Polytope of Type {810}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {810}*1620
Also Known As : 810-gon, {810}. if this polytope has another name.
Group : SmallGroup(1620,11)
Rank : 2
Schlafli Type : {810}
Number of vertices, edges, etc : 810, 810
Order of s0s1 : 810
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 : {405}*810
3-fold quotients : {270}*540
5-fold quotients : {162}*324
6-fold quotients : {135}*270
9-fold quotients : {90}*180
10-fold quotients : {81}*162
15-fold quotients : {54}*108
18-fold quotients : {45}*90
27-fold quotients : {30}*60
30-fold quotients : {27}*54
45-fold quotients : {18}*36
54-fold quotients : {15}*30
81-fold quotients : {10}*20
90-fold quotients : {9}*18
135-fold quotients : {6}*12
162-fold quotients : {5}*10
270-fold quotients : {3}*6
405-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, 8)( 5, 7)( 6, 9)( 10, 23)( 11, 22)( 12, 24)( 13, 20)( 14, 19)( 15, 21)( 16, 27)( 17, 26)( 18, 25)( 28,109)( 29,111)( 30,110)( 31,116)( 32,115)( 33,117)( 34,113)( 35,112)( 36,114)( 37,131)( 38,130)( 39,132)( 40,128)( 41,127)( 42,129)( 43,135)( 44,134)( 45,133)( 46,122)( 47,121)( 48,123)( 49,119)( 50,118)( 51,120)( 52,126)( 53,125)( 54,124)( 55, 82)( 56, 84)( 57, 83)( 58, 89)( 59, 88)( 60, 90)( 61, 86)( 62, 85)( 63, 87)( 64,104)( 65,103)( 66,105)( 67,101)( 68,100)( 69,102)( 70,108)( 71,107)( 72,106)( 73, 95)( 74, 94)( 75, 96)( 76, 92)( 77, 91)( 78, 93)( 79, 99)( 80, 98)( 81, 97)(136,284)(137,283)(138,285)(139,281)(140,280)(141,282)(142,288)(143,287)(144,286)(145,275)(146,274)(147,276)(148,272)(149,271)(150,273)(151,279)(152,278)(153,277)(154,297)(155,296)(156,295)(157,294)(158,293)(159,292)(160,291)(161,290)(162,289)(163,392)(164,391)(165,393)(166,389)(167,388)(168,390)(169,396)(170,395)(171,394)(172,383)(173,382)(174,384)(175,380)(176,379)(177,381)(178,387)(179,386)(180,385)(181,405)(182,404)(183,403)(184,402)(185,401)(186,400)(187,399)(188,398)(189,397)(190,365)(191,364)(192,366)(193,362)(194,361)(195,363)(196,369)(197,368)(198,367)(199,356)(200,355)(201,357)(202,353)(203,352)(204,354)(205,360)(206,359)(207,358)(208,378)(209,377)(210,376)(211,375)(212,374)(213,373)(214,372)(215,371)(216,370)(217,338)(218,337)(219,339)(220,335)(221,334)(222,336)(223,342)(224,341)(225,340)(226,329)(227,328)(228,330)(229,326)(230,325)(231,327)(232,333)(233,332)(234,331)(235,351)(236,350)(237,349)(238,348)(239,347)(240,346)(241,345)(242,344)(243,343)(244,311)(245,310)(246,312)(247,308)(248,307)(249,309)(250,315)(251,314)(252,313)(253,302)(254,301)(255,303)(256,299)(257,298)(258,300)(259,306)(260,305)(261,304)(262,324)(263,323)(264,322)(265,321)(266,320)(267,319)(268,318)(269,317)(270,316)(407,408)(409,413)(410,412)(411,414)(415,428)(416,427)(417,429)(418,425)(419,424)(420,426)(421,432)(422,431)(423,430)(433,514)(434,516)(435,515)(436,521)(437,520)(438,522)(439,518)(440,517)(441,519)(442,536)(443,535)(444,537)(445,533)(446,532)(447,534)(448,540)(449,539)(450,538)(451,527)(452,526)(453,528)(454,524)(455,523)(456,525)(457,531)(458,530)(459,529)(460,487)(461,489)(462,488)(463,494)(464,493)(465,495)(466,491)(467,490)(468,492)(469,509)(470,508)(471,510)(472,506)(473,505)(474,507)(475,513)(476,512)(477,511)(478,500)(479,499)(480,501)(481,497)(482,496)(483,498)(484,504)(485,503)(486,502)(541,689)(542,688)(543,690)(544,686)(545,685)(546,687)(547,693)(548,692)(549,691)(550,680)(551,679)(552,681)(553,677)(554,676)(555,678)(556,684)(557,683)(558,682)(559,702)(560,701)(561,700)(562,699)(563,698)(564,697)(565,696)(566,695)(567,694)(568,797)(569,796)(570,798)(571,794)(572,793)(573,795)(574,801)(575,800)(576,799)(577,788)(578,787)(579,789)(580,785)(581,784)(582,786)(583,792)(584,791)(585,790)(586,810)(587,809)(588,808)(589,807)(590,806)(591,805)(592,804)(593,803)(594,802)(595,770)(596,769)(597,771)(598,767)(599,766)(600,768)(601,774)(602,773)(603,772)(604,761)(605,760)(606,762)(607,758)(608,757)(609,759)(610,765)(611,764)(612,763)(613,783)(614,782)(615,781)(616,780)(617,779)(618,778)(619,777)(620,776)(621,775)(622,743)(623,742)(624,744)(625,740)(626,739)(627,741)(628,747)(629,746)(630,745)(631,734)(632,733)(633,735)(634,731)(635,730)(636,732)(637,738)(638,737)(639,736)(640,756)(641,755)(642,754)(643,753)(644,752)(645,751)(646,750)(647,749)(648,748)(649,716)(650,715)(651,717)(652,713)(653,712)(654,714)(655,720)(656,719)(657,718)(658,707)(659,706)(660,708)(661,704)(662,703)(663,705)(664,711)(665,710)(666,709)(667,729)(668,728)(669,727)(670,726)(671,725)(672,724)(673,723)(674,722)(675,721);;
s1 := ( 1,568)( 2,570)( 3,569)( 4,575)( 5,574)( 6,576)( 7,572)( 8,571)( 9,573)( 10,590)( 11,589)( 12,591)( 13,587)( 14,586)( 15,588)( 16,594)( 17,593)( 18,592)( 19,581)( 20,580)( 21,582)( 22,578)( 23,577)( 24,579)( 25,585)( 26,584)( 27,583)( 28,541)( 29,543)( 30,542)( 31,548)( 32,547)( 33,549)( 34,545)( 35,544)( 36,546)( 37,563)( 38,562)( 39,564)( 40,560)( 41,559)( 42,561)( 43,567)( 44,566)( 45,565)( 46,554)( 47,553)( 48,555)( 49,551)( 50,550)( 51,552)( 52,558)( 53,557)( 54,556)( 55,649)( 56,651)( 57,650)( 58,656)( 59,655)( 60,657)( 61,653)( 62,652)( 63,654)( 64,671)( 65,670)( 66,672)( 67,668)( 68,667)( 69,669)( 70,675)( 71,674)( 72,673)( 73,662)( 74,661)( 75,663)( 76,659)( 77,658)( 78,660)( 79,666)( 80,665)( 81,664)( 82,622)( 83,624)( 84,623)( 85,629)( 86,628)( 87,630)( 88,626)( 89,625)( 90,627)( 91,644)( 92,643)( 93,645)( 94,641)( 95,640)( 96,642)( 97,648)( 98,647)( 99,646)(100,635)(101,634)(102,636)(103,632)(104,631)(105,633)(106,639)(107,638)(108,637)(109,595)(110,597)(111,596)(112,602)(113,601)(114,603)(115,599)(116,598)(117,600)(118,617)(119,616)(120,618)(121,614)(122,613)(123,615)(124,621)(125,620)(126,619)(127,608)(128,607)(129,609)(130,605)(131,604)(132,606)(133,612)(134,611)(135,610)(136,433)(137,435)(138,434)(139,440)(140,439)(141,441)(142,437)(143,436)(144,438)(145,455)(146,454)(147,456)(148,452)(149,451)(150,453)(151,459)(152,458)(153,457)(154,446)(155,445)(156,447)(157,443)(158,442)(159,444)(160,450)(161,449)(162,448)(163,406)(164,408)(165,407)(166,413)(167,412)(168,414)(169,410)(170,409)(171,411)(172,428)(173,427)(174,429)(175,425)(176,424)(177,426)(178,432)(179,431)(180,430)(181,419)(182,418)(183,420)(184,416)(185,415)(186,417)(187,423)(188,422)(189,421)(190,514)(191,516)(192,515)(193,521)(194,520)(195,522)(196,518)(197,517)(198,519)(199,536)(200,535)(201,537)(202,533)(203,532)(204,534)(205,540)(206,539)(207,538)(208,527)(209,526)(210,528)(211,524)(212,523)(213,525)(214,531)(215,530)(216,529)(217,487)(218,489)(219,488)(220,494)(221,493)(222,495)(223,491)(224,490)(225,492)(226,509)(227,508)(228,510)(229,506)(230,505)(231,507)(232,513)(233,512)(234,511)(235,500)(236,499)(237,501)(238,497)(239,496)(240,498)(241,504)(242,503)(243,502)(244,460)(245,462)(246,461)(247,467)(248,466)(249,468)(250,464)(251,463)(252,465)(253,482)(254,481)(255,483)(256,479)(257,478)(258,480)(259,486)(260,485)(261,484)(262,473)(263,472)(264,474)(265,470)(266,469)(267,471)(268,477)(269,476)(270,475)(271,716)(272,715)(273,717)(274,713)(275,712)(276,714)(277,720)(278,719)(279,718)(280,707)(281,706)(282,708)(283,704)(284,703)(285,705)(286,711)(287,710)(288,709)(289,729)(290,728)(291,727)(292,726)(293,725)(294,724)(295,723)(296,722)(297,721)(298,689)(299,688)(300,690)(301,686)(302,685)(303,687)(304,693)(305,692)(306,691)(307,680)(308,679)(309,681)(310,677)(311,676)(312,678)(313,684)(314,683)(315,682)(316,702)(317,701)(318,700)(319,699)(320,698)(321,697)(322,696)(323,695)(324,694)(325,797)(326,796)(327,798)(328,794)(329,793)(330,795)(331,801)(332,800)(333,799)(334,788)(335,787)(336,789)(337,785)(338,784)(339,786)(340,792)(341,791)(342,790)(343,810)(344,809)(345,808)(346,807)(347,806)(348,805)(349,804)(350,803)(351,802)(352,770)(353,769)(354,771)(355,767)(356,766)(357,768)(358,774)(359,773)(360,772)(361,761)(362,760)(363,762)(364,758)(365,757)(366,759)(367,765)(368,764)(369,763)(370,783)(371,782)(372,781)(373,780)(374,779)(375,778)(376,777)(377,776)(378,775)(379,743)(380,742)(381,744)(382,740)(383,739)(384,741)(385,747)(386,746)(387,745)(388,734)(389,733)(390,735)(391,731)(392,730)(393,732)(394,738)(395,737)(396,736)(397,756)(398,755)(399,754)(400,753)(401,752)(402,751)(403,750)(404,749)(405,748);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(810)!( 2, 3)( 4, 8)( 5, 7)( 6, 9)( 10, 23)( 11, 22)( 12, 24)( 13, 20)( 14, 19)( 15, 21)( 16, 27)( 17, 26)( 18, 25)( 28,109)( 29,111)( 30,110)( 31,116)( 32,115)( 33,117)( 34,113)( 35,112)( 36,114)( 37,131)( 38,130)( 39,132)( 40,128)( 41,127)( 42,129)( 43,135)( 44,134)( 45,133)( 46,122)( 47,121)( 48,123)( 49,119)( 50,118)( 51,120)( 52,126)( 53,125)( 54,124)( 55, 82)( 56, 84)( 57, 83)( 58, 89)( 59, 88)( 60, 90)( 61, 86)( 62, 85)( 63, 87)( 64,104)( 65,103)( 66,105)( 67,101)( 68,100)( 69,102)( 70,108)( 71,107)( 72,106)( 73, 95)( 74, 94)( 75, 96)( 76, 92)( 77, 91)( 78, 93)( 79, 99)( 80, 98)( 81, 97)(136,284)(137,283)(138,285)(139,281)(140,280)(141,282)(142,288)(143,287)(144,286)(145,275)(146,274)(147,276)(148,272)(149,271)(150,273)(151,279)(152,278)(153,277)(154,297)(155,296)(156,295)(157,294)(158,293)(159,292)(160,291)(161,290)(162,289)(163,392)(164,391)(165,393)(166,389)(167,388)(168,390)(169,396)(170,395)(171,394)(172,383)(173,382)(174,384)(175,380)(176,379)(177,381)(178,387)(179,386)(180,385)(181,405)(182,404)(183,403)(184,402)(185,401)(186,400)(187,399)(188,398)(189,397)(190,365)(191,364)(192,366)(193,362)(194,361)(195,363)(196,369)(197,368)(198,367)(199,356)(200,355)(201,357)(202,353)(203,352)(204,354)(205,360)(206,359)(207,358)(208,378)(209,377)(210,376)(211,375)(212,374)(213,373)(214,372)(215,371)(216,370)(217,338)(218,337)(219,339)(220,335)(221,334)(222,336)(223,342)(224,341)(225,340)(226,329)(227,328)(228,330)(229,326)(230,325)(231,327)(232,333)(233,332)(234,331)(235,351)(236,350)(237,349)(238,348)(239,347)(240,346)(241,345)(242,344)(243,343)(244,311)(245,310)(246,312)(247,308)(248,307)(249,309)(250,315)(251,314)(252,313)(253,302)(254,301)(255,303)(256,299)(257,298)(258,300)(259,306)(260,305)(261,304)(262,324)(263,323)(264,322)(265,321)(266,320)(267,319)(268,318)(269,317)(270,316)(407,408)(409,413)(410,412)(411,414)(415,428)(416,427)(417,429)(418,425)(419,424)(420,426)(421,432)(422,431)(423,430)(433,514)(434,516)(435,515)(436,521)(437,520)(438,522)(439,518)(440,517)(441,519)(442,536)(443,535)(444,537)(445,533)(446,532)(447,534)(448,540)(449,539)(450,538)(451,527)(452,526)(453,528)(454,524)(455,523)(456,525)(457,531)(458,530)(459,529)(460,487)(461,489)(462,488)(463,494)(464,493)(465,495)(466,491)(467,490)(468,492)(469,509)(470,508)(471,510)(472,506)(473,505)(474,507)(475,513)(476,512)(477,511)(478,500)(479,499)(480,501)(481,497)(482,496)(483,498)(484,504)(485,503)(486,502)(541,689)(542,688)(543,690)(544,686)(545,685)(546,687)(547,693)(548,692)(549,691)(550,680)(551,679)(552,681)(553,677)(554,676)(555,678)(556,684)(557,683)(558,682)(559,702)(560,701)(561,700)(562,699)(563,698)(564,697)(565,696)(566,695)(567,694)(568,797)(569,796)(570,798)(571,794)(572,793)(573,795)(574,801)(575,800)(576,799)(577,788)(578,787)(579,789)(580,785)(581,784)(582,786)(583,792)(584,791)(585,790)(586,810)(587,809)(588,808)(589,807)(590,806)(591,805)(592,804)(593,803)(594,802)(595,770)(596,769)(597,771)(598,767)(599,766)(600,768)(601,774)(602,773)(603,772)(604,761)(605,760)(606,762)(607,758)(608,757)(609,759)(610,765)(611,764)(612,763)(613,783)(614,782)(615,781)(616,780)(617,779)(618,778)(619,777)(620,776)(621,775)(622,743)(623,742)(624,744)(625,740)(626,739)(627,741)(628,747)(629,746)(630,745)(631,734)(632,733)(633,735)(634,731)(635,730)(636,732)(637,738)(638,737)(639,736)(640,756)(641,755)(642,754)(643,753)(644,752)(645,751)(646,750)(647,749)(648,748)(649,716)(650,715)(651,717)(652,713)(653,712)(654,714)(655,720)(656,719)(657,718)(658,707)(659,706)(660,708)(661,704)(662,703)(663,705)(664,711)(665,710)(666,709)(667,729)(668,728)(669,727)(670,726)(671,725)(672,724)(673,723)(674,722)(675,721);
s1 := Sym(810)!( 1,568)( 2,570)( 3,569)( 4,575)( 5,574)( 6,576)( 7,572)( 8,571)( 9,573)( 10,590)( 11,589)( 12,591)( 13,587)( 14,586)( 15,588)( 16,594)( 17,593)( 18,592)( 19,581)( 20,580)( 21,582)( 22,578)( 23,577)( 24,579)( 25,585)( 26,584)( 27,583)( 28,541)( 29,543)( 30,542)( 31,548)( 32,547)( 33,549)( 34,545)( 35,544)( 36,546)( 37,563)( 38,562)( 39,564)( 40,560)( 41,559)( 42,561)( 43,567)( 44,566)( 45,565)( 46,554)( 47,553)( 48,555)( 49,551)( 50,550)( 51,552)( 52,558)( 53,557)( 54,556)( 55,649)( 56,651)( 57,650)( 58,656)( 59,655)( 60,657)( 61,653)( 62,652)( 63,654)( 64,671)( 65,670)( 66,672)( 67,668)( 68,667)( 69,669)( 70,675)( 71,674)( 72,673)( 73,662)( 74,661)( 75,663)( 76,659)( 77,658)( 78,660)( 79,666)( 80,665)( 81,664)( 82,622)( 83,624)( 84,623)( 85,629)( 86,628)( 87,630)( 88,626)( 89,625)( 90,627)( 91,644)( 92,643)( 93,645)( 94,641)( 95,640)( 96,642)( 97,648)( 98,647)( 99,646)(100,635)(101,634)(102,636)(103,632)(104,631)(105,633)(106,639)(107,638)(108,637)(109,595)(110,597)(111,596)(112,602)(113,601)(114,603)(115,599)(116,598)(117,600)(118,617)(119,616)(120,618)(121,614)(122,613)(123,615)(124,621)(125,620)(126,619)(127,608)(128,607)(129,609)(130,605)(131,604)(132,606)(133,612)(134,611)(135,610)(136,433)(137,435)(138,434)(139,440)(140,439)(141,441)(142,437)(143,436)(144,438)(145,455)(146,454)(147,456)(148,452)(149,451)(150,453)(151,459)(152,458)(153,457)(154,446)(155,445)(156,447)(157,443)(158,442)(159,444)(160,450)(161,449)(162,448)(163,406)(164,408)(165,407)(166,413)(167,412)(168,414)(169,410)(170,409)(171,411)(172,428)(173,427)(174,429)(175,425)(176,424)(177,426)(178,432)(179,431)(180,430)(181,419)(182,418)(183,420)(184,416)(185,415)(186,417)(187,423)(188,422)(189,421)(190,514)(191,516)(192,515)(193,521)(194,520)(195,522)(196,518)(197,517)(198,519)(199,536)(200,535)(201,537)(202,533)(203,532)(204,534)(205,540)(206,539)(207,538)(208,527)(209,526)(210,528)(211,524)(212,523)(213,525)(214,531)(215,530)(216,529)(217,487)(218,489)(219,488)(220,494)(221,493)(222,495)(223,491)(224,490)(225,492)(226,509)(227,508)(228,510)(229,506)(230,505)(231,507)(232,513)(233,512)(234,511)(235,500)(236,499)(237,501)(238,497)(239,496)(240,498)(241,504)(242,503)(243,502)(244,460)(245,462)(246,461)(247,467)(248,466)(249,468)(250,464)(251,463)(252,465)(253,482)(254,481)(255,483)(256,479)(257,478)(258,480)(259,486)(260,485)(261,484)(262,473)(263,472)(264,474)(265,470)(266,469)(267,471)(268,477)(269,476)(270,475)(271,716)(272,715)(273,717)(274,713)(275,712)(276,714)(277,720)(278,719)(279,718)(280,707)(281,706)(282,708)(283,704)(284,703)(285,705)(286,711)(287,710)(288,709)(289,729)(290,728)(291,727)(292,726)(293,725)(294,724)(295,723)(296,722)(297,721)(298,689)(299,688)(300,690)(301,686)(302,685)(303,687)(304,693)(305,692)(306,691)(307,680)(308,679)(309,681)(310,677)(311,676)(312,678)(313,684)(314,683)(315,682)(316,702)(317,701)(318,700)(319,699)(320,698)(321,697)(322,696)(323,695)(324,694)(325,797)(326,796)(327,798)(328,794)(329,793)(330,795)(331,801)(332,800)(333,799)(334,788)(335,787)(336,789)(337,785)(338,784)(339,786)(340,792)(341,791)(342,790)(343,810)(344,809)(345,808)(346,807)(347,806)(348,805)(349,804)(350,803)(351,802)(352,770)(353,769)(354,771)(355,767)(356,766)(357,768)(358,774)(359,773)(360,772)(361,761)(362,760)(363,762)(364,758)(365,757)(366,759)(367,765)(368,764)(369,763)(370,783)(371,782)(372,781)(373,780)(374,779)(375,778)(376,777)(377,776)(378,775)(379,743)(380,742)(381,744)(382,740)(383,739)(384,741)(385,747)(386,746)(387,745)(388,734)(389,733)(390,735)(391,731)(392,730)(393,732)(394,738)(395,737)(396,736)(397,756)(398,755)(399,754)(400,753)(401,752)(402,751)(403,750)(404,749)(405,748);
poly := sub<Sym(810)|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 >;
References : None.
to this polytope