Part of the Atlas of Small Regular Polytopes

Polytope of Type {900}

Atlas Canonical Name {900}*1800

Overview

Group
SmallGroup(1800,27)
Rank
2
Schläfli Type
{900}
Vertices, edges, …
900, 900
Order of s0s1
900
Also known as
900-gon, {900}. 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

5-fold

6-fold

9-fold

10-fold

12-fold

15-fold

18-fold

20-fold

25-fold

30-fold

36-fold

45-fold

50-fold

60-fold

75-fold

90-fold

100-fold

150-fold

180-fold

225-fold

300-fold

450-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,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)( 16, 65)( 17, 64)( 18, 63)( 19, 62)( 20, 61)( 21, 75)( 22, 74)( 23, 73)( 24, 72)( 25, 71)( 26, 70)( 27, 69)( 28, 68)( 29, 67)( 30, 66)( 31, 50)( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 60)( 37, 59)( 38, 58)( 39, 57)( 40, 56)( 41, 55)( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 76,161)( 77,165)( 78,164)( 79,163)( 80,162)( 81,156)( 82,160)( 83,159)( 84,158)( 85,157)( 86,151)( 87,155)( 88,154)( 89,153)( 90,152)( 91,225)( 92,224)( 93,223)( 94,222)( 95,221)( 96,220)( 97,219)( 98,218)( 99,217)(100,216)(101,215)(102,214)(103,213)(104,212)(105,211)(106,210)(107,209)(108,208)(109,207)(110,206)(111,205)(112,204)(113,203)(114,202)(115,201)(116,200)(117,199)(118,198)(119,197)(120,196)(121,195)(122,194)(123,193)(124,192)(125,191)(126,190)(127,189)(128,188)(129,187)(130,186)(131,185)(132,184)(133,183)(134,182)(135,181)(136,180)(137,179)(138,178)(139,177)(140,176)(141,175)(142,174)(143,173)(144,172)(145,171)(146,170)(147,169)(148,168)(149,167)(150,166)(227,230)(228,229)(231,236)(232,240)(233,239)(234,238)(235,237)(241,290)(242,289)(243,288)(244,287)(245,286)(246,300)(247,299)(248,298)(249,297)(250,296)(251,295)(252,294)(253,293)(254,292)(255,291)(256,275)(257,274)(258,273)(259,272)(260,271)(261,285)(262,284)(263,283)(264,282)(265,281)(266,280)(267,279)(268,278)(269,277)(270,276)(301,386)(302,390)(303,389)(304,388)(305,387)(306,381)(307,385)(308,384)(309,383)(310,382)(311,376)(312,380)(313,379)(314,378)(315,377)(316,450)(317,449)(318,448)(319,447)(320,446)(321,445)(322,444)(323,443)(324,442)(325,441)(326,440)(327,439)(328,438)(329,437)(330,436)(331,435)(332,434)(333,433)(334,432)(335,431)(336,430)(337,429)(338,428)(339,427)(340,426)(341,425)(342,424)(343,423)(344,422)(345,421)(346,420)(347,419)(348,418)(349,417)(350,416)(351,415)(352,414)(353,413)(354,412)(355,411)(356,410)(357,409)(358,408)(359,407)(360,406)(361,405)(362,404)(363,403)(364,402)(365,401)(366,400)(367,399)(368,398)(369,397)(370,396)(371,395)(372,394)(373,393)(374,392)(375,391)(451,676)(452,680)(453,679)(454,678)(455,677)(456,686)(457,690)(458,689)(459,688)(460,687)(461,681)(462,685)(463,684)(464,683)(465,682)(466,740)(467,739)(468,738)(469,737)(470,736)(471,750)(472,749)(473,748)(474,747)(475,746)(476,745)(477,744)(478,743)(479,742)(480,741)(481,725)(482,724)(483,723)(484,722)(485,721)(486,735)(487,734)(488,733)(489,732)(490,731)(491,730)(492,729)(493,728)(494,727)(495,726)(496,710)(497,709)(498,708)(499,707)(500,706)(501,720)(502,719)(503,718)(504,717)(505,716)(506,715)(507,714)(508,713)(509,712)(510,711)(511,695)(512,694)(513,693)(514,692)(515,691)(516,705)(517,704)(518,703)(519,702)(520,701)(521,700)(522,699)(523,698)(524,697)(525,696)(526,836)(527,840)(528,839)(529,838)(530,837)(531,831)(532,835)(533,834)(534,833)(535,832)(536,826)(537,830)(538,829)(539,828)(540,827)(541,900)(542,899)(543,898)(544,897)(545,896)(546,895)(547,894)(548,893)(549,892)(550,891)(551,890)(552,889)(553,888)(554,887)(555,886)(556,885)(557,884)(558,883)(559,882)(560,881)(561,880)(562,879)(563,878)(564,877)(565,876)(566,875)(567,874)(568,873)(569,872)(570,871)(571,870)(572,869)(573,868)(574,867)(575,866)(576,865)(577,864)(578,863)(579,862)(580,861)(581,860)(582,859)(583,858)(584,857)(585,856)(586,855)(587,854)(588,853)(589,852)(590,851)(591,850)(592,849)(593,848)(594,847)(595,846)(596,845)(597,844)(598,843)(599,842)(600,841)(601,761)(602,765)(603,764)(604,763)(605,762)(606,756)(607,760)(608,759)(609,758)(610,757)(611,751)(612,755)(613,754)(614,753)(615,752)(616,825)(617,824)(618,823)(619,822)(620,821)(621,820)(622,819)(623,818)(624,817)(625,816)(626,815)(627,814)(628,813)(629,812)(630,811)(631,810)(632,809)(633,808)(634,807)(635,806)(636,805)(637,804)(638,803)(639,802)(640,801)(641,800)(642,799)(643,798)(644,797)(645,796)(646,795)(647,794)(648,793)(649,792)(650,791)(651,790)(652,789)(653,788)(654,787)(655,786)(656,785)(657,784)(658,783)(659,782)(660,781)(661,780)(662,779)(663,778)(664,777)(665,776)(666,775)(667,774)(668,773)(669,772)(670,771)(671,770)(672,769)(673,768)(674,767)(675,766);;
s1 := (  1,541)(  2,545)(  3,544)(  4,543)(  5,542)(  6,551)(  7,555)(  8,554)(  9,553)( 10,552)( 11,546)( 12,550)( 13,549)( 14,548)( 15,547)( 16,526)( 17,530)( 18,529)( 19,528)( 20,527)( 21,536)( 22,540)( 23,539)( 24,538)( 25,537)( 26,531)( 27,535)( 28,534)( 29,533)( 30,532)( 31,590)( 32,589)( 33,588)( 34,587)( 35,586)( 36,600)( 37,599)( 38,598)( 39,597)( 40,596)( 41,595)( 42,594)( 43,593)( 44,592)( 45,591)( 46,575)( 47,574)( 48,573)( 49,572)( 50,571)( 51,585)( 52,584)( 53,583)( 54,582)( 55,581)( 56,580)( 57,579)( 58,578)( 59,577)( 60,576)( 61,560)( 62,559)( 63,558)( 64,557)( 65,556)( 66,570)( 67,569)( 68,568)( 69,567)( 70,566)( 71,565)( 72,564)( 73,563)( 74,562)( 75,561)( 76,466)( 77,470)( 78,469)( 79,468)( 80,467)( 81,476)( 82,480)( 83,479)( 84,478)( 85,477)( 86,471)( 87,475)( 88,474)( 89,473)( 90,472)( 91,451)( 92,455)( 93,454)( 94,453)( 95,452)( 96,461)( 97,465)( 98,464)( 99,463)(100,462)(101,456)(102,460)(103,459)(104,458)(105,457)(106,515)(107,514)(108,513)(109,512)(110,511)(111,525)(112,524)(113,523)(114,522)(115,521)(116,520)(117,519)(118,518)(119,517)(120,516)(121,500)(122,499)(123,498)(124,497)(125,496)(126,510)(127,509)(128,508)(129,507)(130,506)(131,505)(132,504)(133,503)(134,502)(135,501)(136,485)(137,484)(138,483)(139,482)(140,481)(141,495)(142,494)(143,493)(144,492)(145,491)(146,490)(147,489)(148,488)(149,487)(150,486)(151,626)(152,630)(153,629)(154,628)(155,627)(156,621)(157,625)(158,624)(159,623)(160,622)(161,616)(162,620)(163,619)(164,618)(165,617)(166,611)(167,615)(168,614)(169,613)(170,612)(171,606)(172,610)(173,609)(174,608)(175,607)(176,601)(177,605)(178,604)(179,603)(180,602)(181,675)(182,674)(183,673)(184,672)(185,671)(186,670)(187,669)(188,668)(189,667)(190,666)(191,665)(192,664)(193,663)(194,662)(195,661)(196,660)(197,659)(198,658)(199,657)(200,656)(201,655)(202,654)(203,653)(204,652)(205,651)(206,650)(207,649)(208,648)(209,647)(210,646)(211,645)(212,644)(213,643)(214,642)(215,641)(216,640)(217,639)(218,638)(219,637)(220,636)(221,635)(222,634)(223,633)(224,632)(225,631)(226,766)(227,770)(228,769)(229,768)(230,767)(231,776)(232,780)(233,779)(234,778)(235,777)(236,771)(237,775)(238,774)(239,773)(240,772)(241,751)(242,755)(243,754)(244,753)(245,752)(246,761)(247,765)(248,764)(249,763)(250,762)(251,756)(252,760)(253,759)(254,758)(255,757)(256,815)(257,814)(258,813)(259,812)(260,811)(261,825)(262,824)(263,823)(264,822)(265,821)(266,820)(267,819)(268,818)(269,817)(270,816)(271,800)(272,799)(273,798)(274,797)(275,796)(276,810)(277,809)(278,808)(279,807)(280,806)(281,805)(282,804)(283,803)(284,802)(285,801)(286,785)(287,784)(288,783)(289,782)(290,781)(291,795)(292,794)(293,793)(294,792)(295,791)(296,790)(297,789)(298,788)(299,787)(300,786)(301,691)(302,695)(303,694)(304,693)(305,692)(306,701)(307,705)(308,704)(309,703)(310,702)(311,696)(312,700)(313,699)(314,698)(315,697)(316,676)(317,680)(318,679)(319,678)(320,677)(321,686)(322,690)(323,689)(324,688)(325,687)(326,681)(327,685)(328,684)(329,683)(330,682)(331,740)(332,739)(333,738)(334,737)(335,736)(336,750)(337,749)(338,748)(339,747)(340,746)(341,745)(342,744)(343,743)(344,742)(345,741)(346,725)(347,724)(348,723)(349,722)(350,721)(351,735)(352,734)(353,733)(354,732)(355,731)(356,730)(357,729)(358,728)(359,727)(360,726)(361,710)(362,709)(363,708)(364,707)(365,706)(366,720)(367,719)(368,718)(369,717)(370,716)(371,715)(372,714)(373,713)(374,712)(375,711)(376,851)(377,855)(378,854)(379,853)(380,852)(381,846)(382,850)(383,849)(384,848)(385,847)(386,841)(387,845)(388,844)(389,843)(390,842)(391,836)(392,840)(393,839)(394,838)(395,837)(396,831)(397,835)(398,834)(399,833)(400,832)(401,826)(402,830)(403,829)(404,828)(405,827)(406,900)(407,899)(408,898)(409,897)(410,896)(411,895)(412,894)(413,893)(414,892)(415,891)(416,890)(417,889)(418,888)(419,887)(420,886)(421,885)(422,884)(423,883)(424,882)(425,881)(426,880)(427,879)(428,878)(429,877)(430,876)(431,875)(432,874)(433,873)(434,872)(435,871)(436,870)(437,869)(438,868)(439,867)(440,866)(441,865)(442,864)(443,863)(444,862)(445,861)(446,860)(447,859)(448,858)(449,857)(450,856);;
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(900)!(  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)( 16, 65)( 17, 64)( 18, 63)( 19, 62)( 20, 61)( 21, 75)( 22, 74)( 23, 73)( 24, 72)( 25, 71)( 26, 70)( 27, 69)( 28, 68)( 29, 67)( 30, 66)( 31, 50)( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 60)( 37, 59)( 38, 58)( 39, 57)( 40, 56)( 41, 55)( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 76,161)( 77,165)( 78,164)( 79,163)( 80,162)( 81,156)( 82,160)( 83,159)( 84,158)( 85,157)( 86,151)( 87,155)( 88,154)( 89,153)( 90,152)( 91,225)( 92,224)( 93,223)( 94,222)( 95,221)( 96,220)( 97,219)( 98,218)( 99,217)(100,216)(101,215)(102,214)(103,213)(104,212)(105,211)(106,210)(107,209)(108,208)(109,207)(110,206)(111,205)(112,204)(113,203)(114,202)(115,201)(116,200)(117,199)(118,198)(119,197)(120,196)(121,195)(122,194)(123,193)(124,192)(125,191)(126,190)(127,189)(128,188)(129,187)(130,186)(131,185)(132,184)(133,183)(134,182)(135,181)(136,180)(137,179)(138,178)(139,177)(140,176)(141,175)(142,174)(143,173)(144,172)(145,171)(146,170)(147,169)(148,168)(149,167)(150,166)(227,230)(228,229)(231,236)(232,240)(233,239)(234,238)(235,237)(241,290)(242,289)(243,288)(244,287)(245,286)(246,300)(247,299)(248,298)(249,297)(250,296)(251,295)(252,294)(253,293)(254,292)(255,291)(256,275)(257,274)(258,273)(259,272)(260,271)(261,285)(262,284)(263,283)(264,282)(265,281)(266,280)(267,279)(268,278)(269,277)(270,276)(301,386)(302,390)(303,389)(304,388)(305,387)(306,381)(307,385)(308,384)(309,383)(310,382)(311,376)(312,380)(313,379)(314,378)(315,377)(316,450)(317,449)(318,448)(319,447)(320,446)(321,445)(322,444)(323,443)(324,442)(325,441)(326,440)(327,439)(328,438)(329,437)(330,436)(331,435)(332,434)(333,433)(334,432)(335,431)(336,430)(337,429)(338,428)(339,427)(340,426)(341,425)(342,424)(343,423)(344,422)(345,421)(346,420)(347,419)(348,418)(349,417)(350,416)(351,415)(352,414)(353,413)(354,412)(355,411)(356,410)(357,409)(358,408)(359,407)(360,406)(361,405)(362,404)(363,403)(364,402)(365,401)(366,400)(367,399)(368,398)(369,397)(370,396)(371,395)(372,394)(373,393)(374,392)(375,391)(451,676)(452,680)(453,679)(454,678)(455,677)(456,686)(457,690)(458,689)(459,688)(460,687)(461,681)(462,685)(463,684)(464,683)(465,682)(466,740)(467,739)(468,738)(469,737)(470,736)(471,750)(472,749)(473,748)(474,747)(475,746)(476,745)(477,744)(478,743)(479,742)(480,741)(481,725)(482,724)(483,723)(484,722)(485,721)(486,735)(487,734)(488,733)(489,732)(490,731)(491,730)(492,729)(493,728)(494,727)(495,726)(496,710)(497,709)(498,708)(499,707)(500,706)(501,720)(502,719)(503,718)(504,717)(505,716)(506,715)(507,714)(508,713)(509,712)(510,711)(511,695)(512,694)(513,693)(514,692)(515,691)(516,705)(517,704)(518,703)(519,702)(520,701)(521,700)(522,699)(523,698)(524,697)(525,696)(526,836)(527,840)(528,839)(529,838)(530,837)(531,831)(532,835)(533,834)(534,833)(535,832)(536,826)(537,830)(538,829)(539,828)(540,827)(541,900)(542,899)(543,898)(544,897)(545,896)(546,895)(547,894)(548,893)(549,892)(550,891)(551,890)(552,889)(553,888)(554,887)(555,886)(556,885)(557,884)(558,883)(559,882)(560,881)(561,880)(562,879)(563,878)(564,877)(565,876)(566,875)(567,874)(568,873)(569,872)(570,871)(571,870)(572,869)(573,868)(574,867)(575,866)(576,865)(577,864)(578,863)(579,862)(580,861)(581,860)(582,859)(583,858)(584,857)(585,856)(586,855)(587,854)(588,853)(589,852)(590,851)(591,850)(592,849)(593,848)(594,847)(595,846)(596,845)(597,844)(598,843)(599,842)(600,841)(601,761)(602,765)(603,764)(604,763)(605,762)(606,756)(607,760)(608,759)(609,758)(610,757)(611,751)(612,755)(613,754)(614,753)(615,752)(616,825)(617,824)(618,823)(619,822)(620,821)(621,820)(622,819)(623,818)(624,817)(625,816)(626,815)(627,814)(628,813)(629,812)(630,811)(631,810)(632,809)(633,808)(634,807)(635,806)(636,805)(637,804)(638,803)(639,802)(640,801)(641,800)(642,799)(643,798)(644,797)(645,796)(646,795)(647,794)(648,793)(649,792)(650,791)(651,790)(652,789)(653,788)(654,787)(655,786)(656,785)(657,784)(658,783)(659,782)(660,781)(661,780)(662,779)(663,778)(664,777)(665,776)(666,775)(667,774)(668,773)(669,772)(670,771)(671,770)(672,769)(673,768)(674,767)(675,766);
s1 := Sym(900)!(  1,541)(  2,545)(  3,544)(  4,543)(  5,542)(  6,551)(  7,555)(  8,554)(  9,553)( 10,552)( 11,546)( 12,550)( 13,549)( 14,548)( 15,547)( 16,526)( 17,530)( 18,529)( 19,528)( 20,527)( 21,536)( 22,540)( 23,539)( 24,538)( 25,537)( 26,531)( 27,535)( 28,534)( 29,533)( 30,532)( 31,590)( 32,589)( 33,588)( 34,587)( 35,586)( 36,600)( 37,599)( 38,598)( 39,597)( 40,596)( 41,595)( 42,594)( 43,593)( 44,592)( 45,591)( 46,575)( 47,574)( 48,573)( 49,572)( 50,571)( 51,585)( 52,584)( 53,583)( 54,582)( 55,581)( 56,580)( 57,579)( 58,578)( 59,577)( 60,576)( 61,560)( 62,559)( 63,558)( 64,557)( 65,556)( 66,570)( 67,569)( 68,568)( 69,567)( 70,566)( 71,565)( 72,564)( 73,563)( 74,562)( 75,561)( 76,466)( 77,470)( 78,469)( 79,468)( 80,467)( 81,476)( 82,480)( 83,479)( 84,478)( 85,477)( 86,471)( 87,475)( 88,474)( 89,473)( 90,472)( 91,451)( 92,455)( 93,454)( 94,453)( 95,452)( 96,461)( 97,465)( 98,464)( 99,463)(100,462)(101,456)(102,460)(103,459)(104,458)(105,457)(106,515)(107,514)(108,513)(109,512)(110,511)(111,525)(112,524)(113,523)(114,522)(115,521)(116,520)(117,519)(118,518)(119,517)(120,516)(121,500)(122,499)(123,498)(124,497)(125,496)(126,510)(127,509)(128,508)(129,507)(130,506)(131,505)(132,504)(133,503)(134,502)(135,501)(136,485)(137,484)(138,483)(139,482)(140,481)(141,495)(142,494)(143,493)(144,492)(145,491)(146,490)(147,489)(148,488)(149,487)(150,486)(151,626)(152,630)(153,629)(154,628)(155,627)(156,621)(157,625)(158,624)(159,623)(160,622)(161,616)(162,620)(163,619)(164,618)(165,617)(166,611)(167,615)(168,614)(169,613)(170,612)(171,606)(172,610)(173,609)(174,608)(175,607)(176,601)(177,605)(178,604)(179,603)(180,602)(181,675)(182,674)(183,673)(184,672)(185,671)(186,670)(187,669)(188,668)(189,667)(190,666)(191,665)(192,664)(193,663)(194,662)(195,661)(196,660)(197,659)(198,658)(199,657)(200,656)(201,655)(202,654)(203,653)(204,652)(205,651)(206,650)(207,649)(208,648)(209,647)(210,646)(211,645)(212,644)(213,643)(214,642)(215,641)(216,640)(217,639)(218,638)(219,637)(220,636)(221,635)(222,634)(223,633)(224,632)(225,631)(226,766)(227,770)(228,769)(229,768)(230,767)(231,776)(232,780)(233,779)(234,778)(235,777)(236,771)(237,775)(238,774)(239,773)(240,772)(241,751)(242,755)(243,754)(244,753)(245,752)(246,761)(247,765)(248,764)(249,763)(250,762)(251,756)(252,760)(253,759)(254,758)(255,757)(256,815)(257,814)(258,813)(259,812)(260,811)(261,825)(262,824)(263,823)(264,822)(265,821)(266,820)(267,819)(268,818)(269,817)(270,816)(271,800)(272,799)(273,798)(274,797)(275,796)(276,810)(277,809)(278,808)(279,807)(280,806)(281,805)(282,804)(283,803)(284,802)(285,801)(286,785)(287,784)(288,783)(289,782)(290,781)(291,795)(292,794)(293,793)(294,792)(295,791)(296,790)(297,789)(298,788)(299,787)(300,786)(301,691)(302,695)(303,694)(304,693)(305,692)(306,701)(307,705)(308,704)(309,703)(310,702)(311,696)(312,700)(313,699)(314,698)(315,697)(316,676)(317,680)(318,679)(319,678)(320,677)(321,686)(322,690)(323,689)(324,688)(325,687)(326,681)(327,685)(328,684)(329,683)(330,682)(331,740)(332,739)(333,738)(334,737)(335,736)(336,750)(337,749)(338,748)(339,747)(340,746)(341,745)(342,744)(343,743)(344,742)(345,741)(346,725)(347,724)(348,723)(349,722)(350,721)(351,735)(352,734)(353,733)(354,732)(355,731)(356,730)(357,729)(358,728)(359,727)(360,726)(361,710)(362,709)(363,708)(364,707)(365,706)(366,720)(367,719)(368,718)(369,717)(370,716)(371,715)(372,714)(373,713)(374,712)(375,711)(376,851)(377,855)(378,854)(379,853)(380,852)(381,846)(382,850)(383,849)(384,848)(385,847)(386,841)(387,845)(388,844)(389,843)(390,842)(391,836)(392,840)(393,839)(394,838)(395,837)(396,831)(397,835)(398,834)(399,833)(400,832)(401,826)(402,830)(403,829)(404,828)(405,827)(406,900)(407,899)(408,898)(409,897)(410,896)(411,895)(412,894)(413,893)(414,892)(415,891)(416,890)(417,889)(418,888)(419,887)(420,886)(421,885)(422,884)(423,883)(424,882)(425,881)(426,880)(427,879)(428,878)(429,877)(430,876)(431,875)(432,874)(433,873)(434,872)(435,871)(436,870)(437,869)(438,868)(439,867)(440,866)(441,865)(442,864)(443,863)(444,862)(445,861)(446,860)(447,859)(448,858)(449,857)(450,856);
poly := sub<Sym(900)|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*s0*s1*s0*s1*s0*s1*s0*s1 >; 

References

None.

to this polytope.