Overview
- Group
- SmallGroup(1776,96)
- Rank
- 2
- Schläfli Type
- {888}
- Vertices, edges, …
- 888, 888
- Order of s0s1
- 888
- Also known as
- 888-gon, {888}. if this polytope has another name.
Special Properties
- Universal
- Spherical
- Locally Spherical
- Orientable
- Self-Dual
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
12-fold
24-fold
37-fold
74-fold
111-fold
148-fold
222-fold
296-fold
444-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 2, 37)( 3, 36)( 4, 35)( 5, 34)( 6, 33)( 7, 32)( 8, 31)( 9, 30)( 10, 29)( 11, 28)( 12, 27)( 13, 26)( 14, 25)( 15, 24)( 16, 23)( 17, 22)( 18, 21)( 19, 20)( 38, 75)( 39,111)( 40,110)( 41,109)( 42,108)( 43,107)( 44,106)( 45,105)( 46,104)( 47,103)( 48,102)( 49,101)( 50,100)( 51, 99)( 52, 98)( 53, 97)( 54, 96)( 55, 95)( 56, 94)( 57, 93)( 58, 92)( 59, 91)( 60, 90)( 61, 89)( 62, 88)( 63, 87)( 64, 86)( 65, 85)( 66, 84)( 67, 83)( 68, 82)( 69, 81)( 70, 80)( 71, 79)( 72, 78)( 73, 77)( 74, 76)(113,148)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,141)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)(130,131)(149,186)(150,222)(151,221)(152,220)(153,219)(154,218)(155,217)(156,216)(157,215)(158,214)(159,213)(160,212)(161,211)(162,210)(163,209)(164,208)(165,207)(166,206)(167,205)(168,204)(169,203)(170,202)(171,201)(172,200)(173,199)(174,198)(175,197)(176,196)(177,195)(178,194)(179,193)(180,192)(181,191)(182,190)(183,189)(184,188)(185,187)(223,334)(224,370)(225,369)(226,368)(227,367)(228,366)(229,365)(230,364)(231,363)(232,362)(233,361)(234,360)(235,359)(236,358)(237,357)(238,356)(239,355)(240,354)(241,353)(242,352)(243,351)(244,350)(245,349)(246,348)(247,347)(248,346)(249,345)(250,344)(251,343)(252,342)(253,341)(254,340)(255,339)(256,338)(257,337)(258,336)(259,335)(260,408)(261,444)(262,443)(263,442)(264,441)(265,440)(266,439)(267,438)(268,437)(269,436)(270,435)(271,434)(272,433)(273,432)(274,431)(275,430)(276,429)(277,428)(278,427)(279,426)(280,425)(281,424)(282,423)(283,422)(284,421)(285,420)(286,419)(287,418)(288,417)(289,416)(290,415)(291,414)(292,413)(293,412)(294,411)(295,410)(296,409)(297,371)(298,407)(299,406)(300,405)(301,404)(302,403)(303,402)(304,401)(305,400)(306,399)(307,398)(308,397)(309,396)(310,395)(311,394)(312,393)(313,392)(314,391)(315,390)(316,389)(317,388)(318,387)(319,386)(320,385)(321,384)(322,383)(323,382)(324,381)(325,380)(326,379)(327,378)(328,377)(329,376)(330,375)(331,374)(332,373)(333,372)(445,667)(446,703)(447,702)(448,701)(449,700)(450,699)(451,698)(452,697)(453,696)(454,695)(455,694)(456,693)(457,692)(458,691)(459,690)(460,689)(461,688)(462,687)(463,686)(464,685)(465,684)(466,683)(467,682)(468,681)(469,680)(470,679)(471,678)(472,677)(473,676)(474,675)(475,674)(476,673)(477,672)(478,671)(479,670)(480,669)(481,668)(482,741)(483,777)(484,776)(485,775)(486,774)(487,773)(488,772)(489,771)(490,770)(491,769)(492,768)(493,767)(494,766)(495,765)(496,764)(497,763)(498,762)(499,761)(500,760)(501,759)(502,758)(503,757)(504,756)(505,755)(506,754)(507,753)(508,752)(509,751)(510,750)(511,749)(512,748)(513,747)(514,746)(515,745)(516,744)(517,743)(518,742)(519,704)(520,740)(521,739)(522,738)(523,737)(524,736)(525,735)(526,734)(527,733)(528,732)(529,731)(530,730)(531,729)(532,728)(533,727)(534,726)(535,725)(536,724)(537,723)(538,722)(539,721)(540,720)(541,719)(542,718)(543,717)(544,716)(545,715)(546,714)(547,713)(548,712)(549,711)(550,710)(551,709)(552,708)(553,707)(554,706)(555,705)(556,778)(557,814)(558,813)(559,812)(560,811)(561,810)(562,809)(563,808)(564,807)(565,806)(566,805)(567,804)(568,803)(569,802)(570,801)(571,800)(572,799)(573,798)(574,797)(575,796)(576,795)(577,794)(578,793)(579,792)(580,791)(581,790)(582,789)(583,788)(584,787)(585,786)(586,785)(587,784)(588,783)(589,782)(590,781)(591,780)(592,779)(593,852)(594,888)(595,887)(596,886)(597,885)(598,884)(599,883)(600,882)(601,881)(602,880)(603,879)(604,878)(605,877)(606,876)(607,875)(608,874)(609,873)(610,872)(611,871)(612,870)(613,869)(614,868)(615,867)(616,866)(617,865)(618,864)(619,863)(620,862)(621,861)(622,860)(623,859)(624,858)(625,857)(626,856)(627,855)(628,854)(629,853)(630,815)(631,851)(632,850)(633,849)(634,848)(635,847)(636,846)(637,845)(638,844)(639,843)(640,842)(641,841)(642,840)(643,839)(644,838)(645,837)(646,836)(647,835)(648,834)(649,833)(650,832)(651,831)(652,830)(653,829)(654,828)(655,827)(656,826)(657,825)(658,824)(659,823)(660,822)(661,821)(662,820)(663,819)(664,818)(665,817)(666,816);; s1 := ( 1,483)( 2,482)( 3,518)( 4,517)( 5,516)( 6,515)( 7,514)( 8,513)( 9,512)( 10,511)( 11,510)( 12,509)( 13,508)( 14,507)( 15,506)( 16,505)( 17,504)( 18,503)( 19,502)( 20,501)( 21,500)( 22,499)( 23,498)( 24,497)( 25,496)( 26,495)( 27,494)( 28,493)( 29,492)( 30,491)( 31,490)( 32,489)( 33,488)( 34,487)( 35,486)( 36,485)( 37,484)( 38,446)( 39,445)( 40,481)( 41,480)( 42,479)( 43,478)( 44,477)( 45,476)( 46,475)( 47,474)( 48,473)( 49,472)( 50,471)( 51,470)( 52,469)( 53,468)( 54,467)( 55,466)( 56,465)( 57,464)( 58,463)( 59,462)( 60,461)( 61,460)( 62,459)( 63,458)( 64,457)( 65,456)( 66,455)( 67,454)( 68,453)( 69,452)( 70,451)( 71,450)( 72,449)( 73,448)( 74,447)( 75,520)( 76,519)( 77,555)( 78,554)( 79,553)( 80,552)( 81,551)( 82,550)( 83,549)( 84,548)( 85,547)( 86,546)( 87,545)( 88,544)( 89,543)( 90,542)( 91,541)( 92,540)( 93,539)( 94,538)( 95,537)( 96,536)( 97,535)( 98,534)( 99,533)(100,532)(101,531)(102,530)(103,529)(104,528)(105,527)(106,526)(107,525)(108,524)(109,523)(110,522)(111,521)(112,594)(113,593)(114,629)(115,628)(116,627)(117,626)(118,625)(119,624)(120,623)(121,622)(122,621)(123,620)(124,619)(125,618)(126,617)(127,616)(128,615)(129,614)(130,613)(131,612)(132,611)(133,610)(134,609)(135,608)(136,607)(137,606)(138,605)(139,604)(140,603)(141,602)(142,601)(143,600)(144,599)(145,598)(146,597)(147,596)(148,595)(149,557)(150,556)(151,592)(152,591)(153,590)(154,589)(155,588)(156,587)(157,586)(158,585)(159,584)(160,583)(161,582)(162,581)(163,580)(164,579)(165,578)(166,577)(167,576)(168,575)(169,574)(170,573)(171,572)(172,571)(173,570)(174,569)(175,568)(176,567)(177,566)(178,565)(179,564)(180,563)(181,562)(182,561)(183,560)(184,559)(185,558)(186,631)(187,630)(188,666)(189,665)(190,664)(191,663)(192,662)(193,661)(194,660)(195,659)(196,658)(197,657)(198,656)(199,655)(200,654)(201,653)(202,652)(203,651)(204,650)(205,649)(206,648)(207,647)(208,646)(209,645)(210,644)(211,643)(212,642)(213,641)(214,640)(215,639)(216,638)(217,637)(218,636)(219,635)(220,634)(221,633)(222,632)(223,816)(224,815)(225,851)(226,850)(227,849)(228,848)(229,847)(230,846)(231,845)(232,844)(233,843)(234,842)(235,841)(236,840)(237,839)(238,838)(239,837)(240,836)(241,835)(242,834)(243,833)(244,832)(245,831)(246,830)(247,829)(248,828)(249,827)(250,826)(251,825)(252,824)(253,823)(254,822)(255,821)(256,820)(257,819)(258,818)(259,817)(260,779)(261,778)(262,814)(263,813)(264,812)(265,811)(266,810)(267,809)(268,808)(269,807)(270,806)(271,805)(272,804)(273,803)(274,802)(275,801)(276,800)(277,799)(278,798)(279,797)(280,796)(281,795)(282,794)(283,793)(284,792)(285,791)(286,790)(287,789)(288,788)(289,787)(290,786)(291,785)(292,784)(293,783)(294,782)(295,781)(296,780)(297,853)(298,852)(299,888)(300,887)(301,886)(302,885)(303,884)(304,883)(305,882)(306,881)(307,880)(308,879)(309,878)(310,877)(311,876)(312,875)(313,874)(314,873)(315,872)(316,871)(317,870)(318,869)(319,868)(320,867)(321,866)(322,865)(323,864)(324,863)(325,862)(326,861)(327,860)(328,859)(329,858)(330,857)(331,856)(332,855)(333,854)(334,705)(335,704)(336,740)(337,739)(338,738)(339,737)(340,736)(341,735)(342,734)(343,733)(344,732)(345,731)(346,730)(347,729)(348,728)(349,727)(350,726)(351,725)(352,724)(353,723)(354,722)(355,721)(356,720)(357,719)(358,718)(359,717)(360,716)(361,715)(362,714)(363,713)(364,712)(365,711)(366,710)(367,709)(368,708)(369,707)(370,706)(371,668)(372,667)(373,703)(374,702)(375,701)(376,700)(377,699)(378,698)(379,697)(380,696)(381,695)(382,694)(383,693)(384,692)(385,691)(386,690)(387,689)(388,688)(389,687)(390,686)(391,685)(392,684)(393,683)(394,682)(395,681)(396,680)(397,679)(398,678)(399,677)(400,676)(401,675)(402,674)(403,673)(404,672)(405,671)(406,670)(407,669)(408,742)(409,741)(410,777)(411,776)(412,775)(413,774)(414,773)(415,772)(416,771)(417,770)(418,769)(419,768)(420,767)(421,766)(422,765)(423,764)(424,763)(425,762)(426,761)(427,760)(428,759)(429,758)(430,757)(431,756)(432,755)(433,754)(434,753)(435,752)(436,751)(437,750)(438,749)(439,748)(440,747)(441,746)(442,745)(443,744)(444,743);; 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(888)!( 2, 37)( 3, 36)( 4, 35)( 5, 34)( 6, 33)( 7, 32)( 8, 31)( 9, 30)( 10, 29)( 11, 28)( 12, 27)( 13, 26)( 14, 25)( 15, 24)( 16, 23)( 17, 22)( 18, 21)( 19, 20)( 38, 75)( 39,111)( 40,110)( 41,109)( 42,108)( 43,107)( 44,106)( 45,105)( 46,104)( 47,103)( 48,102)( 49,101)( 50,100)( 51, 99)( 52, 98)( 53, 97)( 54, 96)( 55, 95)( 56, 94)( 57, 93)( 58, 92)( 59, 91)( 60, 90)( 61, 89)( 62, 88)( 63, 87)( 64, 86)( 65, 85)( 66, 84)( 67, 83)( 68, 82)( 69, 81)( 70, 80)( 71, 79)( 72, 78)( 73, 77)( 74, 76)(113,148)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,141)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)(130,131)(149,186)(150,222)(151,221)(152,220)(153,219)(154,218)(155,217)(156,216)(157,215)(158,214)(159,213)(160,212)(161,211)(162,210)(163,209)(164,208)(165,207)(166,206)(167,205)(168,204)(169,203)(170,202)(171,201)(172,200)(173,199)(174,198)(175,197)(176,196)(177,195)(178,194)(179,193)(180,192)(181,191)(182,190)(183,189)(184,188)(185,187)(223,334)(224,370)(225,369)(226,368)(227,367)(228,366)(229,365)(230,364)(231,363)(232,362)(233,361)(234,360)(235,359)(236,358)(237,357)(238,356)(239,355)(240,354)(241,353)(242,352)(243,351)(244,350)(245,349)(246,348)(247,347)(248,346)(249,345)(250,344)(251,343)(252,342)(253,341)(254,340)(255,339)(256,338)(257,337)(258,336)(259,335)(260,408)(261,444)(262,443)(263,442)(264,441)(265,440)(266,439)(267,438)(268,437)(269,436)(270,435)(271,434)(272,433)(273,432)(274,431)(275,430)(276,429)(277,428)(278,427)(279,426)(280,425)(281,424)(282,423)(283,422)(284,421)(285,420)(286,419)(287,418)(288,417)(289,416)(290,415)(291,414)(292,413)(293,412)(294,411)(295,410)(296,409)(297,371)(298,407)(299,406)(300,405)(301,404)(302,403)(303,402)(304,401)(305,400)(306,399)(307,398)(308,397)(309,396)(310,395)(311,394)(312,393)(313,392)(314,391)(315,390)(316,389)(317,388)(318,387)(319,386)(320,385)(321,384)(322,383)(323,382)(324,381)(325,380)(326,379)(327,378)(328,377)(329,376)(330,375)(331,374)(332,373)(333,372)(445,667)(446,703)(447,702)(448,701)(449,700)(450,699)(451,698)(452,697)(453,696)(454,695)(455,694)(456,693)(457,692)(458,691)(459,690)(460,689)(461,688)(462,687)(463,686)(464,685)(465,684)(466,683)(467,682)(468,681)(469,680)(470,679)(471,678)(472,677)(473,676)(474,675)(475,674)(476,673)(477,672)(478,671)(479,670)(480,669)(481,668)(482,741)(483,777)(484,776)(485,775)(486,774)(487,773)(488,772)(489,771)(490,770)(491,769)(492,768)(493,767)(494,766)(495,765)(496,764)(497,763)(498,762)(499,761)(500,760)(501,759)(502,758)(503,757)(504,756)(505,755)(506,754)(507,753)(508,752)(509,751)(510,750)(511,749)(512,748)(513,747)(514,746)(515,745)(516,744)(517,743)(518,742)(519,704)(520,740)(521,739)(522,738)(523,737)(524,736)(525,735)(526,734)(527,733)(528,732)(529,731)(530,730)(531,729)(532,728)(533,727)(534,726)(535,725)(536,724)(537,723)(538,722)(539,721)(540,720)(541,719)(542,718)(543,717)(544,716)(545,715)(546,714)(547,713)(548,712)(549,711)(550,710)(551,709)(552,708)(553,707)(554,706)(555,705)(556,778)(557,814)(558,813)(559,812)(560,811)(561,810)(562,809)(563,808)(564,807)(565,806)(566,805)(567,804)(568,803)(569,802)(570,801)(571,800)(572,799)(573,798)(574,797)(575,796)(576,795)(577,794)(578,793)(579,792)(580,791)(581,790)(582,789)(583,788)(584,787)(585,786)(586,785)(587,784)(588,783)(589,782)(590,781)(591,780)(592,779)(593,852)(594,888)(595,887)(596,886)(597,885)(598,884)(599,883)(600,882)(601,881)(602,880)(603,879)(604,878)(605,877)(606,876)(607,875)(608,874)(609,873)(610,872)(611,871)(612,870)(613,869)(614,868)(615,867)(616,866)(617,865)(618,864)(619,863)(620,862)(621,861)(622,860)(623,859)(624,858)(625,857)(626,856)(627,855)(628,854)(629,853)(630,815)(631,851)(632,850)(633,849)(634,848)(635,847)(636,846)(637,845)(638,844)(639,843)(640,842)(641,841)(642,840)(643,839)(644,838)(645,837)(646,836)(647,835)(648,834)(649,833)(650,832)(651,831)(652,830)(653,829)(654,828)(655,827)(656,826)(657,825)(658,824)(659,823)(660,822)(661,821)(662,820)(663,819)(664,818)(665,817)(666,816); s1 := Sym(888)!( 1,483)( 2,482)( 3,518)( 4,517)( 5,516)( 6,515)( 7,514)( 8,513)( 9,512)( 10,511)( 11,510)( 12,509)( 13,508)( 14,507)( 15,506)( 16,505)( 17,504)( 18,503)( 19,502)( 20,501)( 21,500)( 22,499)( 23,498)( 24,497)( 25,496)( 26,495)( 27,494)( 28,493)( 29,492)( 30,491)( 31,490)( 32,489)( 33,488)( 34,487)( 35,486)( 36,485)( 37,484)( 38,446)( 39,445)( 40,481)( 41,480)( 42,479)( 43,478)( 44,477)( 45,476)( 46,475)( 47,474)( 48,473)( 49,472)( 50,471)( 51,470)( 52,469)( 53,468)( 54,467)( 55,466)( 56,465)( 57,464)( 58,463)( 59,462)( 60,461)( 61,460)( 62,459)( 63,458)( 64,457)( 65,456)( 66,455)( 67,454)( 68,453)( 69,452)( 70,451)( 71,450)( 72,449)( 73,448)( 74,447)( 75,520)( 76,519)( 77,555)( 78,554)( 79,553)( 80,552)( 81,551)( 82,550)( 83,549)( 84,548)( 85,547)( 86,546)( 87,545)( 88,544)( 89,543)( 90,542)( 91,541)( 92,540)( 93,539)( 94,538)( 95,537)( 96,536)( 97,535)( 98,534)( 99,533)(100,532)(101,531)(102,530)(103,529)(104,528)(105,527)(106,526)(107,525)(108,524)(109,523)(110,522)(111,521)(112,594)(113,593)(114,629)(115,628)(116,627)(117,626)(118,625)(119,624)(120,623)(121,622)(122,621)(123,620)(124,619)(125,618)(126,617)(127,616)(128,615)(129,614)(130,613)(131,612)(132,611)(133,610)(134,609)(135,608)(136,607)(137,606)(138,605)(139,604)(140,603)(141,602)(142,601)(143,600)(144,599)(145,598)(146,597)(147,596)(148,595)(149,557)(150,556)(151,592)(152,591)(153,590)(154,589)(155,588)(156,587)(157,586)(158,585)(159,584)(160,583)(161,582)(162,581)(163,580)(164,579)(165,578)(166,577)(167,576)(168,575)(169,574)(170,573)(171,572)(172,571)(173,570)(174,569)(175,568)(176,567)(177,566)(178,565)(179,564)(180,563)(181,562)(182,561)(183,560)(184,559)(185,558)(186,631)(187,630)(188,666)(189,665)(190,664)(191,663)(192,662)(193,661)(194,660)(195,659)(196,658)(197,657)(198,656)(199,655)(200,654)(201,653)(202,652)(203,651)(204,650)(205,649)(206,648)(207,647)(208,646)(209,645)(210,644)(211,643)(212,642)(213,641)(214,640)(215,639)(216,638)(217,637)(218,636)(219,635)(220,634)(221,633)(222,632)(223,816)(224,815)(225,851)(226,850)(227,849)(228,848)(229,847)(230,846)(231,845)(232,844)(233,843)(234,842)(235,841)(236,840)(237,839)(238,838)(239,837)(240,836)(241,835)(242,834)(243,833)(244,832)(245,831)(246,830)(247,829)(248,828)(249,827)(250,826)(251,825)(252,824)(253,823)(254,822)(255,821)(256,820)(257,819)(258,818)(259,817)(260,779)(261,778)(262,814)(263,813)(264,812)(265,811)(266,810)(267,809)(268,808)(269,807)(270,806)(271,805)(272,804)(273,803)(274,802)(275,801)(276,800)(277,799)(278,798)(279,797)(280,796)(281,795)(282,794)(283,793)(284,792)(285,791)(286,790)(287,789)(288,788)(289,787)(290,786)(291,785)(292,784)(293,783)(294,782)(295,781)(296,780)(297,853)(298,852)(299,888)(300,887)(301,886)(302,885)(303,884)(304,883)(305,882)(306,881)(307,880)(308,879)(309,878)(310,877)(311,876)(312,875)(313,874)(314,873)(315,872)(316,871)(317,870)(318,869)(319,868)(320,867)(321,866)(322,865)(323,864)(324,863)(325,862)(326,861)(327,860)(328,859)(329,858)(330,857)(331,856)(332,855)(333,854)(334,705)(335,704)(336,740)(337,739)(338,738)(339,737)(340,736)(341,735)(342,734)(343,733)(344,732)(345,731)(346,730)(347,729)(348,728)(349,727)(350,726)(351,725)(352,724)(353,723)(354,722)(355,721)(356,720)(357,719)(358,718)(359,717)(360,716)(361,715)(362,714)(363,713)(364,712)(365,711)(366,710)(367,709)(368,708)(369,707)(370,706)(371,668)(372,667)(373,703)(374,702)(375,701)(376,700)(377,699)(378,698)(379,697)(380,696)(381,695)(382,694)(383,693)(384,692)(385,691)(386,690)(387,689)(388,688)(389,687)(390,686)(391,685)(392,684)(393,683)(394,682)(395,681)(396,680)(397,679)(398,678)(399,677)(400,676)(401,675)(402,674)(403,673)(404,672)(405,671)(406,670)(407,669)(408,742)(409,741)(410,777)(411,776)(412,775)(413,774)(414,773)(415,772)(416,771)(417,770)(418,769)(419,768)(420,767)(421,766)(422,765)(423,764)(424,763)(425,762)(426,761)(427,760)(428,759)(429,758)(430,757)(431,756)(432,755)(433,754)(434,753)(435,752)(436,751)(437,750)(438,749)(439,748)(440,747)(441,746)(442,745)(443,744)(444,743); poly := sub<Sym(888)|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*s0*s1*s0*s1*s0*s1*s0*s1*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.