Part of the Atlas of Small Regular Polytopes

Polytope of Type {896}

Atlas Canonical Name {896}*1792

Overview

Group
SmallGroup(1792,57481)
Rank
2
Schläfli Type
{896}
Vertices, edges, …
896, 896
Order of s0s1
896
Also known as
896-gon, {896}. if this polytope has another name.

Special Properties

  • Universal
  • Spherical
  • Locally Spherical
  • Orientable
  • Self-Dual

Quotients maximal quotients in bold

2-fold

4-fold

7-fold

8-fold

14-fold

16-fold

28-fold

32-fold

56-fold

64-fold

112-fold

128-fold

224-fold

448-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,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 15, 22)( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 29, 43)( 30, 49)( 31, 48)( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 36, 50)( 37, 56)( 38, 55)( 39, 54)( 40, 53)( 41, 52)( 42, 51)( 57, 85)( 58, 91)( 59, 90)( 60, 89)( 61, 88)( 62, 87)( 63, 86)( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71,106)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)( 77,107)( 78, 99)( 79,105)( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)(113,169)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,176)(121,182)(122,181)(123,180)(124,179)(125,178)(126,177)(127,190)(128,196)(129,195)(130,194)(131,193)(132,192)(133,191)(134,183)(135,189)(136,188)(137,187)(138,186)(139,185)(140,184)(141,211)(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)(148,218)(149,224)(150,223)(151,222)(152,221)(153,220)(154,219)(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)(162,204)(163,210)(164,209)(165,208)(166,207)(167,206)(168,205)(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,344)(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,358)(240,364)(241,363)(242,362)(243,361)(244,360)(245,359)(246,351)(247,357)(248,356)(249,355)(250,354)(251,353)(252,352)(253,379)(254,385)(255,384)(256,383)(257,382)(258,381)(259,380)(260,386)(261,392)(262,391)(263,390)(264,389)(265,388)(266,387)(267,365)(268,371)(269,370)(270,369)(271,368)(272,367)(273,366)(274,372)(275,378)(276,377)(277,376)(278,375)(279,374)(280,373)(281,421)(282,427)(283,426)(284,425)(285,424)(286,423)(287,422)(288,428)(289,434)(290,433)(291,432)(292,431)(293,430)(294,429)(295,442)(296,448)(297,447)(298,446)(299,445)(300,444)(301,443)(302,435)(303,441)(304,440)(305,439)(306,438)(307,437)(308,436)(309,393)(310,399)(311,398)(312,397)(313,396)(314,395)(315,394)(316,400)(317,406)(318,405)(319,404)(320,403)(321,402)(322,401)(323,414)(324,420)(325,419)(326,418)(327,417)(328,416)(329,415)(330,407)(331,413)(332,412)(333,411)(334,410)(335,409)(336,408)(449,673)(450,679)(451,678)(452,677)(453,676)(454,675)(455,674)(456,680)(457,686)(458,685)(459,684)(460,683)(461,682)(462,681)(463,694)(464,700)(465,699)(466,698)(467,697)(468,696)(469,695)(470,687)(471,693)(472,692)(473,691)(474,690)(475,689)(476,688)(477,715)(478,721)(479,720)(480,719)(481,718)(482,717)(483,716)(484,722)(485,728)(486,727)(487,726)(488,725)(489,724)(490,723)(491,701)(492,707)(493,706)(494,705)(495,704)(496,703)(497,702)(498,708)(499,714)(500,713)(501,712)(502,711)(503,710)(504,709)(505,757)(506,763)(507,762)(508,761)(509,760)(510,759)(511,758)(512,764)(513,770)(514,769)(515,768)(516,767)(517,766)(518,765)(519,778)(520,784)(521,783)(522,782)(523,781)(524,780)(525,779)(526,771)(527,777)(528,776)(529,775)(530,774)(531,773)(532,772)(533,729)(534,735)(535,734)(536,733)(537,732)(538,731)(539,730)(540,736)(541,742)(542,741)(543,740)(544,739)(545,738)(546,737)(547,750)(548,756)(549,755)(550,754)(551,753)(552,752)(553,751)(554,743)(555,749)(556,748)(557,747)(558,746)(559,745)(560,744)(561,841)(562,847)(563,846)(564,845)(565,844)(566,843)(567,842)(568,848)(569,854)(570,853)(571,852)(572,851)(573,850)(574,849)(575,862)(576,868)(577,867)(578,866)(579,865)(580,864)(581,863)(582,855)(583,861)(584,860)(585,859)(586,858)(587,857)(588,856)(589,883)(590,889)(591,888)(592,887)(593,886)(594,885)(595,884)(596,890)(597,896)(598,895)(599,894)(600,893)(601,892)(602,891)(603,869)(604,875)(605,874)(606,873)(607,872)(608,871)(609,870)(610,876)(611,882)(612,881)(613,880)(614,879)(615,878)(616,877)(617,785)(618,791)(619,790)(620,789)(621,788)(622,787)(623,786)(624,792)(625,798)(626,797)(627,796)(628,795)(629,794)(630,793)(631,806)(632,812)(633,811)(634,810)(635,809)(636,808)(637,807)(638,799)(639,805)(640,804)(641,803)(642,802)(643,801)(644,800)(645,827)(646,833)(647,832)(648,831)(649,830)(650,829)(651,828)(652,834)(653,840)(654,839)(655,838)(656,837)(657,836)(658,835)(659,813)(660,819)(661,818)(662,817)(663,816)(664,815)(665,814)(666,820)(667,826)(668,825)(669,824)(670,823)(671,822)(672,821);;
s1 := (  1,450)(  2,449)(  3,455)(  4,454)(  5,453)(  6,452)(  7,451)(  8,457)(  9,456)( 10,462)( 11,461)( 12,460)( 13,459)( 14,458)( 15,471)( 16,470)( 17,476)( 18,475)( 19,474)( 20,473)( 21,472)( 22,464)( 23,463)( 24,469)( 25,468)( 26,467)( 27,466)( 28,465)( 29,492)( 30,491)( 31,497)( 32,496)( 33,495)( 34,494)( 35,493)( 36,499)( 37,498)( 38,504)( 39,503)( 40,502)( 41,501)( 42,500)( 43,478)( 44,477)( 45,483)( 46,482)( 47,481)( 48,480)( 49,479)( 50,485)( 51,484)( 52,490)( 53,489)( 54,488)( 55,487)( 56,486)( 57,534)( 58,533)( 59,539)( 60,538)( 61,537)( 62,536)( 63,535)( 64,541)( 65,540)( 66,546)( 67,545)( 68,544)( 69,543)( 70,542)( 71,555)( 72,554)( 73,560)( 74,559)( 75,558)( 76,557)( 77,556)( 78,548)( 79,547)( 80,553)( 81,552)( 82,551)( 83,550)( 84,549)( 85,506)( 86,505)( 87,511)( 88,510)( 89,509)( 90,508)( 91,507)( 92,513)( 93,512)( 94,518)( 95,517)( 96,516)( 97,515)( 98,514)( 99,527)(100,526)(101,532)(102,531)(103,530)(104,529)(105,528)(106,520)(107,519)(108,525)(109,524)(110,523)(111,522)(112,521)(113,618)(114,617)(115,623)(116,622)(117,621)(118,620)(119,619)(120,625)(121,624)(122,630)(123,629)(124,628)(125,627)(126,626)(127,639)(128,638)(129,644)(130,643)(131,642)(132,641)(133,640)(134,632)(135,631)(136,637)(137,636)(138,635)(139,634)(140,633)(141,660)(142,659)(143,665)(144,664)(145,663)(146,662)(147,661)(148,667)(149,666)(150,672)(151,671)(152,670)(153,669)(154,668)(155,646)(156,645)(157,651)(158,650)(159,649)(160,648)(161,647)(162,653)(163,652)(164,658)(165,657)(166,656)(167,655)(168,654)(169,562)(170,561)(171,567)(172,566)(173,565)(174,564)(175,563)(176,569)(177,568)(178,574)(179,573)(180,572)(181,571)(182,570)(183,583)(184,582)(185,588)(186,587)(187,586)(188,585)(189,584)(190,576)(191,575)(192,581)(193,580)(194,579)(195,578)(196,577)(197,604)(198,603)(199,609)(200,608)(201,607)(202,606)(203,605)(204,611)(205,610)(206,616)(207,615)(208,614)(209,613)(210,612)(211,590)(212,589)(213,595)(214,594)(215,593)(216,592)(217,591)(218,597)(219,596)(220,602)(221,601)(222,600)(223,599)(224,598)(225,786)(226,785)(227,791)(228,790)(229,789)(230,788)(231,787)(232,793)(233,792)(234,798)(235,797)(236,796)(237,795)(238,794)(239,807)(240,806)(241,812)(242,811)(243,810)(244,809)(245,808)(246,800)(247,799)(248,805)(249,804)(250,803)(251,802)(252,801)(253,828)(254,827)(255,833)(256,832)(257,831)(258,830)(259,829)(260,835)(261,834)(262,840)(263,839)(264,838)(265,837)(266,836)(267,814)(268,813)(269,819)(270,818)(271,817)(272,816)(273,815)(274,821)(275,820)(276,826)(277,825)(278,824)(279,823)(280,822)(281,870)(282,869)(283,875)(284,874)(285,873)(286,872)(287,871)(288,877)(289,876)(290,882)(291,881)(292,880)(293,879)(294,878)(295,891)(296,890)(297,896)(298,895)(299,894)(300,893)(301,892)(302,884)(303,883)(304,889)(305,888)(306,887)(307,886)(308,885)(309,842)(310,841)(311,847)(312,846)(313,845)(314,844)(315,843)(316,849)(317,848)(318,854)(319,853)(320,852)(321,851)(322,850)(323,863)(324,862)(325,868)(326,867)(327,866)(328,865)(329,864)(330,856)(331,855)(332,861)(333,860)(334,859)(335,858)(336,857)(337,674)(338,673)(339,679)(340,678)(341,677)(342,676)(343,675)(344,681)(345,680)(346,686)(347,685)(348,684)(349,683)(350,682)(351,695)(352,694)(353,700)(354,699)(355,698)(356,697)(357,696)(358,688)(359,687)(360,693)(361,692)(362,691)(363,690)(364,689)(365,716)(366,715)(367,721)(368,720)(369,719)(370,718)(371,717)(372,723)(373,722)(374,728)(375,727)(376,726)(377,725)(378,724)(379,702)(380,701)(381,707)(382,706)(383,705)(384,704)(385,703)(386,709)(387,708)(388,714)(389,713)(390,712)(391,711)(392,710)(393,758)(394,757)(395,763)(396,762)(397,761)(398,760)(399,759)(400,765)(401,764)(402,770)(403,769)(404,768)(405,767)(406,766)(407,779)(408,778)(409,784)(410,783)(411,782)(412,781)(413,780)(414,772)(415,771)(416,777)(417,776)(418,775)(419,774)(420,773)(421,730)(422,729)(423,735)(424,734)(425,733)(426,732)(427,731)(428,737)(429,736)(430,742)(431,741)(432,740)(433,739)(434,738)(435,751)(436,750)(437,756)(438,755)(439,754)(440,753)(441,752)(442,744)(443,743)(444,749)(445,748)(446,747)(447,746)(448,745);;
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(896)!(  2,  7)(  3,  6)(  4,  5)(  9, 14)( 10, 13)( 11, 12)( 15, 22)( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)( 21, 23)( 29, 43)( 30, 49)( 31, 48)( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 36, 50)( 37, 56)( 38, 55)( 39, 54)( 40, 53)( 41, 52)( 42, 51)( 57, 85)( 58, 91)( 59, 90)( 60, 89)( 61, 88)( 62, 87)( 63, 86)( 64, 92)( 65, 98)( 66, 97)( 67, 96)( 68, 95)( 69, 94)( 70, 93)( 71,106)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)( 77,107)( 78, 99)( 79,105)( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)(113,169)(114,175)(115,174)(116,173)(117,172)(118,171)(119,170)(120,176)(121,182)(122,181)(123,180)(124,179)(125,178)(126,177)(127,190)(128,196)(129,195)(130,194)(131,193)(132,192)(133,191)(134,183)(135,189)(136,188)(137,187)(138,186)(139,185)(140,184)(141,211)(142,217)(143,216)(144,215)(145,214)(146,213)(147,212)(148,218)(149,224)(150,223)(151,222)(152,221)(153,220)(154,219)(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)(161,198)(162,204)(163,210)(164,209)(165,208)(166,207)(167,206)(168,205)(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,344)(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,358)(240,364)(241,363)(242,362)(243,361)(244,360)(245,359)(246,351)(247,357)(248,356)(249,355)(250,354)(251,353)(252,352)(253,379)(254,385)(255,384)(256,383)(257,382)(258,381)(259,380)(260,386)(261,392)(262,391)(263,390)(264,389)(265,388)(266,387)(267,365)(268,371)(269,370)(270,369)(271,368)(272,367)(273,366)(274,372)(275,378)(276,377)(277,376)(278,375)(279,374)(280,373)(281,421)(282,427)(283,426)(284,425)(285,424)(286,423)(287,422)(288,428)(289,434)(290,433)(291,432)(292,431)(293,430)(294,429)(295,442)(296,448)(297,447)(298,446)(299,445)(300,444)(301,443)(302,435)(303,441)(304,440)(305,439)(306,438)(307,437)(308,436)(309,393)(310,399)(311,398)(312,397)(313,396)(314,395)(315,394)(316,400)(317,406)(318,405)(319,404)(320,403)(321,402)(322,401)(323,414)(324,420)(325,419)(326,418)(327,417)(328,416)(329,415)(330,407)(331,413)(332,412)(333,411)(334,410)(335,409)(336,408)(449,673)(450,679)(451,678)(452,677)(453,676)(454,675)(455,674)(456,680)(457,686)(458,685)(459,684)(460,683)(461,682)(462,681)(463,694)(464,700)(465,699)(466,698)(467,697)(468,696)(469,695)(470,687)(471,693)(472,692)(473,691)(474,690)(475,689)(476,688)(477,715)(478,721)(479,720)(480,719)(481,718)(482,717)(483,716)(484,722)(485,728)(486,727)(487,726)(488,725)(489,724)(490,723)(491,701)(492,707)(493,706)(494,705)(495,704)(496,703)(497,702)(498,708)(499,714)(500,713)(501,712)(502,711)(503,710)(504,709)(505,757)(506,763)(507,762)(508,761)(509,760)(510,759)(511,758)(512,764)(513,770)(514,769)(515,768)(516,767)(517,766)(518,765)(519,778)(520,784)(521,783)(522,782)(523,781)(524,780)(525,779)(526,771)(527,777)(528,776)(529,775)(530,774)(531,773)(532,772)(533,729)(534,735)(535,734)(536,733)(537,732)(538,731)(539,730)(540,736)(541,742)(542,741)(543,740)(544,739)(545,738)(546,737)(547,750)(548,756)(549,755)(550,754)(551,753)(552,752)(553,751)(554,743)(555,749)(556,748)(557,747)(558,746)(559,745)(560,744)(561,841)(562,847)(563,846)(564,845)(565,844)(566,843)(567,842)(568,848)(569,854)(570,853)(571,852)(572,851)(573,850)(574,849)(575,862)(576,868)(577,867)(578,866)(579,865)(580,864)(581,863)(582,855)(583,861)(584,860)(585,859)(586,858)(587,857)(588,856)(589,883)(590,889)(591,888)(592,887)(593,886)(594,885)(595,884)(596,890)(597,896)(598,895)(599,894)(600,893)(601,892)(602,891)(603,869)(604,875)(605,874)(606,873)(607,872)(608,871)(609,870)(610,876)(611,882)(612,881)(613,880)(614,879)(615,878)(616,877)(617,785)(618,791)(619,790)(620,789)(621,788)(622,787)(623,786)(624,792)(625,798)(626,797)(627,796)(628,795)(629,794)(630,793)(631,806)(632,812)(633,811)(634,810)(635,809)(636,808)(637,807)(638,799)(639,805)(640,804)(641,803)(642,802)(643,801)(644,800)(645,827)(646,833)(647,832)(648,831)(649,830)(650,829)(651,828)(652,834)(653,840)(654,839)(655,838)(656,837)(657,836)(658,835)(659,813)(660,819)(661,818)(662,817)(663,816)(664,815)(665,814)(666,820)(667,826)(668,825)(669,824)(670,823)(671,822)(672,821);
s1 := Sym(896)!(  1,450)(  2,449)(  3,455)(  4,454)(  5,453)(  6,452)(  7,451)(  8,457)(  9,456)( 10,462)( 11,461)( 12,460)( 13,459)( 14,458)( 15,471)( 16,470)( 17,476)( 18,475)( 19,474)( 20,473)( 21,472)( 22,464)( 23,463)( 24,469)( 25,468)( 26,467)( 27,466)( 28,465)( 29,492)( 30,491)( 31,497)( 32,496)( 33,495)( 34,494)( 35,493)( 36,499)( 37,498)( 38,504)( 39,503)( 40,502)( 41,501)( 42,500)( 43,478)( 44,477)( 45,483)( 46,482)( 47,481)( 48,480)( 49,479)( 50,485)( 51,484)( 52,490)( 53,489)( 54,488)( 55,487)( 56,486)( 57,534)( 58,533)( 59,539)( 60,538)( 61,537)( 62,536)( 63,535)( 64,541)( 65,540)( 66,546)( 67,545)( 68,544)( 69,543)( 70,542)( 71,555)( 72,554)( 73,560)( 74,559)( 75,558)( 76,557)( 77,556)( 78,548)( 79,547)( 80,553)( 81,552)( 82,551)( 83,550)( 84,549)( 85,506)( 86,505)( 87,511)( 88,510)( 89,509)( 90,508)( 91,507)( 92,513)( 93,512)( 94,518)( 95,517)( 96,516)( 97,515)( 98,514)( 99,527)(100,526)(101,532)(102,531)(103,530)(104,529)(105,528)(106,520)(107,519)(108,525)(109,524)(110,523)(111,522)(112,521)(113,618)(114,617)(115,623)(116,622)(117,621)(118,620)(119,619)(120,625)(121,624)(122,630)(123,629)(124,628)(125,627)(126,626)(127,639)(128,638)(129,644)(130,643)(131,642)(132,641)(133,640)(134,632)(135,631)(136,637)(137,636)(138,635)(139,634)(140,633)(141,660)(142,659)(143,665)(144,664)(145,663)(146,662)(147,661)(148,667)(149,666)(150,672)(151,671)(152,670)(153,669)(154,668)(155,646)(156,645)(157,651)(158,650)(159,649)(160,648)(161,647)(162,653)(163,652)(164,658)(165,657)(166,656)(167,655)(168,654)(169,562)(170,561)(171,567)(172,566)(173,565)(174,564)(175,563)(176,569)(177,568)(178,574)(179,573)(180,572)(181,571)(182,570)(183,583)(184,582)(185,588)(186,587)(187,586)(188,585)(189,584)(190,576)(191,575)(192,581)(193,580)(194,579)(195,578)(196,577)(197,604)(198,603)(199,609)(200,608)(201,607)(202,606)(203,605)(204,611)(205,610)(206,616)(207,615)(208,614)(209,613)(210,612)(211,590)(212,589)(213,595)(214,594)(215,593)(216,592)(217,591)(218,597)(219,596)(220,602)(221,601)(222,600)(223,599)(224,598)(225,786)(226,785)(227,791)(228,790)(229,789)(230,788)(231,787)(232,793)(233,792)(234,798)(235,797)(236,796)(237,795)(238,794)(239,807)(240,806)(241,812)(242,811)(243,810)(244,809)(245,808)(246,800)(247,799)(248,805)(249,804)(250,803)(251,802)(252,801)(253,828)(254,827)(255,833)(256,832)(257,831)(258,830)(259,829)(260,835)(261,834)(262,840)(263,839)(264,838)(265,837)(266,836)(267,814)(268,813)(269,819)(270,818)(271,817)(272,816)(273,815)(274,821)(275,820)(276,826)(277,825)(278,824)(279,823)(280,822)(281,870)(282,869)(283,875)(284,874)(285,873)(286,872)(287,871)(288,877)(289,876)(290,882)(291,881)(292,880)(293,879)(294,878)(295,891)(296,890)(297,896)(298,895)(299,894)(300,893)(301,892)(302,884)(303,883)(304,889)(305,888)(306,887)(307,886)(308,885)(309,842)(310,841)(311,847)(312,846)(313,845)(314,844)(315,843)(316,849)(317,848)(318,854)(319,853)(320,852)(321,851)(322,850)(323,863)(324,862)(325,868)(326,867)(327,866)(328,865)(329,864)(330,856)(331,855)(332,861)(333,860)(334,859)(335,858)(336,857)(337,674)(338,673)(339,679)(340,678)(341,677)(342,676)(343,675)(344,681)(345,680)(346,686)(347,685)(348,684)(349,683)(350,682)(351,695)(352,694)(353,700)(354,699)(355,698)(356,697)(357,696)(358,688)(359,687)(360,693)(361,692)(362,691)(363,690)(364,689)(365,716)(366,715)(367,721)(368,720)(369,719)(370,718)(371,717)(372,723)(373,722)(374,728)(375,727)(376,726)(377,725)(378,724)(379,702)(380,701)(381,707)(382,706)(383,705)(384,704)(385,703)(386,709)(387,708)(388,714)(389,713)(390,712)(391,711)(392,710)(393,758)(394,757)(395,763)(396,762)(397,761)(398,760)(399,759)(400,765)(401,764)(402,770)(403,769)(404,768)(405,767)(406,766)(407,779)(408,778)(409,784)(410,783)(411,782)(412,781)(413,780)(414,772)(415,771)(416,777)(417,776)(418,775)(419,774)(420,773)(421,730)(422,729)(423,735)(424,734)(425,733)(426,732)(427,731)(428,737)(429,736)(430,742)(431,741)(432,740)(433,739)(434,738)(435,751)(436,750)(437,756)(438,755)(439,754)(440,753)(441,752)(442,744)(443,743)(444,749)(445,748)(446,747)(447,746)(448,745);
poly := sub<Sym(896)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 

References

None.

to this polytope.