Polytope of Type {822}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {822}*1644
Also Known As : 822-gon, {822}. if this polytope has another name.
Group : SmallGroup(1644,11)
Rank : 2
Schlafli Type : {822}
Number of vertices, edges, etc : 822, 822
Order of s0s1 : 822
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 : {411}*822
3-fold quotients : {274}*548
6-fold quotients : {137}*274
137-fold quotients : {6}*12
274-fold quotients : {3}*6
411-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2,137)( 3,136)( 4,135)( 5,134)( 6,133)( 7,132)( 8,131)( 9,130)
( 10,129)( 11,128)( 12,127)( 13,126)( 14,125)( 15,124)( 16,123)( 17,122)
( 18,121)( 19,120)( 20,119)( 21,118)( 22,117)( 23,116)( 24,115)( 25,114)
( 26,113)( 27,112)( 28,111)( 29,110)( 30,109)( 31,108)( 32,107)( 33,106)
( 34,105)( 35,104)( 36,103)( 37,102)( 38,101)( 39,100)( 40, 99)( 41, 98)
( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 92)( 48, 91)( 49, 90)
( 50, 89)( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)( 56, 83)( 57, 82)
( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)
( 66, 73)( 67, 72)( 68, 71)( 69, 70)(138,275)(139,411)(140,410)(141,409)
(142,408)(143,407)(144,406)(145,405)(146,404)(147,403)(148,402)(149,401)
(150,400)(151,399)(152,398)(153,397)(154,396)(155,395)(156,394)(157,393)
(158,392)(159,391)(160,390)(161,389)(162,388)(163,387)(164,386)(165,385)
(166,384)(167,383)(168,382)(169,381)(170,380)(171,379)(172,378)(173,377)
(174,376)(175,375)(176,374)(177,373)(178,372)(179,371)(180,370)(181,369)
(182,368)(183,367)(184,366)(185,365)(186,364)(187,363)(188,362)(189,361)
(190,360)(191,359)(192,358)(193,357)(194,356)(195,355)(196,354)(197,353)
(198,352)(199,351)(200,350)(201,349)(202,348)(203,347)(204,346)(205,345)
(206,344)(207,343)(208,342)(209,341)(210,340)(211,339)(212,338)(213,337)
(214,336)(215,335)(216,334)(217,333)(218,332)(219,331)(220,330)(221,329)
(222,328)(223,327)(224,326)(225,325)(226,324)(227,323)(228,322)(229,321)
(230,320)(231,319)(232,318)(233,317)(234,316)(235,315)(236,314)(237,313)
(238,312)(239,311)(240,310)(241,309)(242,308)(243,307)(244,306)(245,305)
(246,304)(247,303)(248,302)(249,301)(250,300)(251,299)(252,298)(253,297)
(254,296)(255,295)(256,294)(257,293)(258,292)(259,291)(260,290)(261,289)
(262,288)(263,287)(264,286)(265,285)(266,284)(267,283)(268,282)(269,281)
(270,280)(271,279)(272,278)(273,277)(274,276)(413,548)(414,547)(415,546)
(416,545)(417,544)(418,543)(419,542)(420,541)(421,540)(422,539)(423,538)
(424,537)(425,536)(426,535)(427,534)(428,533)(429,532)(430,531)(431,530)
(432,529)(433,528)(434,527)(435,526)(436,525)(437,524)(438,523)(439,522)
(440,521)(441,520)(442,519)(443,518)(444,517)(445,516)(446,515)(447,514)
(448,513)(449,512)(450,511)(451,510)(452,509)(453,508)(454,507)(455,506)
(456,505)(457,504)(458,503)(459,502)(460,501)(461,500)(462,499)(463,498)
(464,497)(465,496)(466,495)(467,494)(468,493)(469,492)(470,491)(471,490)
(472,489)(473,488)(474,487)(475,486)(476,485)(477,484)(478,483)(479,482)
(480,481)(549,686)(550,822)(551,821)(552,820)(553,819)(554,818)(555,817)
(556,816)(557,815)(558,814)(559,813)(560,812)(561,811)(562,810)(563,809)
(564,808)(565,807)(566,806)(567,805)(568,804)(569,803)(570,802)(571,801)
(572,800)(573,799)(574,798)(575,797)(576,796)(577,795)(578,794)(579,793)
(580,792)(581,791)(582,790)(583,789)(584,788)(585,787)(586,786)(587,785)
(588,784)(589,783)(590,782)(591,781)(592,780)(593,779)(594,778)(595,777)
(596,776)(597,775)(598,774)(599,773)(600,772)(601,771)(602,770)(603,769)
(604,768)(605,767)(606,766)(607,765)(608,764)(609,763)(610,762)(611,761)
(612,760)(613,759)(614,758)(615,757)(616,756)(617,755)(618,754)(619,753)
(620,752)(621,751)(622,750)(623,749)(624,748)(625,747)(626,746)(627,745)
(628,744)(629,743)(630,742)(631,741)(632,740)(633,739)(634,738)(635,737)
(636,736)(637,735)(638,734)(639,733)(640,732)(641,731)(642,730)(643,729)
(644,728)(645,727)(646,726)(647,725)(648,724)(649,723)(650,722)(651,721)
(652,720)(653,719)(654,718)(655,717)(656,716)(657,715)(658,714)(659,713)
(660,712)(661,711)(662,710)(663,709)(664,708)(665,707)(666,706)(667,705)
(668,704)(669,703)(670,702)(671,701)(672,700)(673,699)(674,698)(675,697)
(676,696)(677,695)(678,694)(679,693)(680,692)(681,691)(682,690)(683,689)
(684,688)(685,687);;
s1 := ( 1,550)( 2,549)( 3,685)( 4,684)( 5,683)( 6,682)( 7,681)( 8,680)
( 9,679)( 10,678)( 11,677)( 12,676)( 13,675)( 14,674)( 15,673)( 16,672)
( 17,671)( 18,670)( 19,669)( 20,668)( 21,667)( 22,666)( 23,665)( 24,664)
( 25,663)( 26,662)( 27,661)( 28,660)( 29,659)( 30,658)( 31,657)( 32,656)
( 33,655)( 34,654)( 35,653)( 36,652)( 37,651)( 38,650)( 39,649)( 40,648)
( 41,647)( 42,646)( 43,645)( 44,644)( 45,643)( 46,642)( 47,641)( 48,640)
( 49,639)( 50,638)( 51,637)( 52,636)( 53,635)( 54,634)( 55,633)( 56,632)
( 57,631)( 58,630)( 59,629)( 60,628)( 61,627)( 62,626)( 63,625)( 64,624)
( 65,623)( 66,622)( 67,621)( 68,620)( 69,619)( 70,618)( 71,617)( 72,616)
( 73,615)( 74,614)( 75,613)( 76,612)( 77,611)( 78,610)( 79,609)( 80,608)
( 81,607)( 82,606)( 83,605)( 84,604)( 85,603)( 86,602)( 87,601)( 88,600)
( 89,599)( 90,598)( 91,597)( 92,596)( 93,595)( 94,594)( 95,593)( 96,592)
( 97,591)( 98,590)( 99,589)(100,588)(101,587)(102,586)(103,585)(104,584)
(105,583)(106,582)(107,581)(108,580)(109,579)(110,578)(111,577)(112,576)
(113,575)(114,574)(115,573)(116,572)(117,571)(118,570)(119,569)(120,568)
(121,567)(122,566)(123,565)(124,564)(125,563)(126,562)(127,561)(128,560)
(129,559)(130,558)(131,557)(132,556)(133,555)(134,554)(135,553)(136,552)
(137,551)(138,413)(139,412)(140,548)(141,547)(142,546)(143,545)(144,544)
(145,543)(146,542)(147,541)(148,540)(149,539)(150,538)(151,537)(152,536)
(153,535)(154,534)(155,533)(156,532)(157,531)(158,530)(159,529)(160,528)
(161,527)(162,526)(163,525)(164,524)(165,523)(166,522)(167,521)(168,520)
(169,519)(170,518)(171,517)(172,516)(173,515)(174,514)(175,513)(176,512)
(177,511)(178,510)(179,509)(180,508)(181,507)(182,506)(183,505)(184,504)
(185,503)(186,502)(187,501)(188,500)(189,499)(190,498)(191,497)(192,496)
(193,495)(194,494)(195,493)(196,492)(197,491)(198,490)(199,489)(200,488)
(201,487)(202,486)(203,485)(204,484)(205,483)(206,482)(207,481)(208,480)
(209,479)(210,478)(211,477)(212,476)(213,475)(214,474)(215,473)(216,472)
(217,471)(218,470)(219,469)(220,468)(221,467)(222,466)(223,465)(224,464)
(225,463)(226,462)(227,461)(228,460)(229,459)(230,458)(231,457)(232,456)
(233,455)(234,454)(235,453)(236,452)(237,451)(238,450)(239,449)(240,448)
(241,447)(242,446)(243,445)(244,444)(245,443)(246,442)(247,441)(248,440)
(249,439)(250,438)(251,437)(252,436)(253,435)(254,434)(255,433)(256,432)
(257,431)(258,430)(259,429)(260,428)(261,427)(262,426)(263,425)(264,424)
(265,423)(266,422)(267,421)(268,420)(269,419)(270,418)(271,417)(272,416)
(273,415)(274,414)(275,687)(276,686)(277,822)(278,821)(279,820)(280,819)
(281,818)(282,817)(283,816)(284,815)(285,814)(286,813)(287,812)(288,811)
(289,810)(290,809)(291,808)(292,807)(293,806)(294,805)(295,804)(296,803)
(297,802)(298,801)(299,800)(300,799)(301,798)(302,797)(303,796)(304,795)
(305,794)(306,793)(307,792)(308,791)(309,790)(310,789)(311,788)(312,787)
(313,786)(314,785)(315,784)(316,783)(317,782)(318,781)(319,780)(320,779)
(321,778)(322,777)(323,776)(324,775)(325,774)(326,773)(327,772)(328,771)
(329,770)(330,769)(331,768)(332,767)(333,766)(334,765)(335,764)(336,763)
(337,762)(338,761)(339,760)(340,759)(341,758)(342,757)(343,756)(344,755)
(345,754)(346,753)(347,752)(348,751)(349,750)(350,749)(351,748)(352,747)
(353,746)(354,745)(355,744)(356,743)(357,742)(358,741)(359,740)(360,739)
(361,738)(362,737)(363,736)(364,735)(365,734)(366,733)(367,732)(368,731)
(369,730)(370,729)(371,728)(372,727)(373,726)(374,725)(375,724)(376,723)
(377,722)(378,721)(379,720)(380,719)(381,718)(382,717)(383,716)(384,715)
(385,714)(386,713)(387,712)(388,711)(389,710)(390,709)(391,708)(392,707)
(393,706)(394,705)(395,704)(396,703)(397,702)(398,701)(399,700)(400,699)
(401,698)(402,697)(403,696)(404,695)(405,694)(406,693)(407,692)(408,691)
(409,690)(410,689)(411,688);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(822)!( 2,137)( 3,136)( 4,135)( 5,134)( 6,133)( 7,132)( 8,131)
( 9,130)( 10,129)( 11,128)( 12,127)( 13,126)( 14,125)( 15,124)( 16,123)
( 17,122)( 18,121)( 19,120)( 20,119)( 21,118)( 22,117)( 23,116)( 24,115)
( 25,114)( 26,113)( 27,112)( 28,111)( 29,110)( 30,109)( 31,108)( 32,107)
( 33,106)( 34,105)( 35,104)( 36,103)( 37,102)( 38,101)( 39,100)( 40, 99)
( 41, 98)( 42, 97)( 43, 96)( 44, 95)( 45, 94)( 46, 93)( 47, 92)( 48, 91)
( 49, 90)( 50, 89)( 51, 88)( 52, 87)( 53, 86)( 54, 85)( 55, 84)( 56, 83)
( 57, 82)( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)
( 65, 74)( 66, 73)( 67, 72)( 68, 71)( 69, 70)(138,275)(139,411)(140,410)
(141,409)(142,408)(143,407)(144,406)(145,405)(146,404)(147,403)(148,402)
(149,401)(150,400)(151,399)(152,398)(153,397)(154,396)(155,395)(156,394)
(157,393)(158,392)(159,391)(160,390)(161,389)(162,388)(163,387)(164,386)
(165,385)(166,384)(167,383)(168,382)(169,381)(170,380)(171,379)(172,378)
(173,377)(174,376)(175,375)(176,374)(177,373)(178,372)(179,371)(180,370)
(181,369)(182,368)(183,367)(184,366)(185,365)(186,364)(187,363)(188,362)
(189,361)(190,360)(191,359)(192,358)(193,357)(194,356)(195,355)(196,354)
(197,353)(198,352)(199,351)(200,350)(201,349)(202,348)(203,347)(204,346)
(205,345)(206,344)(207,343)(208,342)(209,341)(210,340)(211,339)(212,338)
(213,337)(214,336)(215,335)(216,334)(217,333)(218,332)(219,331)(220,330)
(221,329)(222,328)(223,327)(224,326)(225,325)(226,324)(227,323)(228,322)
(229,321)(230,320)(231,319)(232,318)(233,317)(234,316)(235,315)(236,314)
(237,313)(238,312)(239,311)(240,310)(241,309)(242,308)(243,307)(244,306)
(245,305)(246,304)(247,303)(248,302)(249,301)(250,300)(251,299)(252,298)
(253,297)(254,296)(255,295)(256,294)(257,293)(258,292)(259,291)(260,290)
(261,289)(262,288)(263,287)(264,286)(265,285)(266,284)(267,283)(268,282)
(269,281)(270,280)(271,279)(272,278)(273,277)(274,276)(413,548)(414,547)
(415,546)(416,545)(417,544)(418,543)(419,542)(420,541)(421,540)(422,539)
(423,538)(424,537)(425,536)(426,535)(427,534)(428,533)(429,532)(430,531)
(431,530)(432,529)(433,528)(434,527)(435,526)(436,525)(437,524)(438,523)
(439,522)(440,521)(441,520)(442,519)(443,518)(444,517)(445,516)(446,515)
(447,514)(448,513)(449,512)(450,511)(451,510)(452,509)(453,508)(454,507)
(455,506)(456,505)(457,504)(458,503)(459,502)(460,501)(461,500)(462,499)
(463,498)(464,497)(465,496)(466,495)(467,494)(468,493)(469,492)(470,491)
(471,490)(472,489)(473,488)(474,487)(475,486)(476,485)(477,484)(478,483)
(479,482)(480,481)(549,686)(550,822)(551,821)(552,820)(553,819)(554,818)
(555,817)(556,816)(557,815)(558,814)(559,813)(560,812)(561,811)(562,810)
(563,809)(564,808)(565,807)(566,806)(567,805)(568,804)(569,803)(570,802)
(571,801)(572,800)(573,799)(574,798)(575,797)(576,796)(577,795)(578,794)
(579,793)(580,792)(581,791)(582,790)(583,789)(584,788)(585,787)(586,786)
(587,785)(588,784)(589,783)(590,782)(591,781)(592,780)(593,779)(594,778)
(595,777)(596,776)(597,775)(598,774)(599,773)(600,772)(601,771)(602,770)
(603,769)(604,768)(605,767)(606,766)(607,765)(608,764)(609,763)(610,762)
(611,761)(612,760)(613,759)(614,758)(615,757)(616,756)(617,755)(618,754)
(619,753)(620,752)(621,751)(622,750)(623,749)(624,748)(625,747)(626,746)
(627,745)(628,744)(629,743)(630,742)(631,741)(632,740)(633,739)(634,738)
(635,737)(636,736)(637,735)(638,734)(639,733)(640,732)(641,731)(642,730)
(643,729)(644,728)(645,727)(646,726)(647,725)(648,724)(649,723)(650,722)
(651,721)(652,720)(653,719)(654,718)(655,717)(656,716)(657,715)(658,714)
(659,713)(660,712)(661,711)(662,710)(663,709)(664,708)(665,707)(666,706)
(667,705)(668,704)(669,703)(670,702)(671,701)(672,700)(673,699)(674,698)
(675,697)(676,696)(677,695)(678,694)(679,693)(680,692)(681,691)(682,690)
(683,689)(684,688)(685,687);
s1 := Sym(822)!( 1,550)( 2,549)( 3,685)( 4,684)( 5,683)( 6,682)( 7,681)
( 8,680)( 9,679)( 10,678)( 11,677)( 12,676)( 13,675)( 14,674)( 15,673)
( 16,672)( 17,671)( 18,670)( 19,669)( 20,668)( 21,667)( 22,666)( 23,665)
( 24,664)( 25,663)( 26,662)( 27,661)( 28,660)( 29,659)( 30,658)( 31,657)
( 32,656)( 33,655)( 34,654)( 35,653)( 36,652)( 37,651)( 38,650)( 39,649)
( 40,648)( 41,647)( 42,646)( 43,645)( 44,644)( 45,643)( 46,642)( 47,641)
( 48,640)( 49,639)( 50,638)( 51,637)( 52,636)( 53,635)( 54,634)( 55,633)
( 56,632)( 57,631)( 58,630)( 59,629)( 60,628)( 61,627)( 62,626)( 63,625)
( 64,624)( 65,623)( 66,622)( 67,621)( 68,620)( 69,619)( 70,618)( 71,617)
( 72,616)( 73,615)( 74,614)( 75,613)( 76,612)( 77,611)( 78,610)( 79,609)
( 80,608)( 81,607)( 82,606)( 83,605)( 84,604)( 85,603)( 86,602)( 87,601)
( 88,600)( 89,599)( 90,598)( 91,597)( 92,596)( 93,595)( 94,594)( 95,593)
( 96,592)( 97,591)( 98,590)( 99,589)(100,588)(101,587)(102,586)(103,585)
(104,584)(105,583)(106,582)(107,581)(108,580)(109,579)(110,578)(111,577)
(112,576)(113,575)(114,574)(115,573)(116,572)(117,571)(118,570)(119,569)
(120,568)(121,567)(122,566)(123,565)(124,564)(125,563)(126,562)(127,561)
(128,560)(129,559)(130,558)(131,557)(132,556)(133,555)(134,554)(135,553)
(136,552)(137,551)(138,413)(139,412)(140,548)(141,547)(142,546)(143,545)
(144,544)(145,543)(146,542)(147,541)(148,540)(149,539)(150,538)(151,537)
(152,536)(153,535)(154,534)(155,533)(156,532)(157,531)(158,530)(159,529)
(160,528)(161,527)(162,526)(163,525)(164,524)(165,523)(166,522)(167,521)
(168,520)(169,519)(170,518)(171,517)(172,516)(173,515)(174,514)(175,513)
(176,512)(177,511)(178,510)(179,509)(180,508)(181,507)(182,506)(183,505)
(184,504)(185,503)(186,502)(187,501)(188,500)(189,499)(190,498)(191,497)
(192,496)(193,495)(194,494)(195,493)(196,492)(197,491)(198,490)(199,489)
(200,488)(201,487)(202,486)(203,485)(204,484)(205,483)(206,482)(207,481)
(208,480)(209,479)(210,478)(211,477)(212,476)(213,475)(214,474)(215,473)
(216,472)(217,471)(218,470)(219,469)(220,468)(221,467)(222,466)(223,465)
(224,464)(225,463)(226,462)(227,461)(228,460)(229,459)(230,458)(231,457)
(232,456)(233,455)(234,454)(235,453)(236,452)(237,451)(238,450)(239,449)
(240,448)(241,447)(242,446)(243,445)(244,444)(245,443)(246,442)(247,441)
(248,440)(249,439)(250,438)(251,437)(252,436)(253,435)(254,434)(255,433)
(256,432)(257,431)(258,430)(259,429)(260,428)(261,427)(262,426)(263,425)
(264,424)(265,423)(266,422)(267,421)(268,420)(269,419)(270,418)(271,417)
(272,416)(273,415)(274,414)(275,687)(276,686)(277,822)(278,821)(279,820)
(280,819)(281,818)(282,817)(283,816)(284,815)(285,814)(286,813)(287,812)
(288,811)(289,810)(290,809)(291,808)(292,807)(293,806)(294,805)(295,804)
(296,803)(297,802)(298,801)(299,800)(300,799)(301,798)(302,797)(303,796)
(304,795)(305,794)(306,793)(307,792)(308,791)(309,790)(310,789)(311,788)
(312,787)(313,786)(314,785)(315,784)(316,783)(317,782)(318,781)(319,780)
(320,779)(321,778)(322,777)(323,776)(324,775)(325,774)(326,773)(327,772)
(328,771)(329,770)(330,769)(331,768)(332,767)(333,766)(334,765)(335,764)
(336,763)(337,762)(338,761)(339,760)(340,759)(341,758)(342,757)(343,756)
(344,755)(345,754)(346,753)(347,752)(348,751)(349,750)(350,749)(351,748)
(352,747)(353,746)(354,745)(355,744)(356,743)(357,742)(358,741)(359,740)
(360,739)(361,738)(362,737)(363,736)(364,735)(365,734)(366,733)(367,732)
(368,731)(369,730)(370,729)(371,728)(372,727)(373,726)(374,725)(375,724)
(376,723)(377,722)(378,721)(379,720)(380,719)(381,718)(382,717)(383,716)
(384,715)(385,714)(386,713)(387,712)(388,711)(389,710)(390,709)(391,708)
(392,707)(393,706)(394,705)(395,704)(396,703)(397,702)(398,701)(399,700)
(400,699)(401,698)(402,697)(403,696)(404,695)(405,694)(406,693)(407,692)
(408,691)(409,690)(410,689)(411,688);
poly := sub<Sym(822)|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 >;
References : None.
to this polytope