Polytope of Type {830}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {830}*1660
Also Known As : 830-gon, {830}. if this polytope has another name.
Group : SmallGroup(1660,10)
Rank : 2
Schlafli Type : {830}
Number of vertices, edges, etc : 830, 830
Order of s0s1 : 830
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 : {415}*830
5-fold quotients : {166}*332
10-fold quotients : {83}*166
83-fold quotients : {10}*20
166-fold quotients : {5}*10
415-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 83)( 3, 82)( 4, 81)( 5, 80)( 6, 79)( 7, 78)( 8, 77)( 9, 76)
( 10, 75)( 11, 74)( 12, 73)( 13, 72)( 14, 71)( 15, 70)( 16, 69)( 17, 68)
( 18, 67)( 19, 66)( 20, 65)( 21, 64)( 22, 63)( 23, 62)( 24, 61)( 25, 60)
( 26, 59)( 27, 58)( 28, 57)( 29, 56)( 30, 55)( 31, 54)( 32, 53)( 33, 52)
( 34, 51)( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)
( 42, 43)( 84,333)( 85,415)( 86,414)( 87,413)( 88,412)( 89,411)( 90,410)
( 91,409)( 92,408)( 93,407)( 94,406)( 95,405)( 96,404)( 97,403)( 98,402)
( 99,401)(100,400)(101,399)(102,398)(103,397)(104,396)(105,395)(106,394)
(107,393)(108,392)(109,391)(110,390)(111,389)(112,388)(113,387)(114,386)
(115,385)(116,384)(117,383)(118,382)(119,381)(120,380)(121,379)(122,378)
(123,377)(124,376)(125,375)(126,374)(127,373)(128,372)(129,371)(130,370)
(131,369)(132,368)(133,367)(134,366)(135,365)(136,364)(137,363)(138,362)
(139,361)(140,360)(141,359)(142,358)(143,357)(144,356)(145,355)(146,354)
(147,353)(148,352)(149,351)(150,350)(151,349)(152,348)(153,347)(154,346)
(155,345)(156,344)(157,343)(158,342)(159,341)(160,340)(161,339)(162,338)
(163,337)(164,336)(165,335)(166,334)(167,250)(168,332)(169,331)(170,330)
(171,329)(172,328)(173,327)(174,326)(175,325)(176,324)(177,323)(178,322)
(179,321)(180,320)(181,319)(182,318)(183,317)(184,316)(185,315)(186,314)
(187,313)(188,312)(189,311)(190,310)(191,309)(192,308)(193,307)(194,306)
(195,305)(196,304)(197,303)(198,302)(199,301)(200,300)(201,299)(202,298)
(203,297)(204,296)(205,295)(206,294)(207,293)(208,292)(209,291)(210,290)
(211,289)(212,288)(213,287)(214,286)(215,285)(216,284)(217,283)(218,282)
(219,281)(220,280)(221,279)(222,278)(223,277)(224,276)(225,275)(226,274)
(227,273)(228,272)(229,271)(230,270)(231,269)(232,268)(233,267)(234,266)
(235,265)(236,264)(237,263)(238,262)(239,261)(240,260)(241,259)(242,258)
(243,257)(244,256)(245,255)(246,254)(247,253)(248,252)(249,251)(417,498)
(418,497)(419,496)(420,495)(421,494)(422,493)(423,492)(424,491)(425,490)
(426,489)(427,488)(428,487)(429,486)(430,485)(431,484)(432,483)(433,482)
(434,481)(435,480)(436,479)(437,478)(438,477)(439,476)(440,475)(441,474)
(442,473)(443,472)(444,471)(445,470)(446,469)(447,468)(448,467)(449,466)
(450,465)(451,464)(452,463)(453,462)(454,461)(455,460)(456,459)(457,458)
(499,748)(500,830)(501,829)(502,828)(503,827)(504,826)(505,825)(506,824)
(507,823)(508,822)(509,821)(510,820)(511,819)(512,818)(513,817)(514,816)
(515,815)(516,814)(517,813)(518,812)(519,811)(520,810)(521,809)(522,808)
(523,807)(524,806)(525,805)(526,804)(527,803)(528,802)(529,801)(530,800)
(531,799)(532,798)(533,797)(534,796)(535,795)(536,794)(537,793)(538,792)
(539,791)(540,790)(541,789)(542,788)(543,787)(544,786)(545,785)(546,784)
(547,783)(548,782)(549,781)(550,780)(551,779)(552,778)(553,777)(554,776)
(555,775)(556,774)(557,773)(558,772)(559,771)(560,770)(561,769)(562,768)
(563,767)(564,766)(565,765)(566,764)(567,763)(568,762)(569,761)(570,760)
(571,759)(572,758)(573,757)(574,756)(575,755)(576,754)(577,753)(578,752)
(579,751)(580,750)(581,749)(582,665)(583,747)(584,746)(585,745)(586,744)
(587,743)(588,742)(589,741)(590,740)(591,739)(592,738)(593,737)(594,736)
(595,735)(596,734)(597,733)(598,732)(599,731)(600,730)(601,729)(602,728)
(603,727)(604,726)(605,725)(606,724)(607,723)(608,722)(609,721)(610,720)
(611,719)(612,718)(613,717)(614,716)(615,715)(616,714)(617,713)(618,712)
(619,711)(620,710)(621,709)(622,708)(623,707)(624,706)(625,705)(626,704)
(627,703)(628,702)(629,701)(630,700)(631,699)(632,698)(633,697)(634,696)
(635,695)(636,694)(637,693)(638,692)(639,691)(640,690)(641,689)(642,688)
(643,687)(644,686)(645,685)(646,684)(647,683)(648,682)(649,681)(650,680)
(651,679)(652,678)(653,677)(654,676)(655,675)(656,674)(657,673)(658,672)
(659,671)(660,670)(661,669)(662,668)(663,667)(664,666);;
s1 := ( 1,500)( 2,499)( 3,581)( 4,580)( 5,579)( 6,578)( 7,577)( 8,576)
( 9,575)( 10,574)( 11,573)( 12,572)( 13,571)( 14,570)( 15,569)( 16,568)
( 17,567)( 18,566)( 19,565)( 20,564)( 21,563)( 22,562)( 23,561)( 24,560)
( 25,559)( 26,558)( 27,557)( 28,556)( 29,555)( 30,554)( 31,553)( 32,552)
( 33,551)( 34,550)( 35,549)( 36,548)( 37,547)( 38,546)( 39,545)( 40,544)
( 41,543)( 42,542)( 43,541)( 44,540)( 45,539)( 46,538)( 47,537)( 48,536)
( 49,535)( 50,534)( 51,533)( 52,532)( 53,531)( 54,530)( 55,529)( 56,528)
( 57,527)( 58,526)( 59,525)( 60,524)( 61,523)( 62,522)( 63,521)( 64,520)
( 65,519)( 66,518)( 67,517)( 68,516)( 69,515)( 70,514)( 71,513)( 72,512)
( 73,511)( 74,510)( 75,509)( 76,508)( 77,507)( 78,506)( 79,505)( 80,504)
( 81,503)( 82,502)( 83,501)( 84,417)( 85,416)( 86,498)( 87,497)( 88,496)
( 89,495)( 90,494)( 91,493)( 92,492)( 93,491)( 94,490)( 95,489)( 96,488)
( 97,487)( 98,486)( 99,485)(100,484)(101,483)(102,482)(103,481)(104,480)
(105,479)(106,478)(107,477)(108,476)(109,475)(110,474)(111,473)(112,472)
(113,471)(114,470)(115,469)(116,468)(117,467)(118,466)(119,465)(120,464)
(121,463)(122,462)(123,461)(124,460)(125,459)(126,458)(127,457)(128,456)
(129,455)(130,454)(131,453)(132,452)(133,451)(134,450)(135,449)(136,448)
(137,447)(138,446)(139,445)(140,444)(141,443)(142,442)(143,441)(144,440)
(145,439)(146,438)(147,437)(148,436)(149,435)(150,434)(151,433)(152,432)
(153,431)(154,430)(155,429)(156,428)(157,427)(158,426)(159,425)(160,424)
(161,423)(162,422)(163,421)(164,420)(165,419)(166,418)(167,749)(168,748)
(169,830)(170,829)(171,828)(172,827)(173,826)(174,825)(175,824)(176,823)
(177,822)(178,821)(179,820)(180,819)(181,818)(182,817)(183,816)(184,815)
(185,814)(186,813)(187,812)(188,811)(189,810)(190,809)(191,808)(192,807)
(193,806)(194,805)(195,804)(196,803)(197,802)(198,801)(199,800)(200,799)
(201,798)(202,797)(203,796)(204,795)(205,794)(206,793)(207,792)(208,791)
(209,790)(210,789)(211,788)(212,787)(213,786)(214,785)(215,784)(216,783)
(217,782)(218,781)(219,780)(220,779)(221,778)(222,777)(223,776)(224,775)
(225,774)(226,773)(227,772)(228,771)(229,770)(230,769)(231,768)(232,767)
(233,766)(234,765)(235,764)(236,763)(237,762)(238,761)(239,760)(240,759)
(241,758)(242,757)(243,756)(244,755)(245,754)(246,753)(247,752)(248,751)
(249,750)(250,666)(251,665)(252,747)(253,746)(254,745)(255,744)(256,743)
(257,742)(258,741)(259,740)(260,739)(261,738)(262,737)(263,736)(264,735)
(265,734)(266,733)(267,732)(268,731)(269,730)(270,729)(271,728)(272,727)
(273,726)(274,725)(275,724)(276,723)(277,722)(278,721)(279,720)(280,719)
(281,718)(282,717)(283,716)(284,715)(285,714)(286,713)(287,712)(288,711)
(289,710)(290,709)(291,708)(292,707)(293,706)(294,705)(295,704)(296,703)
(297,702)(298,701)(299,700)(300,699)(301,698)(302,697)(303,696)(304,695)
(305,694)(306,693)(307,692)(308,691)(309,690)(310,689)(311,688)(312,687)
(313,686)(314,685)(315,684)(316,683)(317,682)(318,681)(319,680)(320,679)
(321,678)(322,677)(323,676)(324,675)(325,674)(326,673)(327,672)(328,671)
(329,670)(330,669)(331,668)(332,667)(333,583)(334,582)(335,664)(336,663)
(337,662)(338,661)(339,660)(340,659)(341,658)(342,657)(343,656)(344,655)
(345,654)(346,653)(347,652)(348,651)(349,650)(350,649)(351,648)(352,647)
(353,646)(354,645)(355,644)(356,643)(357,642)(358,641)(359,640)(360,639)
(361,638)(362,637)(363,636)(364,635)(365,634)(366,633)(367,632)(368,631)
(369,630)(370,629)(371,628)(372,627)(373,626)(374,625)(375,624)(376,623)
(377,622)(378,621)(379,620)(380,619)(381,618)(382,617)(383,616)(384,615)
(385,614)(386,613)(387,612)(388,611)(389,610)(390,609)(391,608)(392,607)
(393,606)(394,605)(395,604)(396,603)(397,602)(398,601)(399,600)(400,599)
(401,598)(402,597)(403,596)(404,595)(405,594)(406,593)(407,592)(408,591)
(409,590)(410,589)(411,588)(412,587)(413,586)(414,585)(415,584);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(830)!( 2, 83)( 3, 82)( 4, 81)( 5, 80)( 6, 79)( 7, 78)( 8, 77)
( 9, 76)( 10, 75)( 11, 74)( 12, 73)( 13, 72)( 14, 71)( 15, 70)( 16, 69)
( 17, 68)( 18, 67)( 19, 66)( 20, 65)( 21, 64)( 22, 63)( 23, 62)( 24, 61)
( 25, 60)( 26, 59)( 27, 58)( 28, 57)( 29, 56)( 30, 55)( 31, 54)( 32, 53)
( 33, 52)( 34, 51)( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)( 40, 45)
( 41, 44)( 42, 43)( 84,333)( 85,415)( 86,414)( 87,413)( 88,412)( 89,411)
( 90,410)( 91,409)( 92,408)( 93,407)( 94,406)( 95,405)( 96,404)( 97,403)
( 98,402)( 99,401)(100,400)(101,399)(102,398)(103,397)(104,396)(105,395)
(106,394)(107,393)(108,392)(109,391)(110,390)(111,389)(112,388)(113,387)
(114,386)(115,385)(116,384)(117,383)(118,382)(119,381)(120,380)(121,379)
(122,378)(123,377)(124,376)(125,375)(126,374)(127,373)(128,372)(129,371)
(130,370)(131,369)(132,368)(133,367)(134,366)(135,365)(136,364)(137,363)
(138,362)(139,361)(140,360)(141,359)(142,358)(143,357)(144,356)(145,355)
(146,354)(147,353)(148,352)(149,351)(150,350)(151,349)(152,348)(153,347)
(154,346)(155,345)(156,344)(157,343)(158,342)(159,341)(160,340)(161,339)
(162,338)(163,337)(164,336)(165,335)(166,334)(167,250)(168,332)(169,331)
(170,330)(171,329)(172,328)(173,327)(174,326)(175,325)(176,324)(177,323)
(178,322)(179,321)(180,320)(181,319)(182,318)(183,317)(184,316)(185,315)
(186,314)(187,313)(188,312)(189,311)(190,310)(191,309)(192,308)(193,307)
(194,306)(195,305)(196,304)(197,303)(198,302)(199,301)(200,300)(201,299)
(202,298)(203,297)(204,296)(205,295)(206,294)(207,293)(208,292)(209,291)
(210,290)(211,289)(212,288)(213,287)(214,286)(215,285)(216,284)(217,283)
(218,282)(219,281)(220,280)(221,279)(222,278)(223,277)(224,276)(225,275)
(226,274)(227,273)(228,272)(229,271)(230,270)(231,269)(232,268)(233,267)
(234,266)(235,265)(236,264)(237,263)(238,262)(239,261)(240,260)(241,259)
(242,258)(243,257)(244,256)(245,255)(246,254)(247,253)(248,252)(249,251)
(417,498)(418,497)(419,496)(420,495)(421,494)(422,493)(423,492)(424,491)
(425,490)(426,489)(427,488)(428,487)(429,486)(430,485)(431,484)(432,483)
(433,482)(434,481)(435,480)(436,479)(437,478)(438,477)(439,476)(440,475)
(441,474)(442,473)(443,472)(444,471)(445,470)(446,469)(447,468)(448,467)
(449,466)(450,465)(451,464)(452,463)(453,462)(454,461)(455,460)(456,459)
(457,458)(499,748)(500,830)(501,829)(502,828)(503,827)(504,826)(505,825)
(506,824)(507,823)(508,822)(509,821)(510,820)(511,819)(512,818)(513,817)
(514,816)(515,815)(516,814)(517,813)(518,812)(519,811)(520,810)(521,809)
(522,808)(523,807)(524,806)(525,805)(526,804)(527,803)(528,802)(529,801)
(530,800)(531,799)(532,798)(533,797)(534,796)(535,795)(536,794)(537,793)
(538,792)(539,791)(540,790)(541,789)(542,788)(543,787)(544,786)(545,785)
(546,784)(547,783)(548,782)(549,781)(550,780)(551,779)(552,778)(553,777)
(554,776)(555,775)(556,774)(557,773)(558,772)(559,771)(560,770)(561,769)
(562,768)(563,767)(564,766)(565,765)(566,764)(567,763)(568,762)(569,761)
(570,760)(571,759)(572,758)(573,757)(574,756)(575,755)(576,754)(577,753)
(578,752)(579,751)(580,750)(581,749)(582,665)(583,747)(584,746)(585,745)
(586,744)(587,743)(588,742)(589,741)(590,740)(591,739)(592,738)(593,737)
(594,736)(595,735)(596,734)(597,733)(598,732)(599,731)(600,730)(601,729)
(602,728)(603,727)(604,726)(605,725)(606,724)(607,723)(608,722)(609,721)
(610,720)(611,719)(612,718)(613,717)(614,716)(615,715)(616,714)(617,713)
(618,712)(619,711)(620,710)(621,709)(622,708)(623,707)(624,706)(625,705)
(626,704)(627,703)(628,702)(629,701)(630,700)(631,699)(632,698)(633,697)
(634,696)(635,695)(636,694)(637,693)(638,692)(639,691)(640,690)(641,689)
(642,688)(643,687)(644,686)(645,685)(646,684)(647,683)(648,682)(649,681)
(650,680)(651,679)(652,678)(653,677)(654,676)(655,675)(656,674)(657,673)
(658,672)(659,671)(660,670)(661,669)(662,668)(663,667)(664,666);
s1 := Sym(830)!( 1,500)( 2,499)( 3,581)( 4,580)( 5,579)( 6,578)( 7,577)
( 8,576)( 9,575)( 10,574)( 11,573)( 12,572)( 13,571)( 14,570)( 15,569)
( 16,568)( 17,567)( 18,566)( 19,565)( 20,564)( 21,563)( 22,562)( 23,561)
( 24,560)( 25,559)( 26,558)( 27,557)( 28,556)( 29,555)( 30,554)( 31,553)
( 32,552)( 33,551)( 34,550)( 35,549)( 36,548)( 37,547)( 38,546)( 39,545)
( 40,544)( 41,543)( 42,542)( 43,541)( 44,540)( 45,539)( 46,538)( 47,537)
( 48,536)( 49,535)( 50,534)( 51,533)( 52,532)( 53,531)( 54,530)( 55,529)
( 56,528)( 57,527)( 58,526)( 59,525)( 60,524)( 61,523)( 62,522)( 63,521)
( 64,520)( 65,519)( 66,518)( 67,517)( 68,516)( 69,515)( 70,514)( 71,513)
( 72,512)( 73,511)( 74,510)( 75,509)( 76,508)( 77,507)( 78,506)( 79,505)
( 80,504)( 81,503)( 82,502)( 83,501)( 84,417)( 85,416)( 86,498)( 87,497)
( 88,496)( 89,495)( 90,494)( 91,493)( 92,492)( 93,491)( 94,490)( 95,489)
( 96,488)( 97,487)( 98,486)( 99,485)(100,484)(101,483)(102,482)(103,481)
(104,480)(105,479)(106,478)(107,477)(108,476)(109,475)(110,474)(111,473)
(112,472)(113,471)(114,470)(115,469)(116,468)(117,467)(118,466)(119,465)
(120,464)(121,463)(122,462)(123,461)(124,460)(125,459)(126,458)(127,457)
(128,456)(129,455)(130,454)(131,453)(132,452)(133,451)(134,450)(135,449)
(136,448)(137,447)(138,446)(139,445)(140,444)(141,443)(142,442)(143,441)
(144,440)(145,439)(146,438)(147,437)(148,436)(149,435)(150,434)(151,433)
(152,432)(153,431)(154,430)(155,429)(156,428)(157,427)(158,426)(159,425)
(160,424)(161,423)(162,422)(163,421)(164,420)(165,419)(166,418)(167,749)
(168,748)(169,830)(170,829)(171,828)(172,827)(173,826)(174,825)(175,824)
(176,823)(177,822)(178,821)(179,820)(180,819)(181,818)(182,817)(183,816)
(184,815)(185,814)(186,813)(187,812)(188,811)(189,810)(190,809)(191,808)
(192,807)(193,806)(194,805)(195,804)(196,803)(197,802)(198,801)(199,800)
(200,799)(201,798)(202,797)(203,796)(204,795)(205,794)(206,793)(207,792)
(208,791)(209,790)(210,789)(211,788)(212,787)(213,786)(214,785)(215,784)
(216,783)(217,782)(218,781)(219,780)(220,779)(221,778)(222,777)(223,776)
(224,775)(225,774)(226,773)(227,772)(228,771)(229,770)(230,769)(231,768)
(232,767)(233,766)(234,765)(235,764)(236,763)(237,762)(238,761)(239,760)
(240,759)(241,758)(242,757)(243,756)(244,755)(245,754)(246,753)(247,752)
(248,751)(249,750)(250,666)(251,665)(252,747)(253,746)(254,745)(255,744)
(256,743)(257,742)(258,741)(259,740)(260,739)(261,738)(262,737)(263,736)
(264,735)(265,734)(266,733)(267,732)(268,731)(269,730)(270,729)(271,728)
(272,727)(273,726)(274,725)(275,724)(276,723)(277,722)(278,721)(279,720)
(280,719)(281,718)(282,717)(283,716)(284,715)(285,714)(286,713)(287,712)
(288,711)(289,710)(290,709)(291,708)(292,707)(293,706)(294,705)(295,704)
(296,703)(297,702)(298,701)(299,700)(300,699)(301,698)(302,697)(303,696)
(304,695)(305,694)(306,693)(307,692)(308,691)(309,690)(310,689)(311,688)
(312,687)(313,686)(314,685)(315,684)(316,683)(317,682)(318,681)(319,680)
(320,679)(321,678)(322,677)(323,676)(324,675)(325,674)(326,673)(327,672)
(328,671)(329,670)(330,669)(331,668)(332,667)(333,583)(334,582)(335,664)
(336,663)(337,662)(338,661)(339,660)(340,659)(341,658)(342,657)(343,656)
(344,655)(345,654)(346,653)(347,652)(348,651)(349,650)(350,649)(351,648)
(352,647)(353,646)(354,645)(355,644)(356,643)(357,642)(358,641)(359,640)
(360,639)(361,638)(362,637)(363,636)(364,635)(365,634)(366,633)(367,632)
(368,631)(369,630)(370,629)(371,628)(372,627)(373,626)(374,625)(375,624)
(376,623)(377,622)(378,621)(379,620)(380,619)(381,618)(382,617)(383,616)
(384,615)(385,614)(386,613)(387,612)(388,611)(389,610)(390,609)(391,608)
(392,607)(393,606)(394,605)(395,604)(396,603)(397,602)(398,601)(399,600)
(400,599)(401,598)(402,597)(403,596)(404,595)(405,594)(406,593)(407,592)
(408,591)(409,590)(410,589)(411,588)(412,587)(413,586)(414,585)(415,584);
poly := sub<Sym(830)|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 >;
References : None.
to this polytope