Polytope of Type {846}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {846}*1692
Also Known As : 846-gon, {846}. if this polytope has another name.
Group : SmallGroup(1692,9)
Rank : 2
Schlafli Type : {846}
Number of vertices, edges, etc : 846, 846
Order of s0s1 : 846
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 : {423}*846
3-fold quotients : {282}*564
6-fold quotients : {141}*282
9-fold quotients : {94}*188
18-fold quotients : {47}*94
47-fold quotients : {18}*36
94-fold quotients : {9}*18
141-fold quotients : {6}*12
282-fold quotients : {3}*6
423-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, 3)( 4,139)( 5,141)( 6,140)( 7,136)( 8,138)( 9,137)( 10,133)( 11,135)( 12,134)( 13,130)( 14,132)( 15,131)( 16,127)( 17,129)( 18,128)( 19,124)( 20,126)( 21,125)( 22,121)( 23,123)( 24,122)( 25,118)( 26,120)( 27,119)( 28,115)( 29,117)( 30,116)( 31,112)( 32,114)( 33,113)( 34,109)( 35,111)( 36,110)( 37,106)( 38,108)( 39,107)( 40,103)( 41,105)( 42,104)( 43,100)( 44,102)( 45,101)( 46, 97)( 47, 99)( 48, 98)( 49, 94)( 50, 96)( 51, 95)( 52, 91)( 53, 93)( 54, 92)( 55, 88)( 56, 90)( 57, 89)( 58, 85)( 59, 87)( 60, 86)( 61, 82)( 62, 84)( 63, 83)( 64, 79)( 65, 81)( 66, 80)( 67, 76)( 68, 78)( 69, 77)( 70, 73)( 71, 75)( 72, 74)(142,284)(143,283)(144,285)(145,422)(146,421)(147,423)(148,419)(149,418)(150,420)(151,416)(152,415)(153,417)(154,413)(155,412)(156,414)(157,410)(158,409)(159,411)(160,407)(161,406)(162,408)(163,404)(164,403)(165,405)(166,401)(167,400)(168,402)(169,398)(170,397)(171,399)(172,395)(173,394)(174,396)(175,392)(176,391)(177,393)(178,389)(179,388)(180,390)(181,386)(182,385)(183,387)(184,383)(185,382)(186,384)(187,380)(188,379)(189,381)(190,377)(191,376)(192,378)(193,374)(194,373)(195,375)(196,371)(197,370)(198,372)(199,368)(200,367)(201,369)(202,365)(203,364)(204,366)(205,362)(206,361)(207,363)(208,359)(209,358)(210,360)(211,356)(212,355)(213,357)(214,353)(215,352)(216,354)(217,350)(218,349)(219,351)(220,347)(221,346)(222,348)(223,344)(224,343)(225,345)(226,341)(227,340)(228,342)(229,338)(230,337)(231,339)(232,335)(233,334)(234,336)(235,332)(236,331)(237,333)(238,329)(239,328)(240,330)(241,326)(242,325)(243,327)(244,323)(245,322)(246,324)(247,320)(248,319)(249,321)(250,317)(251,316)(252,318)(253,314)(254,313)(255,315)(256,311)(257,310)(258,312)(259,308)(260,307)(261,309)(262,305)(263,304)(264,306)(265,302)(266,301)(267,303)(268,299)(269,298)(270,300)(271,296)(272,295)(273,297)(274,293)(275,292)(276,294)(277,290)(278,289)(279,291)(280,287)(281,286)(282,288)(425,426)(427,562)(428,564)(429,563)(430,559)(431,561)(432,560)(433,556)(434,558)(435,557)(436,553)(437,555)(438,554)(439,550)(440,552)(441,551)(442,547)(443,549)(444,548)(445,544)(446,546)(447,545)(448,541)(449,543)(450,542)(451,538)(452,540)(453,539)(454,535)(455,537)(456,536)(457,532)(458,534)(459,533)(460,529)(461,531)(462,530)(463,526)(464,528)(465,527)(466,523)(467,525)(468,524)(469,520)(470,522)(471,521)(472,517)(473,519)(474,518)(475,514)(476,516)(477,515)(478,511)(479,513)(480,512)(481,508)(482,510)(483,509)(484,505)(485,507)(486,506)(487,502)(488,504)(489,503)(490,499)(491,501)(492,500)(493,496)(494,498)(495,497)(565,707)(566,706)(567,708)(568,845)(569,844)(570,846)(571,842)(572,841)(573,843)(574,839)(575,838)(576,840)(577,836)(578,835)(579,837)(580,833)(581,832)(582,834)(583,830)(584,829)(585,831)(586,827)(587,826)(588,828)(589,824)(590,823)(591,825)(592,821)(593,820)(594,822)(595,818)(596,817)(597,819)(598,815)(599,814)(600,816)(601,812)(602,811)(603,813)(604,809)(605,808)(606,810)(607,806)(608,805)(609,807)(610,803)(611,802)(612,804)(613,800)(614,799)(615,801)(616,797)(617,796)(618,798)(619,794)(620,793)(621,795)(622,791)(623,790)(624,792)(625,788)(626,787)(627,789)(628,785)(629,784)(630,786)(631,782)(632,781)(633,783)(634,779)(635,778)(636,780)(637,776)(638,775)(639,777)(640,773)(641,772)(642,774)(643,770)(644,769)(645,771)(646,767)(647,766)(648,768)(649,764)(650,763)(651,765)(652,761)(653,760)(654,762)(655,758)(656,757)(657,759)(658,755)(659,754)(660,756)(661,752)(662,751)(663,753)(664,749)(665,748)(666,750)(667,746)(668,745)(669,747)(670,743)(671,742)(672,744)(673,740)(674,739)(675,741)(676,737)(677,736)(678,738)(679,734)(680,733)(681,735)(682,731)(683,730)(684,732)(685,728)(686,727)(687,729)(688,725)(689,724)(690,726)(691,722)(692,721)(693,723)(694,719)(695,718)(696,720)(697,716)(698,715)(699,717)(700,713)(701,712)(702,714)(703,710)(704,709)(705,711);;
s1 := ( 1,568)( 2,570)( 3,569)( 4,565)( 5,567)( 6,566)( 7,703)( 8,705)( 9,704)( 10,700)( 11,702)( 12,701)( 13,697)( 14,699)( 15,698)( 16,694)( 17,696)( 18,695)( 19,691)( 20,693)( 21,692)( 22,688)( 23,690)( 24,689)( 25,685)( 26,687)( 27,686)( 28,682)( 29,684)( 30,683)( 31,679)( 32,681)( 33,680)( 34,676)( 35,678)( 36,677)( 37,673)( 38,675)( 39,674)( 40,670)( 41,672)( 42,671)( 43,667)( 44,669)( 45,668)( 46,664)( 47,666)( 48,665)( 49,661)( 50,663)( 51,662)( 52,658)( 53,660)( 54,659)( 55,655)( 56,657)( 57,656)( 58,652)( 59,654)( 60,653)( 61,649)( 62,651)( 63,650)( 64,646)( 65,648)( 66,647)( 67,643)( 68,645)( 69,644)( 70,640)( 71,642)( 72,641)( 73,637)( 74,639)( 75,638)( 76,634)( 77,636)( 78,635)( 79,631)( 80,633)( 81,632)( 82,628)( 83,630)( 84,629)( 85,625)( 86,627)( 87,626)( 88,622)( 89,624)( 90,623)( 91,619)( 92,621)( 93,620)( 94,616)( 95,618)( 96,617)( 97,613)( 98,615)( 99,614)(100,610)(101,612)(102,611)(103,607)(104,609)(105,608)(106,604)(107,606)(108,605)(109,601)(110,603)(111,602)(112,598)(113,600)(114,599)(115,595)(116,597)(117,596)(118,592)(119,594)(120,593)(121,589)(122,591)(123,590)(124,586)(125,588)(126,587)(127,583)(128,585)(129,584)(130,580)(131,582)(132,581)(133,577)(134,579)(135,578)(136,574)(137,576)(138,575)(139,571)(140,573)(141,572)(142,427)(143,429)(144,428)(145,424)(146,426)(147,425)(148,562)(149,564)(150,563)(151,559)(152,561)(153,560)(154,556)(155,558)(156,557)(157,553)(158,555)(159,554)(160,550)(161,552)(162,551)(163,547)(164,549)(165,548)(166,544)(167,546)(168,545)(169,541)(170,543)(171,542)(172,538)(173,540)(174,539)(175,535)(176,537)(177,536)(178,532)(179,534)(180,533)(181,529)(182,531)(183,530)(184,526)(185,528)(186,527)(187,523)(188,525)(189,524)(190,520)(191,522)(192,521)(193,517)(194,519)(195,518)(196,514)(197,516)(198,515)(199,511)(200,513)(201,512)(202,508)(203,510)(204,509)(205,505)(206,507)(207,506)(208,502)(209,504)(210,503)(211,499)(212,501)(213,500)(214,496)(215,498)(216,497)(217,493)(218,495)(219,494)(220,490)(221,492)(222,491)(223,487)(224,489)(225,488)(226,484)(227,486)(228,485)(229,481)(230,483)(231,482)(232,478)(233,480)(234,479)(235,475)(236,477)(237,476)(238,472)(239,474)(240,473)(241,469)(242,471)(243,470)(244,466)(245,468)(246,467)(247,463)(248,465)(249,464)(250,460)(251,462)(252,461)(253,457)(254,459)(255,458)(256,454)(257,456)(258,455)(259,451)(260,453)(261,452)(262,448)(263,450)(264,449)(265,445)(266,447)(267,446)(268,442)(269,444)(270,443)(271,439)(272,441)(273,440)(274,436)(275,438)(276,437)(277,433)(278,435)(279,434)(280,430)(281,432)(282,431)(283,710)(284,709)(285,711)(286,707)(287,706)(288,708)(289,845)(290,844)(291,846)(292,842)(293,841)(294,843)(295,839)(296,838)(297,840)(298,836)(299,835)(300,837)(301,833)(302,832)(303,834)(304,830)(305,829)(306,831)(307,827)(308,826)(309,828)(310,824)(311,823)(312,825)(313,821)(314,820)(315,822)(316,818)(317,817)(318,819)(319,815)(320,814)(321,816)(322,812)(323,811)(324,813)(325,809)(326,808)(327,810)(328,806)(329,805)(330,807)(331,803)(332,802)(333,804)(334,800)(335,799)(336,801)(337,797)(338,796)(339,798)(340,794)(341,793)(342,795)(343,791)(344,790)(345,792)(346,788)(347,787)(348,789)(349,785)(350,784)(351,786)(352,782)(353,781)(354,783)(355,779)(356,778)(357,780)(358,776)(359,775)(360,777)(361,773)(362,772)(363,774)(364,770)(365,769)(366,771)(367,767)(368,766)(369,768)(370,764)(371,763)(372,765)(373,761)(374,760)(375,762)(376,758)(377,757)(378,759)(379,755)(380,754)(381,756)(382,752)(383,751)(384,753)(385,749)(386,748)(387,750)(388,746)(389,745)(390,747)(391,743)(392,742)(393,744)(394,740)(395,739)(396,741)(397,737)(398,736)(399,738)(400,734)(401,733)(402,735)(403,731)(404,730)(405,732)(406,728)(407,727)(408,729)(409,725)(410,724)(411,726)(412,722)(413,721)(414,723)(415,719)(416,718)(417,720)(418,716)(419,715)(420,717)(421,713)(422,712)(423,714);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(846)!( 2, 3)( 4,139)( 5,141)( 6,140)( 7,136)( 8,138)( 9,137)( 10,133)( 11,135)( 12,134)( 13,130)( 14,132)( 15,131)( 16,127)( 17,129)( 18,128)( 19,124)( 20,126)( 21,125)( 22,121)( 23,123)( 24,122)( 25,118)( 26,120)( 27,119)( 28,115)( 29,117)( 30,116)( 31,112)( 32,114)( 33,113)( 34,109)( 35,111)( 36,110)( 37,106)( 38,108)( 39,107)( 40,103)( 41,105)( 42,104)( 43,100)( 44,102)( 45,101)( 46, 97)( 47, 99)( 48, 98)( 49, 94)( 50, 96)( 51, 95)( 52, 91)( 53, 93)( 54, 92)( 55, 88)( 56, 90)( 57, 89)( 58, 85)( 59, 87)( 60, 86)( 61, 82)( 62, 84)( 63, 83)( 64, 79)( 65, 81)( 66, 80)( 67, 76)( 68, 78)( 69, 77)( 70, 73)( 71, 75)( 72, 74)(142,284)(143,283)(144,285)(145,422)(146,421)(147,423)(148,419)(149,418)(150,420)(151,416)(152,415)(153,417)(154,413)(155,412)(156,414)(157,410)(158,409)(159,411)(160,407)(161,406)(162,408)(163,404)(164,403)(165,405)(166,401)(167,400)(168,402)(169,398)(170,397)(171,399)(172,395)(173,394)(174,396)(175,392)(176,391)(177,393)(178,389)(179,388)(180,390)(181,386)(182,385)(183,387)(184,383)(185,382)(186,384)(187,380)(188,379)(189,381)(190,377)(191,376)(192,378)(193,374)(194,373)(195,375)(196,371)(197,370)(198,372)(199,368)(200,367)(201,369)(202,365)(203,364)(204,366)(205,362)(206,361)(207,363)(208,359)(209,358)(210,360)(211,356)(212,355)(213,357)(214,353)(215,352)(216,354)(217,350)(218,349)(219,351)(220,347)(221,346)(222,348)(223,344)(224,343)(225,345)(226,341)(227,340)(228,342)(229,338)(230,337)(231,339)(232,335)(233,334)(234,336)(235,332)(236,331)(237,333)(238,329)(239,328)(240,330)(241,326)(242,325)(243,327)(244,323)(245,322)(246,324)(247,320)(248,319)(249,321)(250,317)(251,316)(252,318)(253,314)(254,313)(255,315)(256,311)(257,310)(258,312)(259,308)(260,307)(261,309)(262,305)(263,304)(264,306)(265,302)(266,301)(267,303)(268,299)(269,298)(270,300)(271,296)(272,295)(273,297)(274,293)(275,292)(276,294)(277,290)(278,289)(279,291)(280,287)(281,286)(282,288)(425,426)(427,562)(428,564)(429,563)(430,559)(431,561)(432,560)(433,556)(434,558)(435,557)(436,553)(437,555)(438,554)(439,550)(440,552)(441,551)(442,547)(443,549)(444,548)(445,544)(446,546)(447,545)(448,541)(449,543)(450,542)(451,538)(452,540)(453,539)(454,535)(455,537)(456,536)(457,532)(458,534)(459,533)(460,529)(461,531)(462,530)(463,526)(464,528)(465,527)(466,523)(467,525)(468,524)(469,520)(470,522)(471,521)(472,517)(473,519)(474,518)(475,514)(476,516)(477,515)(478,511)(479,513)(480,512)(481,508)(482,510)(483,509)(484,505)(485,507)(486,506)(487,502)(488,504)(489,503)(490,499)(491,501)(492,500)(493,496)(494,498)(495,497)(565,707)(566,706)(567,708)(568,845)(569,844)(570,846)(571,842)(572,841)(573,843)(574,839)(575,838)(576,840)(577,836)(578,835)(579,837)(580,833)(581,832)(582,834)(583,830)(584,829)(585,831)(586,827)(587,826)(588,828)(589,824)(590,823)(591,825)(592,821)(593,820)(594,822)(595,818)(596,817)(597,819)(598,815)(599,814)(600,816)(601,812)(602,811)(603,813)(604,809)(605,808)(606,810)(607,806)(608,805)(609,807)(610,803)(611,802)(612,804)(613,800)(614,799)(615,801)(616,797)(617,796)(618,798)(619,794)(620,793)(621,795)(622,791)(623,790)(624,792)(625,788)(626,787)(627,789)(628,785)(629,784)(630,786)(631,782)(632,781)(633,783)(634,779)(635,778)(636,780)(637,776)(638,775)(639,777)(640,773)(641,772)(642,774)(643,770)(644,769)(645,771)(646,767)(647,766)(648,768)(649,764)(650,763)(651,765)(652,761)(653,760)(654,762)(655,758)(656,757)(657,759)(658,755)(659,754)(660,756)(661,752)(662,751)(663,753)(664,749)(665,748)(666,750)(667,746)(668,745)(669,747)(670,743)(671,742)(672,744)(673,740)(674,739)(675,741)(676,737)(677,736)(678,738)(679,734)(680,733)(681,735)(682,731)(683,730)(684,732)(685,728)(686,727)(687,729)(688,725)(689,724)(690,726)(691,722)(692,721)(693,723)(694,719)(695,718)(696,720)(697,716)(698,715)(699,717)(700,713)(701,712)(702,714)(703,710)(704,709)(705,711);
s1 := Sym(846)!( 1,568)( 2,570)( 3,569)( 4,565)( 5,567)( 6,566)( 7,703)( 8,705)( 9,704)( 10,700)( 11,702)( 12,701)( 13,697)( 14,699)( 15,698)( 16,694)( 17,696)( 18,695)( 19,691)( 20,693)( 21,692)( 22,688)( 23,690)( 24,689)( 25,685)( 26,687)( 27,686)( 28,682)( 29,684)( 30,683)( 31,679)( 32,681)( 33,680)( 34,676)( 35,678)( 36,677)( 37,673)( 38,675)( 39,674)( 40,670)( 41,672)( 42,671)( 43,667)( 44,669)( 45,668)( 46,664)( 47,666)( 48,665)( 49,661)( 50,663)( 51,662)( 52,658)( 53,660)( 54,659)( 55,655)( 56,657)( 57,656)( 58,652)( 59,654)( 60,653)( 61,649)( 62,651)( 63,650)( 64,646)( 65,648)( 66,647)( 67,643)( 68,645)( 69,644)( 70,640)( 71,642)( 72,641)( 73,637)( 74,639)( 75,638)( 76,634)( 77,636)( 78,635)( 79,631)( 80,633)( 81,632)( 82,628)( 83,630)( 84,629)( 85,625)( 86,627)( 87,626)( 88,622)( 89,624)( 90,623)( 91,619)( 92,621)( 93,620)( 94,616)( 95,618)( 96,617)( 97,613)( 98,615)( 99,614)(100,610)(101,612)(102,611)(103,607)(104,609)(105,608)(106,604)(107,606)(108,605)(109,601)(110,603)(111,602)(112,598)(113,600)(114,599)(115,595)(116,597)(117,596)(118,592)(119,594)(120,593)(121,589)(122,591)(123,590)(124,586)(125,588)(126,587)(127,583)(128,585)(129,584)(130,580)(131,582)(132,581)(133,577)(134,579)(135,578)(136,574)(137,576)(138,575)(139,571)(140,573)(141,572)(142,427)(143,429)(144,428)(145,424)(146,426)(147,425)(148,562)(149,564)(150,563)(151,559)(152,561)(153,560)(154,556)(155,558)(156,557)(157,553)(158,555)(159,554)(160,550)(161,552)(162,551)(163,547)(164,549)(165,548)(166,544)(167,546)(168,545)(169,541)(170,543)(171,542)(172,538)(173,540)(174,539)(175,535)(176,537)(177,536)(178,532)(179,534)(180,533)(181,529)(182,531)(183,530)(184,526)(185,528)(186,527)(187,523)(188,525)(189,524)(190,520)(191,522)(192,521)(193,517)(194,519)(195,518)(196,514)(197,516)(198,515)(199,511)(200,513)(201,512)(202,508)(203,510)(204,509)(205,505)(206,507)(207,506)(208,502)(209,504)(210,503)(211,499)(212,501)(213,500)(214,496)(215,498)(216,497)(217,493)(218,495)(219,494)(220,490)(221,492)(222,491)(223,487)(224,489)(225,488)(226,484)(227,486)(228,485)(229,481)(230,483)(231,482)(232,478)(233,480)(234,479)(235,475)(236,477)(237,476)(238,472)(239,474)(240,473)(241,469)(242,471)(243,470)(244,466)(245,468)(246,467)(247,463)(248,465)(249,464)(250,460)(251,462)(252,461)(253,457)(254,459)(255,458)(256,454)(257,456)(258,455)(259,451)(260,453)(261,452)(262,448)(263,450)(264,449)(265,445)(266,447)(267,446)(268,442)(269,444)(270,443)(271,439)(272,441)(273,440)(274,436)(275,438)(276,437)(277,433)(278,435)(279,434)(280,430)(281,432)(282,431)(283,710)(284,709)(285,711)(286,707)(287,706)(288,708)(289,845)(290,844)(291,846)(292,842)(293,841)(294,843)(295,839)(296,838)(297,840)(298,836)(299,835)(300,837)(301,833)(302,832)(303,834)(304,830)(305,829)(306,831)(307,827)(308,826)(309,828)(310,824)(311,823)(312,825)(313,821)(314,820)(315,822)(316,818)(317,817)(318,819)(319,815)(320,814)(321,816)(322,812)(323,811)(324,813)(325,809)(326,808)(327,810)(328,806)(329,805)(330,807)(331,803)(332,802)(333,804)(334,800)(335,799)(336,801)(337,797)(338,796)(339,798)(340,794)(341,793)(342,795)(343,791)(344,790)(345,792)(346,788)(347,787)(348,789)(349,785)(350,784)(351,786)(352,782)(353,781)(354,783)(355,779)(356,778)(357,780)(358,776)(359,775)(360,777)(361,773)(362,772)(363,774)(364,770)(365,769)(366,771)(367,767)(368,766)(369,768)(370,764)(371,763)(372,765)(373,761)(374,760)(375,762)(376,758)(377,757)(378,759)(379,755)(380,754)(381,756)(382,752)(383,751)(384,753)(385,749)(386,748)(387,750)(388,746)(389,745)(390,747)(391,743)(392,742)(393,744)(394,740)(395,739)(396,741)(397,737)(398,736)(399,738)(400,734)(401,733)(402,735)(403,731)(404,730)(405,732)(406,728)(407,727)(408,729)(409,725)(410,724)(411,726)(412,722)(413,721)(414,723)(415,719)(416,718)(417,720)(418,716)(419,715)(420,717)(421,713)(422,712)(423,714);
poly := sub<Sym(846)|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 >;
References : None.
to this polytope