Polytope of Type {872}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {872}*1744
Also Known As : 872-gon, {872}. if this polytope has another name.
Group : SmallGroup(1744,26)
Rank : 2
Schlafli Type : {872}
Number of vertices, edges, etc : 872, 872
Order of s0s1 : 872
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 : {436}*872
4-fold quotients : {218}*436
8-fold quotients : {109}*218
109-fold quotients : {8}*16
218-fold quotients : {4}*8
436-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 2,109)( 3,108)( 4,107)( 5,106)( 6,105)( 7,104)( 8,103)( 9,102)( 10,101)( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16, 95)( 17, 94)( 18, 93)( 19, 92)( 20, 91)( 21, 90)( 22, 89)( 23, 88)( 24, 87)( 25, 86)( 26, 85)( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 31, 80)( 32, 79)( 33, 78)( 34, 77)( 35, 76)( 36, 75)( 37, 74)( 38, 73)( 39, 72)( 40, 71)( 41, 70)( 42, 69)( 43, 68)( 44, 67)( 45, 66)( 46, 65)( 47, 64)( 48, 63)( 49, 62)( 50, 61)( 51, 60)( 52, 59)( 53, 58)( 54, 57)( 55, 56)(111,218)(112,217)(113,216)(114,215)(115,214)(116,213)(117,212)(118,211)(119,210)(120,209)(121,208)(122,207)(123,206)(124,205)(125,204)(126,203)(127,202)(128,201)(129,200)(130,199)(131,198)(132,197)(133,196)(134,195)(135,194)(136,193)(137,192)(138,191)(139,190)(140,189)(141,188)(142,187)(143,186)(144,185)(145,184)(146,183)(147,182)(148,181)(149,180)(150,179)(151,178)(152,177)(153,176)(154,175)(155,174)(156,173)(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)(163,166)(164,165)(219,328)(220,436)(221,435)(222,434)(223,433)(224,432)(225,431)(226,430)(227,429)(228,428)(229,427)(230,426)(231,425)(232,424)(233,423)(234,422)(235,421)(236,420)(237,419)(238,418)(239,417)(240,416)(241,415)(242,414)(243,413)(244,412)(245,411)(246,410)(247,409)(248,408)(249,407)(250,406)(251,405)(252,404)(253,403)(254,402)(255,401)(256,400)(257,399)(258,398)(259,397)(260,396)(261,395)(262,394)(263,393)(264,392)(265,391)(266,390)(267,389)(268,388)(269,387)(270,386)(271,385)(272,384)(273,383)(274,382)(275,381)(276,380)(277,379)(278,378)(279,377)(280,376)(281,375)(282,374)(283,373)(284,372)(285,371)(286,370)(287,369)(288,368)(289,367)(290,366)(291,365)(292,364)(293,363)(294,362)(295,361)(296,360)(297,359)(298,358)(299,357)(300,356)(301,355)(302,354)(303,353)(304,352)(305,351)(306,350)(307,349)(308,348)(309,347)(310,346)(311,345)(312,344)(313,343)(314,342)(315,341)(316,340)(317,339)(318,338)(319,337)(320,336)(321,335)(322,334)(323,333)(324,332)(325,331)(326,330)(327,329)(437,655)(438,763)(439,762)(440,761)(441,760)(442,759)(443,758)(444,757)(445,756)(446,755)(447,754)(448,753)(449,752)(450,751)(451,750)(452,749)(453,748)(454,747)(455,746)(456,745)(457,744)(458,743)(459,742)(460,741)(461,740)(462,739)(463,738)(464,737)(465,736)(466,735)(467,734)(468,733)(469,732)(470,731)(471,730)(472,729)(473,728)(474,727)(475,726)(476,725)(477,724)(478,723)(479,722)(480,721)(481,720)(482,719)(483,718)(484,717)(485,716)(486,715)(487,714)(488,713)(489,712)(490,711)(491,710)(492,709)(493,708)(494,707)(495,706)(496,705)(497,704)(498,703)(499,702)(500,701)(501,700)(502,699)(503,698)(504,697)(505,696)(506,695)(507,694)(508,693)(509,692)(510,691)(511,690)(512,689)(513,688)(514,687)(515,686)(516,685)(517,684)(518,683)(519,682)(520,681)(521,680)(522,679)(523,678)(524,677)(525,676)(526,675)(527,674)(528,673)(529,672)(530,671)(531,670)(532,669)(533,668)(534,667)(535,666)(536,665)(537,664)(538,663)(539,662)(540,661)(541,660)(542,659)(543,658)(544,657)(545,656)(546,764)(547,872)(548,871)(549,870)(550,869)(551,868)(552,867)(553,866)(554,865)(555,864)(556,863)(557,862)(558,861)(559,860)(560,859)(561,858)(562,857)(563,856)(564,855)(565,854)(566,853)(567,852)(568,851)(569,850)(570,849)(571,848)(572,847)(573,846)(574,845)(575,844)(576,843)(577,842)(578,841)(579,840)(580,839)(581,838)(582,837)(583,836)(584,835)(585,834)(586,833)(587,832)(588,831)(589,830)(590,829)(591,828)(592,827)(593,826)(594,825)(595,824)(596,823)(597,822)(598,821)(599,820)(600,819)(601,818)(602,817)(603,816)(604,815)(605,814)(606,813)(607,812)(608,811)(609,810)(610,809)(611,808)(612,807)(613,806)(614,805)(615,804)(616,803)(617,802)(618,801)(619,800)(620,799)(621,798)(622,797)(623,796)(624,795)(625,794)(626,793)(627,792)(628,791)(629,790)(630,789)(631,788)(632,787)(633,786)(634,785)(635,784)(636,783)(637,782)(638,781)(639,780)(640,779)(641,778)(642,777)(643,776)(644,775)(645,774)(646,773)(647,772)(648,771)(649,770)(650,769)(651,768)(652,767)(653,766)(654,765);;
s1 := ( 1,438)( 2,437)( 3,545)( 4,544)( 5,543)( 6,542)( 7,541)( 8,540)( 9,539)( 10,538)( 11,537)( 12,536)( 13,535)( 14,534)( 15,533)( 16,532)( 17,531)( 18,530)( 19,529)( 20,528)( 21,527)( 22,526)( 23,525)( 24,524)( 25,523)( 26,522)( 27,521)( 28,520)( 29,519)( 30,518)( 31,517)( 32,516)( 33,515)( 34,514)( 35,513)( 36,512)( 37,511)( 38,510)( 39,509)( 40,508)( 41,507)( 42,506)( 43,505)( 44,504)( 45,503)( 46,502)( 47,501)( 48,500)( 49,499)( 50,498)( 51,497)( 52,496)( 53,495)( 54,494)( 55,493)( 56,492)( 57,491)( 58,490)( 59,489)( 60,488)( 61,487)( 62,486)( 63,485)( 64,484)( 65,483)( 66,482)( 67,481)( 68,480)( 69,479)( 70,478)( 71,477)( 72,476)( 73,475)( 74,474)( 75,473)( 76,472)( 77,471)( 78,470)( 79,469)( 80,468)( 81,467)( 82,466)( 83,465)( 84,464)( 85,463)( 86,462)( 87,461)( 88,460)( 89,459)( 90,458)( 91,457)( 92,456)( 93,455)( 94,454)( 95,453)( 96,452)( 97,451)( 98,450)( 99,449)(100,448)(101,447)(102,446)(103,445)(104,444)(105,443)(106,442)(107,441)(108,440)(109,439)(110,547)(111,546)(112,654)(113,653)(114,652)(115,651)(116,650)(117,649)(118,648)(119,647)(120,646)(121,645)(122,644)(123,643)(124,642)(125,641)(126,640)(127,639)(128,638)(129,637)(130,636)(131,635)(132,634)(133,633)(134,632)(135,631)(136,630)(137,629)(138,628)(139,627)(140,626)(141,625)(142,624)(143,623)(144,622)(145,621)(146,620)(147,619)(148,618)(149,617)(150,616)(151,615)(152,614)(153,613)(154,612)(155,611)(156,610)(157,609)(158,608)(159,607)(160,606)(161,605)(162,604)(163,603)(164,602)(165,601)(166,600)(167,599)(168,598)(169,597)(170,596)(171,595)(172,594)(173,593)(174,592)(175,591)(176,590)(177,589)(178,588)(179,587)(180,586)(181,585)(182,584)(183,583)(184,582)(185,581)(186,580)(187,579)(188,578)(189,577)(190,576)(191,575)(192,574)(193,573)(194,572)(195,571)(196,570)(197,569)(198,568)(199,567)(200,566)(201,565)(202,564)(203,563)(204,562)(205,561)(206,560)(207,559)(208,558)(209,557)(210,556)(211,555)(212,554)(213,553)(214,552)(215,551)(216,550)(217,549)(218,548)(219,765)(220,764)(221,872)(222,871)(223,870)(224,869)(225,868)(226,867)(227,866)(228,865)(229,864)(230,863)(231,862)(232,861)(233,860)(234,859)(235,858)(236,857)(237,856)(238,855)(239,854)(240,853)(241,852)(242,851)(243,850)(244,849)(245,848)(246,847)(247,846)(248,845)(249,844)(250,843)(251,842)(252,841)(253,840)(254,839)(255,838)(256,837)(257,836)(258,835)(259,834)(260,833)(261,832)(262,831)(263,830)(264,829)(265,828)(266,827)(267,826)(268,825)(269,824)(270,823)(271,822)(272,821)(273,820)(274,819)(275,818)(276,817)(277,816)(278,815)(279,814)(280,813)(281,812)(282,811)(283,810)(284,809)(285,808)(286,807)(287,806)(288,805)(289,804)(290,803)(291,802)(292,801)(293,800)(294,799)(295,798)(296,797)(297,796)(298,795)(299,794)(300,793)(301,792)(302,791)(303,790)(304,789)(305,788)(306,787)(307,786)(308,785)(309,784)(310,783)(311,782)(312,781)(313,780)(314,779)(315,778)(316,777)(317,776)(318,775)(319,774)(320,773)(321,772)(322,771)(323,770)(324,769)(325,768)(326,767)(327,766)(328,656)(329,655)(330,763)(331,762)(332,761)(333,760)(334,759)(335,758)(336,757)(337,756)(338,755)(339,754)(340,753)(341,752)(342,751)(343,750)(344,749)(345,748)(346,747)(347,746)(348,745)(349,744)(350,743)(351,742)(352,741)(353,740)(354,739)(355,738)(356,737)(357,736)(358,735)(359,734)(360,733)(361,732)(362,731)(363,730)(364,729)(365,728)(366,727)(367,726)(368,725)(369,724)(370,723)(371,722)(372,721)(373,720)(374,719)(375,718)(376,717)(377,716)(378,715)(379,714)(380,713)(381,712)(382,711)(383,710)(384,709)(385,708)(386,707)(387,706)(388,705)(389,704)(390,703)(391,702)(392,701)(393,700)(394,699)(395,698)(396,697)(397,696)(398,695)(399,694)(400,693)(401,692)(402,691)(403,690)(404,689)(405,688)(406,687)(407,686)(408,685)(409,684)(410,683)(411,682)(412,681)(413,680)(414,679)(415,678)(416,677)(417,676)(418,675)(419,674)(420,673)(421,672)(422,671)(423,670)(424,669)(425,668)(426,667)(427,666)(428,665)(429,664)(430,663)(431,662)(432,661)(433,660)(434,659)(435,658)(436,657);;
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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];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(872)!( 2,109)( 3,108)( 4,107)( 5,106)( 6,105)( 7,104)( 8,103)( 9,102)( 10,101)( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16, 95)( 17, 94)( 18, 93)( 19, 92)( 20, 91)( 21, 90)( 22, 89)( 23, 88)( 24, 87)( 25, 86)( 26, 85)( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 31, 80)( 32, 79)( 33, 78)( 34, 77)( 35, 76)( 36, 75)( 37, 74)( 38, 73)( 39, 72)( 40, 71)( 41, 70)( 42, 69)( 43, 68)( 44, 67)( 45, 66)( 46, 65)( 47, 64)( 48, 63)( 49, 62)( 50, 61)( 51, 60)( 52, 59)( 53, 58)( 54, 57)( 55, 56)(111,218)(112,217)(113,216)(114,215)(115,214)(116,213)(117,212)(118,211)(119,210)(120,209)(121,208)(122,207)(123,206)(124,205)(125,204)(126,203)(127,202)(128,201)(129,200)(130,199)(131,198)(132,197)(133,196)(134,195)(135,194)(136,193)(137,192)(138,191)(139,190)(140,189)(141,188)(142,187)(143,186)(144,185)(145,184)(146,183)(147,182)(148,181)(149,180)(150,179)(151,178)(152,177)(153,176)(154,175)(155,174)(156,173)(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)(163,166)(164,165)(219,328)(220,436)(221,435)(222,434)(223,433)(224,432)(225,431)(226,430)(227,429)(228,428)(229,427)(230,426)(231,425)(232,424)(233,423)(234,422)(235,421)(236,420)(237,419)(238,418)(239,417)(240,416)(241,415)(242,414)(243,413)(244,412)(245,411)(246,410)(247,409)(248,408)(249,407)(250,406)(251,405)(252,404)(253,403)(254,402)(255,401)(256,400)(257,399)(258,398)(259,397)(260,396)(261,395)(262,394)(263,393)(264,392)(265,391)(266,390)(267,389)(268,388)(269,387)(270,386)(271,385)(272,384)(273,383)(274,382)(275,381)(276,380)(277,379)(278,378)(279,377)(280,376)(281,375)(282,374)(283,373)(284,372)(285,371)(286,370)(287,369)(288,368)(289,367)(290,366)(291,365)(292,364)(293,363)(294,362)(295,361)(296,360)(297,359)(298,358)(299,357)(300,356)(301,355)(302,354)(303,353)(304,352)(305,351)(306,350)(307,349)(308,348)(309,347)(310,346)(311,345)(312,344)(313,343)(314,342)(315,341)(316,340)(317,339)(318,338)(319,337)(320,336)(321,335)(322,334)(323,333)(324,332)(325,331)(326,330)(327,329)(437,655)(438,763)(439,762)(440,761)(441,760)(442,759)(443,758)(444,757)(445,756)(446,755)(447,754)(448,753)(449,752)(450,751)(451,750)(452,749)(453,748)(454,747)(455,746)(456,745)(457,744)(458,743)(459,742)(460,741)(461,740)(462,739)(463,738)(464,737)(465,736)(466,735)(467,734)(468,733)(469,732)(470,731)(471,730)(472,729)(473,728)(474,727)(475,726)(476,725)(477,724)(478,723)(479,722)(480,721)(481,720)(482,719)(483,718)(484,717)(485,716)(486,715)(487,714)(488,713)(489,712)(490,711)(491,710)(492,709)(493,708)(494,707)(495,706)(496,705)(497,704)(498,703)(499,702)(500,701)(501,700)(502,699)(503,698)(504,697)(505,696)(506,695)(507,694)(508,693)(509,692)(510,691)(511,690)(512,689)(513,688)(514,687)(515,686)(516,685)(517,684)(518,683)(519,682)(520,681)(521,680)(522,679)(523,678)(524,677)(525,676)(526,675)(527,674)(528,673)(529,672)(530,671)(531,670)(532,669)(533,668)(534,667)(535,666)(536,665)(537,664)(538,663)(539,662)(540,661)(541,660)(542,659)(543,658)(544,657)(545,656)(546,764)(547,872)(548,871)(549,870)(550,869)(551,868)(552,867)(553,866)(554,865)(555,864)(556,863)(557,862)(558,861)(559,860)(560,859)(561,858)(562,857)(563,856)(564,855)(565,854)(566,853)(567,852)(568,851)(569,850)(570,849)(571,848)(572,847)(573,846)(574,845)(575,844)(576,843)(577,842)(578,841)(579,840)(580,839)(581,838)(582,837)(583,836)(584,835)(585,834)(586,833)(587,832)(588,831)(589,830)(590,829)(591,828)(592,827)(593,826)(594,825)(595,824)(596,823)(597,822)(598,821)(599,820)(600,819)(601,818)(602,817)(603,816)(604,815)(605,814)(606,813)(607,812)(608,811)(609,810)(610,809)(611,808)(612,807)(613,806)(614,805)(615,804)(616,803)(617,802)(618,801)(619,800)(620,799)(621,798)(622,797)(623,796)(624,795)(625,794)(626,793)(627,792)(628,791)(629,790)(630,789)(631,788)(632,787)(633,786)(634,785)(635,784)(636,783)(637,782)(638,781)(639,780)(640,779)(641,778)(642,777)(643,776)(644,775)(645,774)(646,773)(647,772)(648,771)(649,770)(650,769)(651,768)(652,767)(653,766)(654,765);
s1 := Sym(872)!( 1,438)( 2,437)( 3,545)( 4,544)( 5,543)( 6,542)( 7,541)( 8,540)( 9,539)( 10,538)( 11,537)( 12,536)( 13,535)( 14,534)( 15,533)( 16,532)( 17,531)( 18,530)( 19,529)( 20,528)( 21,527)( 22,526)( 23,525)( 24,524)( 25,523)( 26,522)( 27,521)( 28,520)( 29,519)( 30,518)( 31,517)( 32,516)( 33,515)( 34,514)( 35,513)( 36,512)( 37,511)( 38,510)( 39,509)( 40,508)( 41,507)( 42,506)( 43,505)( 44,504)( 45,503)( 46,502)( 47,501)( 48,500)( 49,499)( 50,498)( 51,497)( 52,496)( 53,495)( 54,494)( 55,493)( 56,492)( 57,491)( 58,490)( 59,489)( 60,488)( 61,487)( 62,486)( 63,485)( 64,484)( 65,483)( 66,482)( 67,481)( 68,480)( 69,479)( 70,478)( 71,477)( 72,476)( 73,475)( 74,474)( 75,473)( 76,472)( 77,471)( 78,470)( 79,469)( 80,468)( 81,467)( 82,466)( 83,465)( 84,464)( 85,463)( 86,462)( 87,461)( 88,460)( 89,459)( 90,458)( 91,457)( 92,456)( 93,455)( 94,454)( 95,453)( 96,452)( 97,451)( 98,450)( 99,449)(100,448)(101,447)(102,446)(103,445)(104,444)(105,443)(106,442)(107,441)(108,440)(109,439)(110,547)(111,546)(112,654)(113,653)(114,652)(115,651)(116,650)(117,649)(118,648)(119,647)(120,646)(121,645)(122,644)(123,643)(124,642)(125,641)(126,640)(127,639)(128,638)(129,637)(130,636)(131,635)(132,634)(133,633)(134,632)(135,631)(136,630)(137,629)(138,628)(139,627)(140,626)(141,625)(142,624)(143,623)(144,622)(145,621)(146,620)(147,619)(148,618)(149,617)(150,616)(151,615)(152,614)(153,613)(154,612)(155,611)(156,610)(157,609)(158,608)(159,607)(160,606)(161,605)(162,604)(163,603)(164,602)(165,601)(166,600)(167,599)(168,598)(169,597)(170,596)(171,595)(172,594)(173,593)(174,592)(175,591)(176,590)(177,589)(178,588)(179,587)(180,586)(181,585)(182,584)(183,583)(184,582)(185,581)(186,580)(187,579)(188,578)(189,577)(190,576)(191,575)(192,574)(193,573)(194,572)(195,571)(196,570)(197,569)(198,568)(199,567)(200,566)(201,565)(202,564)(203,563)(204,562)(205,561)(206,560)(207,559)(208,558)(209,557)(210,556)(211,555)(212,554)(213,553)(214,552)(215,551)(216,550)(217,549)(218,548)(219,765)(220,764)(221,872)(222,871)(223,870)(224,869)(225,868)(226,867)(227,866)(228,865)(229,864)(230,863)(231,862)(232,861)(233,860)(234,859)(235,858)(236,857)(237,856)(238,855)(239,854)(240,853)(241,852)(242,851)(243,850)(244,849)(245,848)(246,847)(247,846)(248,845)(249,844)(250,843)(251,842)(252,841)(253,840)(254,839)(255,838)(256,837)(257,836)(258,835)(259,834)(260,833)(261,832)(262,831)(263,830)(264,829)(265,828)(266,827)(267,826)(268,825)(269,824)(270,823)(271,822)(272,821)(273,820)(274,819)(275,818)(276,817)(277,816)(278,815)(279,814)(280,813)(281,812)(282,811)(283,810)(284,809)(285,808)(286,807)(287,806)(288,805)(289,804)(290,803)(291,802)(292,801)(293,800)(294,799)(295,798)(296,797)(297,796)(298,795)(299,794)(300,793)(301,792)(302,791)(303,790)(304,789)(305,788)(306,787)(307,786)(308,785)(309,784)(310,783)(311,782)(312,781)(313,780)(314,779)(315,778)(316,777)(317,776)(318,775)(319,774)(320,773)(321,772)(322,771)(323,770)(324,769)(325,768)(326,767)(327,766)(328,656)(329,655)(330,763)(331,762)(332,761)(333,760)(334,759)(335,758)(336,757)(337,756)(338,755)(339,754)(340,753)(341,752)(342,751)(343,750)(344,749)(345,748)(346,747)(347,746)(348,745)(349,744)(350,743)(351,742)(352,741)(353,740)(354,739)(355,738)(356,737)(357,736)(358,735)(359,734)(360,733)(361,732)(362,731)(363,730)(364,729)(365,728)(366,727)(367,726)(368,725)(369,724)(370,723)(371,722)(372,721)(373,720)(374,719)(375,718)(376,717)(377,716)(378,715)(379,714)(380,713)(381,712)(382,711)(383,710)(384,709)(385,708)(386,707)(387,706)(388,705)(389,704)(390,703)(391,702)(392,701)(393,700)(394,699)(395,698)(396,697)(397,696)(398,695)(399,694)(400,693)(401,692)(402,691)(403,690)(404,689)(405,688)(406,687)(407,686)(408,685)(409,684)(410,683)(411,682)(412,681)(413,680)(414,679)(415,678)(416,677)(417,676)(418,675)(419,674)(420,673)(421,672)(422,671)(423,670)(424,669)(425,668)(426,667)(427,666)(428,665)(429,664)(430,663)(431,662)(432,661)(433,660)(434,659)(435,658)(436,657);
poly := sub<Sym(872)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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