)(398,775)(399,774)(400,773)(401,772)(402,771)(403,770)(404,756)(405,755)(406,767)(407,766)(408,765)(409,764)(410,763)(411,762)(412,761)(413,760)(414,759)(415,758)(416,757)(417,743)(418,742)(419,754)(420,753)(421,752)(422,751)(423,750)(424,749)(425,748)(426,747)(427,746)(428,745)(429,744);;
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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];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(858)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 14,131)( 15,143)( 16,142)( 17,141)( 18,140)( 19,139)( 20,138)( 21,137)( 22,136)( 23,135)( 24,134)( 25,133)( 26,132)( 27,118)( 28,130)( 29,129)( 30,128)( 31,127)( 32,126)( 33,125)( 34,124)( 35,123)( 36,122)( 37,121)( 38,120)( 39,119)( 40,105)( 41,117)( 42,116)( 43,115)( 44,114)( 45,113)( 46,112)( 47,111)( 48,110)( 49,109)( 50,108)( 51,107)( 52,106)( 53, 92)( 54,104)( 55,103)( 56,102)( 57,101)( 58,100)( 59, 99)( 60, 98)( 61, 97)( 62, 96)( 63, 95)( 64, 94)( 65, 93)( 66, 79)( 67, 91)( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)( 74, 84)( 75, 83)( 76, 82)( 77, 81)( 78, 80)(144,287)(145,299)(146,298)(147,297)(148,296)(149,295)(150,294)(151,293)(152,292)(153,291)(154,290)(155,289)(156,288)(157,417)(158,429)(159,428)(160,427)(161,426)(162,425)(163,424)(164,423)(165,422)(166,421)(167,420)(168,419)(169,418)(170,404)(171,416)(172,415)(173,414)(174,413)(175,412)(176,411)(177,410)(178,409)(179,408)(180,407)(181,406)(182,405)(183,391)(184,403)(185,402)(186,401)(187,400)(188,399)(189,398)(190,397)(191,396)(192,395)(193,394)(194,393)(195,392)(196,378)(197,390)(198,389)(199,388)(200,387)(201,386)(202,385)(203,384)(204,383)(205,382)(206,381)(207,380)(208,379)(209,365)(210,377)(211,376)(212,375)(213,374)(214,373)(215,372)(216,371)(217,370)(218,369)(219,368)(220,367)(221,366)(222,352)(223,364)(224,363)(225,362)(226,361)(227,360)(228,359)(229,358)(230,357)(231,356)(232,355)(233,354)(234,353)(235,339)(236,351)(237,350)(238,349)(239,348)(240,347)(241,346)(242,345)(243,344)(244,343)(245,342)(246,341)(247,340)(248,326)(249,338)(250,337)(251,336)(252,335)(253,334)(254,333)(255,332)(256,331)(257,330)(258,329)(259,328)(260,327)(261,313)(262,325)(263,324)(264,323)(265,322)(266,321)(267,320)(268,319)(269,318)(270,317)(271,316)(272,315)(273,314)(274,300)(275,312)(276,311)(277,310)(278,309)(279,308)(280,307)(281,306)(282,305)(283,304)(284,303)(285,302)(286,301)(431,442)(432,441)(433,440)(434,439)(435,438)(436,437)(443,560)(444,572)(445,571)(446,570)(447,569)(448,568)(449,567)(450,566)(451,565)(452,564)(453,563)(454,562)(455,561)(456,547)(457,559)(458,558)(459,557)(460,556)(461,555)(462,554)(463,553)(464,552)(465,551)(466,550)(467,549)(468,548)(469,534)(470,546)(471,545)(472,544)(473,543)(474,542)(475,541)(476,540)(477,539)(478,538)(479,537)(480,536)(481,535)(482,521)(483,533)(484,532)(485,531)(486,530)(487,529)(488,528)(489,527)(490,526)(491,525)(492,524)(493,523)(494,522)(495,508)(496,520)(497,519)(498,518)(499,517)(500,516)(501,515)(502,514)(503,513)(504,512)(505,511)(506,510)(507,509)(573,716)(574,728)(575,727)(576,726)(577,725)(578,724)(579,723)(580,722)(581,721)(582,720)(583,719)(584,718)(585,717)(586,846)(587,858)(588,857)(589,856)(590,855)(591,854)(592,853)(593,852)(594,851)(595,850)(596,849)(597,848)(598,847)(599,833)(600,845)(601,844)(602,843)(603,842)(604,841)(605,840)(606,839)(607,838)(608,837)(609,836)(610,835)(611,834)(612,820)(613,832)(614,831)(615,830)(616,829)(617,828)(618,827)(619,826)(620,825)(621,824)(622,823)(623,822)(624,821)(625,807)(626,819)(627,818)(628,817)(629,816)(630,815)(631,814)(632,813)(633,812)(634,811)(635,810)(636,809)(637,808)(638,794)(639,806)(640,805)(641,804)(642,803)(643,802)(644,801)(645,800)(646,799)(647,798)(648,797)(649,796)(650,795)(651,781)(652,793)(653,792)(654,791)(655,790)(656,789)(657,788)(658,787)(659,786)(660,785)(661,784)(662,783)(663,782)(664,768)(665,780)(666,779)(667,778)(668,777)(669,776)(670,775)(671,774)(672,773)(673,772)(674,771)(675,770)(676,769)(677,755)(678,767)(679,766)(680,765)(681,764)(682,763)(683,762)(684,761)(685,760)(686,759)(687,758)(688,757)(689,756)(690,742)(691,754)(692,753)(693,752)(694,751)(695,750)(696,749)(697,748)(698,747)(699,746)(700,745)(701,744)(702,743)(703,729)(704,741)(705,740)(706,739)(707,738)(708,737)(709,736)(710,735)(711,734)(712,733)(713,732)(714,731)(715,730);
s1 := Sym(858)!( 1,587)( 2,586)( 3,598)( 4,597)( 5,596)( 6,595)( 7,594)( 8,593)( 9,592)( 10,591)( 11,590)( 12,589)( 13,588)( 14,574)( 15,573)( 16,585)( 17,584)( 18,583)( 19,582)( 20,581)( 21,580)( 22,579)( 23,578)( 24,577)( 25,576)( 26,575)( 27,704)( 28,703)( 29,715)( 30,714)( 31,713)( 32,712)( 33,711)( 34,710)( 35,709)( 36,708)( 37,707)( 38,706)( 39,705)( 40,691)( 41,690)( 42,702)( 43,701)( 44,700)( 45,699)( 46,698)( 47,697)( 48,696)( 49,695)( 50,694)( 51,693)( 52,692)( 53,678)( 54,677)( 55,689)( 56,688)( 57,687)( 58,686)( 59,685)( 60,684)( 61,683)( 62,682)( 63,681)( 64,680)( 65,679)( 66,665)( 67,664)( 68,676)( 69,675)( 70,674)( 71,673)( 72,672)( 73,671)( 74,670)( 75,669)( 76,668)( 77,667)( 78,666)( 79,652)( 80,651)( 81,663)( 82,662)( 83,661)( 84,660)( 85,659)( 86,658)( 87,657)( 88,656)( 89,655)( 90,654)( 91,653)( 92,639)( 93,638)( 94,650)( 95,649)( 96,648)( 97,647)( 98,646)( 99,645)(100,644)(101,643)(102,642)(103,641)(104,640)(105,626)(106,625)(107,637)(108,636)(109,635)(110,634)(111,633)(112,632)(113,631)(114,630)(115,629)(116,628)(117,627)(118,613)(119,612)(120,624)(121,623)(122,622)(123,621)(124,620)(125,619)(126,618)(127,617)(128,616)(129,615)(130,614)(131,600)(132,599)(133,611)(134,610)(135,609)(136,608)(137,607)(138,606)(139,605)(140,604)(141,603)(142,602)(143,601)(144,444)(145,443)(146,455)(147,454)(148,453)(149,452)(150,451)(151,450)(152,449)(153,448)(154,447)(155,446)(156,445)(157,431)(158,430)(159,442)(160,441)(161,440)(162,439)(163,438)(164,437)(165,436)(166,435)(167,434)(168,433)(169,432)(170,561)(171,560)(172,572)(173,571)(174,570)(175,569)(176,568)(177,567)(178,566)(179,565)(180,564)(181,563)(182,562)(183,548)(184,547)(185,559)(186,558)(187,557)(188,556)(189,555)(190,554)(191,553)(192,552)(193,551)(194,550)(195,549)(196,535)(197,534)(198,546)(199,545)(200,544)(201,543)(202,542)(203,541)(204,540)(205,539)(206,538)(207,537)(208,536)(209,522)(210,521)(211,533)(212,532)(213,531)(214,530)(215,529)(216,528)(217,527)(218,526)(219,525)(220,524)(221,523)(222,509)(223,508)(224,520)(225,519)(226,518)(227,517)(228,516)(229,515)(230,514)(231,513)(232,512)(233,511)(234,510)(235,496)(236,495)(237,507)(238,506)(239,505)(240,504)(241,503)(242,502)(243,501)(244,500)(245,499)(246,498)(247,497)(248,483)(249,482)(250,494)(251,493)(252,492)(253,491)(254,490)(255,489)(256,488)(257,487)(258,486)(259,485)(260,484)(261,470)(262,469)(263,481)(264,480)(265,479)(266,478)(267,477)(268,476)(269,475)(270,474)(271,473)(272,472)(273,471)(274,457)(275,456)(276,468)(277,467)(278,466)(279,465)(280,464)(281,463)(282,462)(283,461)(284,460)(285,459)(286,458)(287,730)(288,729)(289,741)(290,740)(291,739)(292,738)(293,737)(294,736)(295,735)(296,734)(297,733)(298,732)(299,731)(300,717)(301,716)(302,728)(303,727)(304,726)(305,725)(306,724)(307,723)(308,722)(309,721)(310,720)(311,719)(312,718)(313,847)(314,846)(315,858)(316,857)(317,856)(318,855)(319,854)(320,853)(321,852)(322,851)(323,850)(324,849)(325,848)(326,834)(327,833)(328,845)(329,844)(330,843)(331,842)(332,841)(333,840)(334,839)(335,838)(336,837)(337,836)(338,835)(339,821)(340,820)(341,832)(342,831)(343,830)(344,829)(345,828)(346,827)(347,826)(348,825)(349,824)(350,823)(351,822)(352,808)(353,807)(354,819)(355,818)(356,817)(357,816)(358,815)(359,814)(360,813)(361,812)(362,811)(363,810)(364,809)(365,795)(366,794)(367,806)(368,805)(369,804)(370,803)(371,802)(372,801)(373,800)(374,799)(375,798)(376,797)(377,796)(378,782)(379,781)(380,793)(381,792)(382,791)(383,790)(384,789)(385,788)(386,787)(387,786)(388,785)(389,784)(390,783)(391,769)(392,768)(393,780)(394,779)(395,778)(396,777)(397,776)(398,775)(399,774)(400,773)(401,772)(402,771)(403,770)(404,756)(405,755)(406,767)(407,766)(408,765)(409,764)(410,763)(411,762)(412,761)(413,760)(414,759)(415,758)(416,757)(417,743)(418,742)(419,754)(420,753)(421,752)(422,751)(423,750)(424,749)(425,748)(426,747)(427,746)(428,745)(429,744);
poly := sub<Sym(858)|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 >;
References : None.
to this polytope