Polytope of Type {852}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {852}*1704
Also Known As : 852-gon, {852}. if this polytope has another name.
Group : SmallGroup(1704,25)
Rank : 2
Schlafli Type : {852}
Number of vertices, edges, etc : 852, 852
Order of s0s1 : 852
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 : {426}*852
3-fold quotients : {284}*568
4-fold quotients : {213}*426
6-fold quotients : {142}*284
12-fold quotients : {71}*142
71-fold quotients : {12}*24
142-fold quotients : {6}*12
213-fold quotients : {4}*8
284-fold quotients : {3}*6
426-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 71)( 3, 70)( 4, 69)( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 64)
( 10, 63)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 58)( 16, 57)( 17, 56)
( 18, 55)( 19, 54)( 20, 53)( 21, 52)( 22, 51)( 23, 50)( 24, 49)( 25, 48)
( 26, 47)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 42)( 32, 41)( 33, 40)
( 34, 39)( 35, 38)( 36, 37)( 72,143)( 73,213)( 74,212)( 75,211)( 76,210)
( 77,209)( 78,208)( 79,207)( 80,206)( 81,205)( 82,204)( 83,203)( 84,202)
( 85,201)( 86,200)( 87,199)( 88,198)( 89,197)( 90,196)( 91,195)( 92,194)
( 93,193)( 94,192)( 95,191)( 96,190)( 97,189)( 98,188)( 99,187)(100,186)
(101,185)(102,184)(103,183)(104,182)(105,181)(106,180)(107,179)(108,178)
(109,177)(110,176)(111,175)(112,174)(113,173)(114,172)(115,171)(116,170)
(117,169)(118,168)(119,167)(120,166)(121,165)(122,164)(123,163)(124,162)
(125,161)(126,160)(127,159)(128,158)(129,157)(130,156)(131,155)(132,154)
(133,153)(134,152)(135,151)(136,150)(137,149)(138,148)(139,147)(140,146)
(141,145)(142,144)(215,284)(216,283)(217,282)(218,281)(219,280)(220,279)
(221,278)(222,277)(223,276)(224,275)(225,274)(226,273)(227,272)(228,271)
(229,270)(230,269)(231,268)(232,267)(233,266)(234,265)(235,264)(236,263)
(237,262)(238,261)(239,260)(240,259)(241,258)(242,257)(243,256)(244,255)
(245,254)(246,253)(247,252)(248,251)(249,250)(285,356)(286,426)(287,425)
(288,424)(289,423)(290,422)(291,421)(292,420)(293,419)(294,418)(295,417)
(296,416)(297,415)(298,414)(299,413)(300,412)(301,411)(302,410)(303,409)
(304,408)(305,407)(306,406)(307,405)(308,404)(309,403)(310,402)(311,401)
(312,400)(313,399)(314,398)(315,397)(316,396)(317,395)(318,394)(319,393)
(320,392)(321,391)(322,390)(323,389)(324,388)(325,387)(326,386)(327,385)
(328,384)(329,383)(330,382)(331,381)(332,380)(333,379)(334,378)(335,377)
(336,376)(337,375)(338,374)(339,373)(340,372)(341,371)(342,370)(343,369)
(344,368)(345,367)(346,366)(347,365)(348,364)(349,363)(350,362)(351,361)
(352,360)(353,359)(354,358)(355,357)(427,640)(428,710)(429,709)(430,708)
(431,707)(432,706)(433,705)(434,704)(435,703)(436,702)(437,701)(438,700)
(439,699)(440,698)(441,697)(442,696)(443,695)(444,694)(445,693)(446,692)
(447,691)(448,690)(449,689)(450,688)(451,687)(452,686)(453,685)(454,684)
(455,683)(456,682)(457,681)(458,680)(459,679)(460,678)(461,677)(462,676)
(463,675)(464,674)(465,673)(466,672)(467,671)(468,670)(469,669)(470,668)
(471,667)(472,666)(473,665)(474,664)(475,663)(476,662)(477,661)(478,660)
(479,659)(480,658)(481,657)(482,656)(483,655)(484,654)(485,653)(486,652)
(487,651)(488,650)(489,649)(490,648)(491,647)(492,646)(493,645)(494,644)
(495,643)(496,642)(497,641)(498,782)(499,852)(500,851)(501,850)(502,849)
(503,848)(504,847)(505,846)(506,845)(507,844)(508,843)(509,842)(510,841)
(511,840)(512,839)(513,838)(514,837)(515,836)(516,835)(517,834)(518,833)
(519,832)(520,831)(521,830)(522,829)(523,828)(524,827)(525,826)(526,825)
(527,824)(528,823)(529,822)(530,821)(531,820)(532,819)(533,818)(534,817)
(535,816)(536,815)(537,814)(538,813)(539,812)(540,811)(541,810)(542,809)
(543,808)(544,807)(545,806)(546,805)(547,804)(548,803)(549,802)(550,801)
(551,800)(552,799)(553,798)(554,797)(555,796)(556,795)(557,794)(558,793)
(559,792)(560,791)(561,790)(562,789)(563,788)(564,787)(565,786)(566,785)
(567,784)(568,783)(569,711)(570,781)(571,780)(572,779)(573,778)(574,777)
(575,776)(576,775)(577,774)(578,773)(579,772)(580,771)(581,770)(582,769)
(583,768)(584,767)(585,766)(586,765)(587,764)(588,763)(589,762)(590,761)
(591,760)(592,759)(593,758)(594,757)(595,756)(596,755)(597,754)(598,753)
(599,752)(600,751)(601,750)(602,749)(603,748)(604,747)(605,746)(606,745)
(607,744)(608,743)(609,742)(610,741)(611,740)(612,739)(613,738)(614,737)
(615,736)(616,735)(617,734)(618,733)(619,732)(620,731)(621,730)(622,729)
(623,728)(624,727)(625,726)(626,725)(627,724)(628,723)(629,722)(630,721)
(631,720)(632,719)(633,718)(634,717)(635,716)(636,715)(637,714)(638,713)
(639,712);;
s1 := ( 1,499)( 2,498)( 3,568)( 4,567)( 5,566)( 6,565)( 7,564)( 8,563)
( 9,562)( 10,561)( 11,560)( 12,559)( 13,558)( 14,557)( 15,556)( 16,555)
( 17,554)( 18,553)( 19,552)( 20,551)( 21,550)( 22,549)( 23,548)( 24,547)
( 25,546)( 26,545)( 27,544)( 28,543)( 29,542)( 30,541)( 31,540)( 32,539)
( 33,538)( 34,537)( 35,536)( 36,535)( 37,534)( 38,533)( 39,532)( 40,531)
( 41,530)( 42,529)( 43,528)( 44,527)( 45,526)( 46,525)( 47,524)( 48,523)
( 49,522)( 50,521)( 51,520)( 52,519)( 53,518)( 54,517)( 55,516)( 56,515)
( 57,514)( 58,513)( 59,512)( 60,511)( 61,510)( 62,509)( 63,508)( 64,507)
( 65,506)( 66,505)( 67,504)( 68,503)( 69,502)( 70,501)( 71,500)( 72,428)
( 73,427)( 74,497)( 75,496)( 76,495)( 77,494)( 78,493)( 79,492)( 80,491)
( 81,490)( 82,489)( 83,488)( 84,487)( 85,486)( 86,485)( 87,484)( 88,483)
( 89,482)( 90,481)( 91,480)( 92,479)( 93,478)( 94,477)( 95,476)( 96,475)
( 97,474)( 98,473)( 99,472)(100,471)(101,470)(102,469)(103,468)(104,467)
(105,466)(106,465)(107,464)(108,463)(109,462)(110,461)(111,460)(112,459)
(113,458)(114,457)(115,456)(116,455)(117,454)(118,453)(119,452)(120,451)
(121,450)(122,449)(123,448)(124,447)(125,446)(126,445)(127,444)(128,443)
(129,442)(130,441)(131,440)(132,439)(133,438)(134,437)(135,436)(136,435)
(137,434)(138,433)(139,432)(140,431)(141,430)(142,429)(143,570)(144,569)
(145,639)(146,638)(147,637)(148,636)(149,635)(150,634)(151,633)(152,632)
(153,631)(154,630)(155,629)(156,628)(157,627)(158,626)(159,625)(160,624)
(161,623)(162,622)(163,621)(164,620)(165,619)(166,618)(167,617)(168,616)
(169,615)(170,614)(171,613)(172,612)(173,611)(174,610)(175,609)(176,608)
(177,607)(178,606)(179,605)(180,604)(181,603)(182,602)(183,601)(184,600)
(185,599)(186,598)(187,597)(188,596)(189,595)(190,594)(191,593)(192,592)
(193,591)(194,590)(195,589)(196,588)(197,587)(198,586)(199,585)(200,584)
(201,583)(202,582)(203,581)(204,580)(205,579)(206,578)(207,577)(208,576)
(209,575)(210,574)(211,573)(212,572)(213,571)(214,712)(215,711)(216,781)
(217,780)(218,779)(219,778)(220,777)(221,776)(222,775)(223,774)(224,773)
(225,772)(226,771)(227,770)(228,769)(229,768)(230,767)(231,766)(232,765)
(233,764)(234,763)(235,762)(236,761)(237,760)(238,759)(239,758)(240,757)
(241,756)(242,755)(243,754)(244,753)(245,752)(246,751)(247,750)(248,749)
(249,748)(250,747)(251,746)(252,745)(253,744)(254,743)(255,742)(256,741)
(257,740)(258,739)(259,738)(260,737)(261,736)(262,735)(263,734)(264,733)
(265,732)(266,731)(267,730)(268,729)(269,728)(270,727)(271,726)(272,725)
(273,724)(274,723)(275,722)(276,721)(277,720)(278,719)(279,718)(280,717)
(281,716)(282,715)(283,714)(284,713)(285,641)(286,640)(287,710)(288,709)
(289,708)(290,707)(291,706)(292,705)(293,704)(294,703)(295,702)(296,701)
(297,700)(298,699)(299,698)(300,697)(301,696)(302,695)(303,694)(304,693)
(305,692)(306,691)(307,690)(308,689)(309,688)(310,687)(311,686)(312,685)
(313,684)(314,683)(315,682)(316,681)(317,680)(318,679)(319,678)(320,677)
(321,676)(322,675)(323,674)(324,673)(325,672)(326,671)(327,670)(328,669)
(329,668)(330,667)(331,666)(332,665)(333,664)(334,663)(335,662)(336,661)
(337,660)(338,659)(339,658)(340,657)(341,656)(342,655)(343,654)(344,653)
(345,652)(346,651)(347,650)(348,649)(349,648)(350,647)(351,646)(352,645)
(353,644)(354,643)(355,642)(356,783)(357,782)(358,852)(359,851)(360,850)
(361,849)(362,848)(363,847)(364,846)(365,845)(366,844)(367,843)(368,842)
(369,841)(370,840)(371,839)(372,838)(373,837)(374,836)(375,835)(376,834)
(377,833)(378,832)(379,831)(380,830)(381,829)(382,828)(383,827)(384,826)
(385,825)(386,824)(387,823)(388,822)(389,821)(390,820)(391,819)(392,818)
(393,817)(394,816)(395,815)(396,814)(397,813)(398,812)(399,811)(400,810)
(401,809)(402,808)(403,807)(404,806)(405,805)(406,804)(407,803)(408,802)
(409,801)(410,800)(411,799)(412,798)(413,797)(414,796)(415,795)(416,794)
(417,793)(418,792)(419,791)(420,790)(421,789)(422,788)(423,787)(424,786)
(425,785)(426,784);;
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*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(852)!( 2, 71)( 3, 70)( 4, 69)( 5, 68)( 6, 67)( 7, 66)( 8, 65)
( 9, 64)( 10, 63)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 58)( 16, 57)
( 17, 56)( 18, 55)( 19, 54)( 20, 53)( 21, 52)( 22, 51)( 23, 50)( 24, 49)
( 25, 48)( 26, 47)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 42)( 32, 41)
( 33, 40)( 34, 39)( 35, 38)( 36, 37)( 72,143)( 73,213)( 74,212)( 75,211)
( 76,210)( 77,209)( 78,208)( 79,207)( 80,206)( 81,205)( 82,204)( 83,203)
( 84,202)( 85,201)( 86,200)( 87,199)( 88,198)( 89,197)( 90,196)( 91,195)
( 92,194)( 93,193)( 94,192)( 95,191)( 96,190)( 97,189)( 98,188)( 99,187)
(100,186)(101,185)(102,184)(103,183)(104,182)(105,181)(106,180)(107,179)
(108,178)(109,177)(110,176)(111,175)(112,174)(113,173)(114,172)(115,171)
(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,164)(123,163)
(124,162)(125,161)(126,160)(127,159)(128,158)(129,157)(130,156)(131,155)
(132,154)(133,153)(134,152)(135,151)(136,150)(137,149)(138,148)(139,147)
(140,146)(141,145)(142,144)(215,284)(216,283)(217,282)(218,281)(219,280)
(220,279)(221,278)(222,277)(223,276)(224,275)(225,274)(226,273)(227,272)
(228,271)(229,270)(230,269)(231,268)(232,267)(233,266)(234,265)(235,264)
(236,263)(237,262)(238,261)(239,260)(240,259)(241,258)(242,257)(243,256)
(244,255)(245,254)(246,253)(247,252)(248,251)(249,250)(285,356)(286,426)
(287,425)(288,424)(289,423)(290,422)(291,421)(292,420)(293,419)(294,418)
(295,417)(296,416)(297,415)(298,414)(299,413)(300,412)(301,411)(302,410)
(303,409)(304,408)(305,407)(306,406)(307,405)(308,404)(309,403)(310,402)
(311,401)(312,400)(313,399)(314,398)(315,397)(316,396)(317,395)(318,394)
(319,393)(320,392)(321,391)(322,390)(323,389)(324,388)(325,387)(326,386)
(327,385)(328,384)(329,383)(330,382)(331,381)(332,380)(333,379)(334,378)
(335,377)(336,376)(337,375)(338,374)(339,373)(340,372)(341,371)(342,370)
(343,369)(344,368)(345,367)(346,366)(347,365)(348,364)(349,363)(350,362)
(351,361)(352,360)(353,359)(354,358)(355,357)(427,640)(428,710)(429,709)
(430,708)(431,707)(432,706)(433,705)(434,704)(435,703)(436,702)(437,701)
(438,700)(439,699)(440,698)(441,697)(442,696)(443,695)(444,694)(445,693)
(446,692)(447,691)(448,690)(449,689)(450,688)(451,687)(452,686)(453,685)
(454,684)(455,683)(456,682)(457,681)(458,680)(459,679)(460,678)(461,677)
(462,676)(463,675)(464,674)(465,673)(466,672)(467,671)(468,670)(469,669)
(470,668)(471,667)(472,666)(473,665)(474,664)(475,663)(476,662)(477,661)
(478,660)(479,659)(480,658)(481,657)(482,656)(483,655)(484,654)(485,653)
(486,652)(487,651)(488,650)(489,649)(490,648)(491,647)(492,646)(493,645)
(494,644)(495,643)(496,642)(497,641)(498,782)(499,852)(500,851)(501,850)
(502,849)(503,848)(504,847)(505,846)(506,845)(507,844)(508,843)(509,842)
(510,841)(511,840)(512,839)(513,838)(514,837)(515,836)(516,835)(517,834)
(518,833)(519,832)(520,831)(521,830)(522,829)(523,828)(524,827)(525,826)
(526,825)(527,824)(528,823)(529,822)(530,821)(531,820)(532,819)(533,818)
(534,817)(535,816)(536,815)(537,814)(538,813)(539,812)(540,811)(541,810)
(542,809)(543,808)(544,807)(545,806)(546,805)(547,804)(548,803)(549,802)
(550,801)(551,800)(552,799)(553,798)(554,797)(555,796)(556,795)(557,794)
(558,793)(559,792)(560,791)(561,790)(562,789)(563,788)(564,787)(565,786)
(566,785)(567,784)(568,783)(569,711)(570,781)(571,780)(572,779)(573,778)
(574,777)(575,776)(576,775)(577,774)(578,773)(579,772)(580,771)(581,770)
(582,769)(583,768)(584,767)(585,766)(586,765)(587,764)(588,763)(589,762)
(590,761)(591,760)(592,759)(593,758)(594,757)(595,756)(596,755)(597,754)
(598,753)(599,752)(600,751)(601,750)(602,749)(603,748)(604,747)(605,746)
(606,745)(607,744)(608,743)(609,742)(610,741)(611,740)(612,739)(613,738)
(614,737)(615,736)(616,735)(617,734)(618,733)(619,732)(620,731)(621,730)
(622,729)(623,728)(624,727)(625,726)(626,725)(627,724)(628,723)(629,722)
(630,721)(631,720)(632,719)(633,718)(634,717)(635,716)(636,715)(637,714)
(638,713)(639,712);
s1 := Sym(852)!( 1,499)( 2,498)( 3,568)( 4,567)( 5,566)( 6,565)( 7,564)
( 8,563)( 9,562)( 10,561)( 11,560)( 12,559)( 13,558)( 14,557)( 15,556)
( 16,555)( 17,554)( 18,553)( 19,552)( 20,551)( 21,550)( 22,549)( 23,548)
( 24,547)( 25,546)( 26,545)( 27,544)( 28,543)( 29,542)( 30,541)( 31,540)
( 32,539)( 33,538)( 34,537)( 35,536)( 36,535)( 37,534)( 38,533)( 39,532)
( 40,531)( 41,530)( 42,529)( 43,528)( 44,527)( 45,526)( 46,525)( 47,524)
( 48,523)( 49,522)( 50,521)( 51,520)( 52,519)( 53,518)( 54,517)( 55,516)
( 56,515)( 57,514)( 58,513)( 59,512)( 60,511)( 61,510)( 62,509)( 63,508)
( 64,507)( 65,506)( 66,505)( 67,504)( 68,503)( 69,502)( 70,501)( 71,500)
( 72,428)( 73,427)( 74,497)( 75,496)( 76,495)( 77,494)( 78,493)( 79,492)
( 80,491)( 81,490)( 82,489)( 83,488)( 84,487)( 85,486)( 86,485)( 87,484)
( 88,483)( 89,482)( 90,481)( 91,480)( 92,479)( 93,478)( 94,477)( 95,476)
( 96,475)( 97,474)( 98,473)( 99,472)(100,471)(101,470)(102,469)(103,468)
(104,467)(105,466)(106,465)(107,464)(108,463)(109,462)(110,461)(111,460)
(112,459)(113,458)(114,457)(115,456)(116,455)(117,454)(118,453)(119,452)
(120,451)(121,450)(122,449)(123,448)(124,447)(125,446)(126,445)(127,444)
(128,443)(129,442)(130,441)(131,440)(132,439)(133,438)(134,437)(135,436)
(136,435)(137,434)(138,433)(139,432)(140,431)(141,430)(142,429)(143,570)
(144,569)(145,639)(146,638)(147,637)(148,636)(149,635)(150,634)(151,633)
(152,632)(153,631)(154,630)(155,629)(156,628)(157,627)(158,626)(159,625)
(160,624)(161,623)(162,622)(163,621)(164,620)(165,619)(166,618)(167,617)
(168,616)(169,615)(170,614)(171,613)(172,612)(173,611)(174,610)(175,609)
(176,608)(177,607)(178,606)(179,605)(180,604)(181,603)(182,602)(183,601)
(184,600)(185,599)(186,598)(187,597)(188,596)(189,595)(190,594)(191,593)
(192,592)(193,591)(194,590)(195,589)(196,588)(197,587)(198,586)(199,585)
(200,584)(201,583)(202,582)(203,581)(204,580)(205,579)(206,578)(207,577)
(208,576)(209,575)(210,574)(211,573)(212,572)(213,571)(214,712)(215,711)
(216,781)(217,780)(218,779)(219,778)(220,777)(221,776)(222,775)(223,774)
(224,773)(225,772)(226,771)(227,770)(228,769)(229,768)(230,767)(231,766)
(232,765)(233,764)(234,763)(235,762)(236,761)(237,760)(238,759)(239,758)
(240,757)(241,756)(242,755)(243,754)(244,753)(245,752)(246,751)(247,750)
(248,749)(249,748)(250,747)(251,746)(252,745)(253,744)(254,743)(255,742)
(256,741)(257,740)(258,739)(259,738)(260,737)(261,736)(262,735)(263,734)
(264,733)(265,732)(266,731)(267,730)(268,729)(269,728)(270,727)(271,726)
(272,725)(273,724)(274,723)(275,722)(276,721)(277,720)(278,719)(279,718)
(280,717)(281,716)(282,715)(283,714)(284,713)(285,641)(286,640)(287,710)
(288,709)(289,708)(290,707)(291,706)(292,705)(293,704)(294,703)(295,702)
(296,701)(297,700)(298,699)(299,698)(300,697)(301,696)(302,695)(303,694)
(304,693)(305,692)(306,691)(307,690)(308,689)(309,688)(310,687)(311,686)
(312,685)(313,684)(314,683)(315,682)(316,681)(317,680)(318,679)(319,678)
(320,677)(321,676)(322,675)(323,674)(324,673)(325,672)(326,671)(327,670)
(328,669)(329,668)(330,667)(331,666)(332,665)(333,664)(334,663)(335,662)
(336,661)(337,660)(338,659)(339,658)(340,657)(341,656)(342,655)(343,654)
(344,653)(345,652)(346,651)(347,650)(348,649)(349,648)(350,647)(351,646)
(352,645)(353,644)(354,643)(355,642)(356,783)(357,782)(358,852)(359,851)
(360,850)(361,849)(362,848)(363,847)(364,846)(365,845)(366,844)(367,843)
(368,842)(369,841)(370,840)(371,839)(372,838)(373,837)(374,836)(375,835)
(376,834)(377,833)(378,832)(379,831)(380,830)(381,829)(382,828)(383,827)
(384,826)(385,825)(386,824)(387,823)(388,822)(389,821)(390,820)(391,819)
(392,818)(393,817)(394,816)(395,815)(396,814)(397,813)(398,812)(399,811)
(400,810)(401,809)(402,808)(403,807)(404,806)(405,805)(406,804)(407,803)
(408,802)(409,801)(410,800)(411,799)(412,798)(413,797)(414,796)(415,795)
(416,794)(417,793)(418,792)(419,791)(420,790)(421,789)(422,788)(423,787)
(424,786)(425,785)(426,784);
poly := sub<Sym(852)|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*s0*s1*s0*s1 >;
References : None.
to this polytope