Polytope of Type {850}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {850}*1700
Also Known As : 850-gon, {850}. if this polytope has another name.
Group : SmallGroup(1700,14)
Rank : 2
Schlafli Type : {850}
Number of vertices, edges, etc : 850, 850
Order of s0s1 : 850
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 : {425}*850
5-fold quotients : {170}*340
10-fold quotients : {85}*170
17-fold quotients : {50}*100
25-fold quotients : {34}*68
34-fold quotients : {25}*50
50-fold quotients : {17}*34
85-fold quotients : {10}*20
170-fold quotients : {5}*10
425-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 6, 81)( 7, 85)( 8, 84)( 9, 83)( 10, 82)( 11, 76)
( 12, 80)( 13, 79)( 14, 78)( 15, 77)( 16, 71)( 17, 75)( 18, 74)( 19, 73)
( 20, 72)( 21, 66)( 22, 70)( 23, 69)( 24, 68)( 25, 67)( 26, 61)( 27, 65)
( 28, 64)( 29, 63)( 30, 62)( 31, 56)( 32, 60)( 33, 59)( 34, 58)( 35, 57)
( 36, 51)( 37, 55)( 38, 54)( 39, 53)( 40, 52)( 41, 46)( 42, 50)( 43, 49)
( 44, 48)( 45, 47)( 86,342)( 87,341)( 88,345)( 89,344)( 90,343)( 91,422)
( 92,421)( 93,425)( 94,424)( 95,423)( 96,417)( 97,416)( 98,420)( 99,419)
(100,418)(101,412)(102,411)(103,415)(104,414)(105,413)(106,407)(107,406)
(108,410)(109,409)(110,408)(111,402)(112,401)(113,405)(114,404)(115,403)
(116,397)(117,396)(118,400)(119,399)(120,398)(121,392)(122,391)(123,395)
(124,394)(125,393)(126,387)(127,386)(128,390)(129,389)(130,388)(131,382)
(132,381)(133,385)(134,384)(135,383)(136,377)(137,376)(138,380)(139,379)
(140,378)(141,372)(142,371)(143,375)(144,374)(145,373)(146,367)(147,366)
(148,370)(149,369)(150,368)(151,362)(152,361)(153,365)(154,364)(155,363)
(156,357)(157,356)(158,360)(159,359)(160,358)(161,352)(162,351)(163,355)
(164,354)(165,353)(166,347)(167,346)(168,350)(169,349)(170,348)(171,257)
(172,256)(173,260)(174,259)(175,258)(176,337)(177,336)(178,340)(179,339)
(180,338)(181,332)(182,331)(183,335)(184,334)(185,333)(186,327)(187,326)
(188,330)(189,329)(190,328)(191,322)(192,321)(193,325)(194,324)(195,323)
(196,317)(197,316)(198,320)(199,319)(200,318)(201,312)(202,311)(203,315)
(204,314)(205,313)(206,307)(207,306)(208,310)(209,309)(210,308)(211,302)
(212,301)(213,305)(214,304)(215,303)(216,297)(217,296)(218,300)(219,299)
(220,298)(221,292)(222,291)(223,295)(224,294)(225,293)(226,287)(227,286)
(228,290)(229,289)(230,288)(231,282)(232,281)(233,285)(234,284)(235,283)
(236,277)(237,276)(238,280)(239,279)(240,278)(241,272)(242,271)(243,275)
(244,274)(245,273)(246,267)(247,266)(248,270)(249,269)(250,268)(251,262)
(252,261)(253,265)(254,264)(255,263)(427,430)(428,429)(431,506)(432,510)
(433,509)(434,508)(435,507)(436,501)(437,505)(438,504)(439,503)(440,502)
(441,496)(442,500)(443,499)(444,498)(445,497)(446,491)(447,495)(448,494)
(449,493)(450,492)(451,486)(452,490)(453,489)(454,488)(455,487)(456,481)
(457,485)(458,484)(459,483)(460,482)(461,476)(462,480)(463,479)(464,478)
(465,477)(466,471)(467,475)(468,474)(469,473)(470,472)(511,767)(512,766)
(513,770)(514,769)(515,768)(516,847)(517,846)(518,850)(519,849)(520,848)
(521,842)(522,841)(523,845)(524,844)(525,843)(526,837)(527,836)(528,840)
(529,839)(530,838)(531,832)(532,831)(533,835)(534,834)(535,833)(536,827)
(537,826)(538,830)(539,829)(540,828)(541,822)(542,821)(543,825)(544,824)
(545,823)(546,817)(547,816)(548,820)(549,819)(550,818)(551,812)(552,811)
(553,815)(554,814)(555,813)(556,807)(557,806)(558,810)(559,809)(560,808)
(561,802)(562,801)(563,805)(564,804)(565,803)(566,797)(567,796)(568,800)
(569,799)(570,798)(571,792)(572,791)(573,795)(574,794)(575,793)(576,787)
(577,786)(578,790)(579,789)(580,788)(581,782)(582,781)(583,785)(584,784)
(585,783)(586,777)(587,776)(588,780)(589,779)(590,778)(591,772)(592,771)
(593,775)(594,774)(595,773)(596,682)(597,681)(598,685)(599,684)(600,683)
(601,762)(602,761)(603,765)(604,764)(605,763)(606,757)(607,756)(608,760)
(609,759)(610,758)(611,752)(612,751)(613,755)(614,754)(615,753)(616,747)
(617,746)(618,750)(619,749)(620,748)(621,742)(622,741)(623,745)(624,744)
(625,743)(626,737)(627,736)(628,740)(629,739)(630,738)(631,732)(632,731)
(633,735)(634,734)(635,733)(636,727)(637,726)(638,730)(639,729)(640,728)
(641,722)(642,721)(643,725)(644,724)(645,723)(646,717)(647,716)(648,720)
(649,719)(650,718)(651,712)(652,711)(653,715)(654,714)(655,713)(656,707)
(657,706)(658,710)(659,709)(660,708)(661,702)(662,701)(663,705)(664,704)
(665,703)(666,697)(667,696)(668,700)(669,699)(670,698)(671,692)(672,691)
(673,695)(674,694)(675,693)(676,687)(677,686)(678,690)(679,689)(680,688);;
s1 := ( 1,516)( 2,520)( 3,519)( 4,518)( 5,517)( 6,511)( 7,515)( 8,514)
( 9,513)( 10,512)( 11,591)( 12,595)( 13,594)( 14,593)( 15,592)( 16,586)
( 17,590)( 18,589)( 19,588)( 20,587)( 21,581)( 22,585)( 23,584)( 24,583)
( 25,582)( 26,576)( 27,580)( 28,579)( 29,578)( 30,577)( 31,571)( 32,575)
( 33,574)( 34,573)( 35,572)( 36,566)( 37,570)( 38,569)( 39,568)( 40,567)
( 41,561)( 42,565)( 43,564)( 44,563)( 45,562)( 46,556)( 47,560)( 48,559)
( 49,558)( 50,557)( 51,551)( 52,555)( 53,554)( 54,553)( 55,552)( 56,546)
( 57,550)( 58,549)( 59,548)( 60,547)( 61,541)( 62,545)( 63,544)( 64,543)
( 65,542)( 66,536)( 67,540)( 68,539)( 69,538)( 70,537)( 71,531)( 72,535)
( 73,534)( 74,533)( 75,532)( 76,526)( 77,530)( 78,529)( 79,528)( 80,527)
( 81,521)( 82,525)( 83,524)( 84,523)( 85,522)( 86,431)( 87,435)( 88,434)
( 89,433)( 90,432)( 91,426)( 92,430)( 93,429)( 94,428)( 95,427)( 96,506)
( 97,510)( 98,509)( 99,508)(100,507)(101,501)(102,505)(103,504)(104,503)
(105,502)(106,496)(107,500)(108,499)(109,498)(110,497)(111,491)(112,495)
(113,494)(114,493)(115,492)(116,486)(117,490)(118,489)(119,488)(120,487)
(121,481)(122,485)(123,484)(124,483)(125,482)(126,476)(127,480)(128,479)
(129,478)(130,477)(131,471)(132,475)(133,474)(134,473)(135,472)(136,466)
(137,470)(138,469)(139,468)(140,467)(141,461)(142,465)(143,464)(144,463)
(145,462)(146,456)(147,460)(148,459)(149,458)(150,457)(151,451)(152,455)
(153,454)(154,453)(155,452)(156,446)(157,450)(158,449)(159,448)(160,447)
(161,441)(162,445)(163,444)(164,443)(165,442)(166,436)(167,440)(168,439)
(169,438)(170,437)(171,772)(172,771)(173,775)(174,774)(175,773)(176,767)
(177,766)(178,770)(179,769)(180,768)(181,847)(182,846)(183,850)(184,849)
(185,848)(186,842)(187,841)(188,845)(189,844)(190,843)(191,837)(192,836)
(193,840)(194,839)(195,838)(196,832)(197,831)(198,835)(199,834)(200,833)
(201,827)(202,826)(203,830)(204,829)(205,828)(206,822)(207,821)(208,825)
(209,824)(210,823)(211,817)(212,816)(213,820)(214,819)(215,818)(216,812)
(217,811)(218,815)(219,814)(220,813)(221,807)(222,806)(223,810)(224,809)
(225,808)(226,802)(227,801)(228,805)(229,804)(230,803)(231,797)(232,796)
(233,800)(234,799)(235,798)(236,792)(237,791)(238,795)(239,794)(240,793)
(241,787)(242,786)(243,790)(244,789)(245,788)(246,782)(247,781)(248,785)
(249,784)(250,783)(251,777)(252,776)(253,780)(254,779)(255,778)(256,687)
(257,686)(258,690)(259,689)(260,688)(261,682)(262,681)(263,685)(264,684)
(265,683)(266,762)(267,761)(268,765)(269,764)(270,763)(271,757)(272,756)
(273,760)(274,759)(275,758)(276,752)(277,751)(278,755)(279,754)(280,753)
(281,747)(282,746)(283,750)(284,749)(285,748)(286,742)(287,741)(288,745)
(289,744)(290,743)(291,737)(292,736)(293,740)(294,739)(295,738)(296,732)
(297,731)(298,735)(299,734)(300,733)(301,727)(302,726)(303,730)(304,729)
(305,728)(306,722)(307,721)(308,725)(309,724)(310,723)(311,717)(312,716)
(313,720)(314,719)(315,718)(316,712)(317,711)(318,715)(319,714)(320,713)
(321,707)(322,706)(323,710)(324,709)(325,708)(326,702)(327,701)(328,705)
(329,704)(330,703)(331,697)(332,696)(333,700)(334,699)(335,698)(336,692)
(337,691)(338,695)(339,694)(340,693)(341,602)(342,601)(343,605)(344,604)
(345,603)(346,597)(347,596)(348,600)(349,599)(350,598)(351,677)(352,676)
(353,680)(354,679)(355,678)(356,672)(357,671)(358,675)(359,674)(360,673)
(361,667)(362,666)(363,670)(364,669)(365,668)(366,662)(367,661)(368,665)
(369,664)(370,663)(371,657)(372,656)(373,660)(374,659)(375,658)(376,652)
(377,651)(378,655)(379,654)(380,653)(381,647)(382,646)(383,650)(384,649)
(385,648)(386,642)(387,641)(388,645)(389,644)(390,643)(391,637)(392,636)
(393,640)(394,639)(395,638)(396,632)(397,631)(398,635)(399,634)(400,633)
(401,627)(402,626)(403,630)(404,629)(405,628)(406,622)(407,621)(408,625)
(409,624)(410,623)(411,617)(412,616)(413,620)(414,619)(415,618)(416,612)
(417,611)(418,615)(419,614)(420,613)(421,607)(422,606)(423,610)(424,609)
(425,608);;
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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(850)!( 2, 5)( 3, 4)( 6, 81)( 7, 85)( 8, 84)( 9, 83)( 10, 82)
( 11, 76)( 12, 80)( 13, 79)( 14, 78)( 15, 77)( 16, 71)( 17, 75)( 18, 74)
( 19, 73)( 20, 72)( 21, 66)( 22, 70)( 23, 69)( 24, 68)( 25, 67)( 26, 61)
( 27, 65)( 28, 64)( 29, 63)( 30, 62)( 31, 56)( 32, 60)( 33, 59)( 34, 58)
( 35, 57)( 36, 51)( 37, 55)( 38, 54)( 39, 53)( 40, 52)( 41, 46)( 42, 50)
( 43, 49)( 44, 48)( 45, 47)( 86,342)( 87,341)( 88,345)( 89,344)( 90,343)
( 91,422)( 92,421)( 93,425)( 94,424)( 95,423)( 96,417)( 97,416)( 98,420)
( 99,419)(100,418)(101,412)(102,411)(103,415)(104,414)(105,413)(106,407)
(107,406)(108,410)(109,409)(110,408)(111,402)(112,401)(113,405)(114,404)
(115,403)(116,397)(117,396)(118,400)(119,399)(120,398)(121,392)(122,391)
(123,395)(124,394)(125,393)(126,387)(127,386)(128,390)(129,389)(130,388)
(131,382)(132,381)(133,385)(134,384)(135,383)(136,377)(137,376)(138,380)
(139,379)(140,378)(141,372)(142,371)(143,375)(144,374)(145,373)(146,367)
(147,366)(148,370)(149,369)(150,368)(151,362)(152,361)(153,365)(154,364)
(155,363)(156,357)(157,356)(158,360)(159,359)(160,358)(161,352)(162,351)
(163,355)(164,354)(165,353)(166,347)(167,346)(168,350)(169,349)(170,348)
(171,257)(172,256)(173,260)(174,259)(175,258)(176,337)(177,336)(178,340)
(179,339)(180,338)(181,332)(182,331)(183,335)(184,334)(185,333)(186,327)
(187,326)(188,330)(189,329)(190,328)(191,322)(192,321)(193,325)(194,324)
(195,323)(196,317)(197,316)(198,320)(199,319)(200,318)(201,312)(202,311)
(203,315)(204,314)(205,313)(206,307)(207,306)(208,310)(209,309)(210,308)
(211,302)(212,301)(213,305)(214,304)(215,303)(216,297)(217,296)(218,300)
(219,299)(220,298)(221,292)(222,291)(223,295)(224,294)(225,293)(226,287)
(227,286)(228,290)(229,289)(230,288)(231,282)(232,281)(233,285)(234,284)
(235,283)(236,277)(237,276)(238,280)(239,279)(240,278)(241,272)(242,271)
(243,275)(244,274)(245,273)(246,267)(247,266)(248,270)(249,269)(250,268)
(251,262)(252,261)(253,265)(254,264)(255,263)(427,430)(428,429)(431,506)
(432,510)(433,509)(434,508)(435,507)(436,501)(437,505)(438,504)(439,503)
(440,502)(441,496)(442,500)(443,499)(444,498)(445,497)(446,491)(447,495)
(448,494)(449,493)(450,492)(451,486)(452,490)(453,489)(454,488)(455,487)
(456,481)(457,485)(458,484)(459,483)(460,482)(461,476)(462,480)(463,479)
(464,478)(465,477)(466,471)(467,475)(468,474)(469,473)(470,472)(511,767)
(512,766)(513,770)(514,769)(515,768)(516,847)(517,846)(518,850)(519,849)
(520,848)(521,842)(522,841)(523,845)(524,844)(525,843)(526,837)(527,836)
(528,840)(529,839)(530,838)(531,832)(532,831)(533,835)(534,834)(535,833)
(536,827)(537,826)(538,830)(539,829)(540,828)(541,822)(542,821)(543,825)
(544,824)(545,823)(546,817)(547,816)(548,820)(549,819)(550,818)(551,812)
(552,811)(553,815)(554,814)(555,813)(556,807)(557,806)(558,810)(559,809)
(560,808)(561,802)(562,801)(563,805)(564,804)(565,803)(566,797)(567,796)
(568,800)(569,799)(570,798)(571,792)(572,791)(573,795)(574,794)(575,793)
(576,787)(577,786)(578,790)(579,789)(580,788)(581,782)(582,781)(583,785)
(584,784)(585,783)(586,777)(587,776)(588,780)(589,779)(590,778)(591,772)
(592,771)(593,775)(594,774)(595,773)(596,682)(597,681)(598,685)(599,684)
(600,683)(601,762)(602,761)(603,765)(604,764)(605,763)(606,757)(607,756)
(608,760)(609,759)(610,758)(611,752)(612,751)(613,755)(614,754)(615,753)
(616,747)(617,746)(618,750)(619,749)(620,748)(621,742)(622,741)(623,745)
(624,744)(625,743)(626,737)(627,736)(628,740)(629,739)(630,738)(631,732)
(632,731)(633,735)(634,734)(635,733)(636,727)(637,726)(638,730)(639,729)
(640,728)(641,722)(642,721)(643,725)(644,724)(645,723)(646,717)(647,716)
(648,720)(649,719)(650,718)(651,712)(652,711)(653,715)(654,714)(655,713)
(656,707)(657,706)(658,710)(659,709)(660,708)(661,702)(662,701)(663,705)
(664,704)(665,703)(666,697)(667,696)(668,700)(669,699)(670,698)(671,692)
(672,691)(673,695)(674,694)(675,693)(676,687)(677,686)(678,690)(679,689)
(680,688);
s1 := Sym(850)!( 1,516)( 2,520)( 3,519)( 4,518)( 5,517)( 6,511)( 7,515)
( 8,514)( 9,513)( 10,512)( 11,591)( 12,595)( 13,594)( 14,593)( 15,592)
( 16,586)( 17,590)( 18,589)( 19,588)( 20,587)( 21,581)( 22,585)( 23,584)
( 24,583)( 25,582)( 26,576)( 27,580)( 28,579)( 29,578)( 30,577)( 31,571)
( 32,575)( 33,574)( 34,573)( 35,572)( 36,566)( 37,570)( 38,569)( 39,568)
( 40,567)( 41,561)( 42,565)( 43,564)( 44,563)( 45,562)( 46,556)( 47,560)
( 48,559)( 49,558)( 50,557)( 51,551)( 52,555)( 53,554)( 54,553)( 55,552)
( 56,546)( 57,550)( 58,549)( 59,548)( 60,547)( 61,541)( 62,545)( 63,544)
( 64,543)( 65,542)( 66,536)( 67,540)( 68,539)( 69,538)( 70,537)( 71,531)
( 72,535)( 73,534)( 74,533)( 75,532)( 76,526)( 77,530)( 78,529)( 79,528)
( 80,527)( 81,521)( 82,525)( 83,524)( 84,523)( 85,522)( 86,431)( 87,435)
( 88,434)( 89,433)( 90,432)( 91,426)( 92,430)( 93,429)( 94,428)( 95,427)
( 96,506)( 97,510)( 98,509)( 99,508)(100,507)(101,501)(102,505)(103,504)
(104,503)(105,502)(106,496)(107,500)(108,499)(109,498)(110,497)(111,491)
(112,495)(113,494)(114,493)(115,492)(116,486)(117,490)(118,489)(119,488)
(120,487)(121,481)(122,485)(123,484)(124,483)(125,482)(126,476)(127,480)
(128,479)(129,478)(130,477)(131,471)(132,475)(133,474)(134,473)(135,472)
(136,466)(137,470)(138,469)(139,468)(140,467)(141,461)(142,465)(143,464)
(144,463)(145,462)(146,456)(147,460)(148,459)(149,458)(150,457)(151,451)
(152,455)(153,454)(154,453)(155,452)(156,446)(157,450)(158,449)(159,448)
(160,447)(161,441)(162,445)(163,444)(164,443)(165,442)(166,436)(167,440)
(168,439)(169,438)(170,437)(171,772)(172,771)(173,775)(174,774)(175,773)
(176,767)(177,766)(178,770)(179,769)(180,768)(181,847)(182,846)(183,850)
(184,849)(185,848)(186,842)(187,841)(188,845)(189,844)(190,843)(191,837)
(192,836)(193,840)(194,839)(195,838)(196,832)(197,831)(198,835)(199,834)
(200,833)(201,827)(202,826)(203,830)(204,829)(205,828)(206,822)(207,821)
(208,825)(209,824)(210,823)(211,817)(212,816)(213,820)(214,819)(215,818)
(216,812)(217,811)(218,815)(219,814)(220,813)(221,807)(222,806)(223,810)
(224,809)(225,808)(226,802)(227,801)(228,805)(229,804)(230,803)(231,797)
(232,796)(233,800)(234,799)(235,798)(236,792)(237,791)(238,795)(239,794)
(240,793)(241,787)(242,786)(243,790)(244,789)(245,788)(246,782)(247,781)
(248,785)(249,784)(250,783)(251,777)(252,776)(253,780)(254,779)(255,778)
(256,687)(257,686)(258,690)(259,689)(260,688)(261,682)(262,681)(263,685)
(264,684)(265,683)(266,762)(267,761)(268,765)(269,764)(270,763)(271,757)
(272,756)(273,760)(274,759)(275,758)(276,752)(277,751)(278,755)(279,754)
(280,753)(281,747)(282,746)(283,750)(284,749)(285,748)(286,742)(287,741)
(288,745)(289,744)(290,743)(291,737)(292,736)(293,740)(294,739)(295,738)
(296,732)(297,731)(298,735)(299,734)(300,733)(301,727)(302,726)(303,730)
(304,729)(305,728)(306,722)(307,721)(308,725)(309,724)(310,723)(311,717)
(312,716)(313,720)(314,719)(315,718)(316,712)(317,711)(318,715)(319,714)
(320,713)(321,707)(322,706)(323,710)(324,709)(325,708)(326,702)(327,701)
(328,705)(329,704)(330,703)(331,697)(332,696)(333,700)(334,699)(335,698)
(336,692)(337,691)(338,695)(339,694)(340,693)(341,602)(342,601)(343,605)
(344,604)(345,603)(346,597)(347,596)(348,600)(349,599)(350,598)(351,677)
(352,676)(353,680)(354,679)(355,678)(356,672)(357,671)(358,675)(359,674)
(360,673)(361,667)(362,666)(363,670)(364,669)(365,668)(366,662)(367,661)
(368,665)(369,664)(370,663)(371,657)(372,656)(373,660)(374,659)(375,658)
(376,652)(377,651)(378,655)(379,654)(380,653)(381,647)(382,646)(383,650)
(384,649)(385,648)(386,642)(387,641)(388,645)(389,644)(390,643)(391,637)
(392,636)(393,640)(394,639)(395,638)(396,632)(397,631)(398,635)(399,634)
(400,633)(401,627)(402,626)(403,630)(404,629)(405,628)(406,622)(407,621)
(408,625)(409,624)(410,623)(411,617)(412,616)(413,620)(414,619)(415,618)
(416,612)(417,611)(418,615)(419,614)(420,613)(421,607)(422,606)(423,610)
(424,609)(425,608);
poly := sub<Sym(850)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope