Polytope of Type {118,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {118,8}*1888
Also Known As : {118,8|2}. if this polytope has another name.
Group : SmallGroup(1888,155)
Rank : 3
Schlafli Type : {118,8}
Number of vertices, edges, etc : 118, 472, 8
Order of s0s1s2 : 472
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {118,4}*944
4-fold quotients : {118,2}*472
8-fold quotients : {59,2}*236
59-fold quotients : {2,8}*32
118-fold quotients : {2,4}*16
236-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,237)( 2,295)( 3,294)( 4,293)( 5,292)( 6,291)( 7,290)( 8,289)
( 9,288)( 10,287)( 11,286)( 12,285)( 13,284)( 14,283)( 15,282)( 16,281)
( 17,280)( 18,279)( 19,278)( 20,277)( 21,276)( 22,275)( 23,274)( 24,273)
( 25,272)( 26,271)( 27,270)( 28,269)( 29,268)( 30,267)( 31,266)( 32,265)
( 33,264)( 34,263)( 35,262)( 36,261)( 37,260)( 38,259)( 39,258)( 40,257)
( 41,256)( 42,255)( 43,254)( 44,253)( 45,252)( 46,251)( 47,250)( 48,249)
( 49,248)( 50,247)( 51,246)( 52,245)( 53,244)( 54,243)( 55,242)( 56,241)
( 57,240)( 58,239)( 59,238)( 60,296)( 61,354)( 62,353)( 63,352)( 64,351)
( 65,350)( 66,349)( 67,348)( 68,347)( 69,346)( 70,345)( 71,344)( 72,343)
( 73,342)( 74,341)( 75,340)( 76,339)( 77,338)( 78,337)( 79,336)( 80,335)
( 81,334)( 82,333)( 83,332)( 84,331)( 85,330)( 86,329)( 87,328)( 88,327)
( 89,326)( 90,325)( 91,324)( 92,323)( 93,322)( 94,321)( 95,320)( 96,319)
( 97,318)( 98,317)( 99,316)(100,315)(101,314)(102,313)(103,312)(104,311)
(105,310)(106,309)(107,308)(108,307)(109,306)(110,305)(111,304)(112,303)
(113,302)(114,301)(115,300)(116,299)(117,298)(118,297)(119,355)(120,413)
(121,412)(122,411)(123,410)(124,409)(125,408)(126,407)(127,406)(128,405)
(129,404)(130,403)(131,402)(132,401)(133,400)(134,399)(135,398)(136,397)
(137,396)(138,395)(139,394)(140,393)(141,392)(142,391)(143,390)(144,389)
(145,388)(146,387)(147,386)(148,385)(149,384)(150,383)(151,382)(152,381)
(153,380)(154,379)(155,378)(156,377)(157,376)(158,375)(159,374)(160,373)
(161,372)(162,371)(163,370)(164,369)(165,368)(166,367)(167,366)(168,365)
(169,364)(170,363)(171,362)(172,361)(173,360)(174,359)(175,358)(176,357)
(177,356)(178,414)(179,472)(180,471)(181,470)(182,469)(183,468)(184,467)
(185,466)(186,465)(187,464)(188,463)(189,462)(190,461)(191,460)(192,459)
(193,458)(194,457)(195,456)(196,455)(197,454)(198,453)(199,452)(200,451)
(201,450)(202,449)(203,448)(204,447)(205,446)(206,445)(207,444)(208,443)
(209,442)(210,441)(211,440)(212,439)(213,438)(214,437)(215,436)(216,435)
(217,434)(218,433)(219,432)(220,431)(221,430)(222,429)(223,428)(224,427)
(225,426)(226,425)(227,424)(228,423)(229,422)(230,421)(231,420)(232,419)
(233,418)(234,417)(235,416)(236,415)(473,709)(474,767)(475,766)(476,765)
(477,764)(478,763)(479,762)(480,761)(481,760)(482,759)(483,758)(484,757)
(485,756)(486,755)(487,754)(488,753)(489,752)(490,751)(491,750)(492,749)
(493,748)(494,747)(495,746)(496,745)(497,744)(498,743)(499,742)(500,741)
(501,740)(502,739)(503,738)(504,737)(505,736)(506,735)(507,734)(508,733)
(509,732)(510,731)(511,730)(512,729)(513,728)(514,727)(515,726)(516,725)
(517,724)(518,723)(519,722)(520,721)(521,720)(522,719)(523,718)(524,717)
(525,716)(526,715)(527,714)(528,713)(529,712)(530,711)(531,710)(532,768)
(533,826)(534,825)(535,824)(536,823)(537,822)(538,821)(539,820)(540,819)
(541,818)(542,817)(543,816)(544,815)(545,814)(546,813)(547,812)(548,811)
(549,810)(550,809)(551,808)(552,807)(553,806)(554,805)(555,804)(556,803)
(557,802)(558,801)(559,800)(560,799)(561,798)(562,797)(563,796)(564,795)
(565,794)(566,793)(567,792)(568,791)(569,790)(570,789)(571,788)(572,787)
(573,786)(574,785)(575,784)(576,783)(577,782)(578,781)(579,780)(580,779)
(581,778)(582,777)(583,776)(584,775)(585,774)(586,773)(587,772)(588,771)
(589,770)(590,769)(591,827)(592,885)(593,884)(594,883)(595,882)(596,881)
(597,880)(598,879)(599,878)(600,877)(601,876)(602,875)(603,874)(604,873)
(605,872)(606,871)(607,870)(608,869)(609,868)(610,867)(611,866)(612,865)
(613,864)(614,863)(615,862)(616,861)(617,860)(618,859)(619,858)(620,857)
(621,856)(622,855)(623,854)(624,853)(625,852)(626,851)(627,850)(628,849)
(629,848)(630,847)(631,846)(632,845)(633,844)(634,843)(635,842)(636,841)
(637,840)(638,839)(639,838)(640,837)(641,836)(642,835)(643,834)(644,833)
(645,832)(646,831)(647,830)(648,829)(649,828)(650,886)(651,944)(652,943)
(653,942)(654,941)(655,940)(656,939)(657,938)(658,937)(659,936)(660,935)
(661,934)(662,933)(663,932)(664,931)(665,930)(666,929)(667,928)(668,927)
(669,926)(670,925)(671,924)(672,923)(673,922)(674,921)(675,920)(676,919)
(677,918)(678,917)(679,916)(680,915)(681,914)(682,913)(683,912)(684,911)
(685,910)(686,909)(687,908)(688,907)(689,906)(690,905)(691,904)(692,903)
(693,902)(694,901)(695,900)(696,899)(697,898)(698,897)(699,896)(700,895)
(701,894)(702,893)(703,892)(704,891)(705,890)(706,889)(707,888)(708,887);;
s1 := ( 1,238)( 2,237)( 3,295)( 4,294)( 5,293)( 6,292)( 7,291)( 8,290)
( 9,289)( 10,288)( 11,287)( 12,286)( 13,285)( 14,284)( 15,283)( 16,282)
( 17,281)( 18,280)( 19,279)( 20,278)( 21,277)( 22,276)( 23,275)( 24,274)
( 25,273)( 26,272)( 27,271)( 28,270)( 29,269)( 30,268)( 31,267)( 32,266)
( 33,265)( 34,264)( 35,263)( 36,262)( 37,261)( 38,260)( 39,259)( 40,258)
( 41,257)( 42,256)( 43,255)( 44,254)( 45,253)( 46,252)( 47,251)( 48,250)
( 49,249)( 50,248)( 51,247)( 52,246)( 53,245)( 54,244)( 55,243)( 56,242)
( 57,241)( 58,240)( 59,239)( 60,297)( 61,296)( 62,354)( 63,353)( 64,352)
( 65,351)( 66,350)( 67,349)( 68,348)( 69,347)( 70,346)( 71,345)( 72,344)
( 73,343)( 74,342)( 75,341)( 76,340)( 77,339)( 78,338)( 79,337)( 80,336)
( 81,335)( 82,334)( 83,333)( 84,332)( 85,331)( 86,330)( 87,329)( 88,328)
( 89,327)( 90,326)( 91,325)( 92,324)( 93,323)( 94,322)( 95,321)( 96,320)
( 97,319)( 98,318)( 99,317)(100,316)(101,315)(102,314)(103,313)(104,312)
(105,311)(106,310)(107,309)(108,308)(109,307)(110,306)(111,305)(112,304)
(113,303)(114,302)(115,301)(116,300)(117,299)(118,298)(119,415)(120,414)
(121,472)(122,471)(123,470)(124,469)(125,468)(126,467)(127,466)(128,465)
(129,464)(130,463)(131,462)(132,461)(133,460)(134,459)(135,458)(136,457)
(137,456)(138,455)(139,454)(140,453)(141,452)(142,451)(143,450)(144,449)
(145,448)(146,447)(147,446)(148,445)(149,444)(150,443)(151,442)(152,441)
(153,440)(154,439)(155,438)(156,437)(157,436)(158,435)(159,434)(160,433)
(161,432)(162,431)(163,430)(164,429)(165,428)(166,427)(167,426)(168,425)
(169,424)(170,423)(171,422)(172,421)(173,420)(174,419)(175,418)(176,417)
(177,416)(178,356)(179,355)(180,413)(181,412)(182,411)(183,410)(184,409)
(185,408)(186,407)(187,406)(188,405)(189,404)(190,403)(191,402)(192,401)
(193,400)(194,399)(195,398)(196,397)(197,396)(198,395)(199,394)(200,393)
(201,392)(202,391)(203,390)(204,389)(205,388)(206,387)(207,386)(208,385)
(209,384)(210,383)(211,382)(212,381)(213,380)(214,379)(215,378)(216,377)
(217,376)(218,375)(219,374)(220,373)(221,372)(222,371)(223,370)(224,369)
(225,368)(226,367)(227,366)(228,365)(229,364)(230,363)(231,362)(232,361)
(233,360)(234,359)(235,358)(236,357)(473,828)(474,827)(475,885)(476,884)
(477,883)(478,882)(479,881)(480,880)(481,879)(482,878)(483,877)(484,876)
(485,875)(486,874)(487,873)(488,872)(489,871)(490,870)(491,869)(492,868)
(493,867)(494,866)(495,865)(496,864)(497,863)(498,862)(499,861)(500,860)
(501,859)(502,858)(503,857)(504,856)(505,855)(506,854)(507,853)(508,852)
(509,851)(510,850)(511,849)(512,848)(513,847)(514,846)(515,845)(516,844)
(517,843)(518,842)(519,841)(520,840)(521,839)(522,838)(523,837)(524,836)
(525,835)(526,834)(527,833)(528,832)(529,831)(530,830)(531,829)(532,887)
(533,886)(534,944)(535,943)(536,942)(537,941)(538,940)(539,939)(540,938)
(541,937)(542,936)(543,935)(544,934)(545,933)(546,932)(547,931)(548,930)
(549,929)(550,928)(551,927)(552,926)(553,925)(554,924)(555,923)(556,922)
(557,921)(558,920)(559,919)(560,918)(561,917)(562,916)(563,915)(564,914)
(565,913)(566,912)(567,911)(568,910)(569,909)(570,908)(571,907)(572,906)
(573,905)(574,904)(575,903)(576,902)(577,901)(578,900)(579,899)(580,898)
(581,897)(582,896)(583,895)(584,894)(585,893)(586,892)(587,891)(588,890)
(589,889)(590,888)(591,710)(592,709)(593,767)(594,766)(595,765)(596,764)
(597,763)(598,762)(599,761)(600,760)(601,759)(602,758)(603,757)(604,756)
(605,755)(606,754)(607,753)(608,752)(609,751)(610,750)(611,749)(612,748)
(613,747)(614,746)(615,745)(616,744)(617,743)(618,742)(619,741)(620,740)
(621,739)(622,738)(623,737)(624,736)(625,735)(626,734)(627,733)(628,732)
(629,731)(630,730)(631,729)(632,728)(633,727)(634,726)(635,725)(636,724)
(637,723)(638,722)(639,721)(640,720)(641,719)(642,718)(643,717)(644,716)
(645,715)(646,714)(647,713)(648,712)(649,711)(650,769)(651,768)(652,826)
(653,825)(654,824)(655,823)(656,822)(657,821)(658,820)(659,819)(660,818)
(661,817)(662,816)(663,815)(664,814)(665,813)(666,812)(667,811)(668,810)
(669,809)(670,808)(671,807)(672,806)(673,805)(674,804)(675,803)(676,802)
(677,801)(678,800)(679,799)(680,798)(681,797)(682,796)(683,795)(684,794)
(685,793)(686,792)(687,791)(688,790)(689,789)(690,788)(691,787)(692,786)
(693,785)(694,784)(695,783)(696,782)(697,781)(698,780)(699,779)(700,778)
(701,777)(702,776)(703,775)(704,774)(705,773)(706,772)(707,771)(708,770);;
s2 := ( 1,473)( 2,474)( 3,475)( 4,476)( 5,477)( 6,478)( 7,479)( 8,480)
( 9,481)( 10,482)( 11,483)( 12,484)( 13,485)( 14,486)( 15,487)( 16,488)
( 17,489)( 18,490)( 19,491)( 20,492)( 21,493)( 22,494)( 23,495)( 24,496)
( 25,497)( 26,498)( 27,499)( 28,500)( 29,501)( 30,502)( 31,503)( 32,504)
( 33,505)( 34,506)( 35,507)( 36,508)( 37,509)( 38,510)( 39,511)( 40,512)
( 41,513)( 42,514)( 43,515)( 44,516)( 45,517)( 46,518)( 47,519)( 48,520)
( 49,521)( 50,522)( 51,523)( 52,524)( 53,525)( 54,526)( 55,527)( 56,528)
( 57,529)( 58,530)( 59,531)( 60,532)( 61,533)( 62,534)( 63,535)( 64,536)
( 65,537)( 66,538)( 67,539)( 68,540)( 69,541)( 70,542)( 71,543)( 72,544)
( 73,545)( 74,546)( 75,547)( 76,548)( 77,549)( 78,550)( 79,551)( 80,552)
( 81,553)( 82,554)( 83,555)( 84,556)( 85,557)( 86,558)( 87,559)( 88,560)
( 89,561)( 90,562)( 91,563)( 92,564)( 93,565)( 94,566)( 95,567)( 96,568)
( 97,569)( 98,570)( 99,571)(100,572)(101,573)(102,574)(103,575)(104,576)
(105,577)(106,578)(107,579)(108,580)(109,581)(110,582)(111,583)(112,584)
(113,585)(114,586)(115,587)(116,588)(117,589)(118,590)(119,650)(120,651)
(121,652)(122,653)(123,654)(124,655)(125,656)(126,657)(127,658)(128,659)
(129,660)(130,661)(131,662)(132,663)(133,664)(134,665)(135,666)(136,667)
(137,668)(138,669)(139,670)(140,671)(141,672)(142,673)(143,674)(144,675)
(145,676)(146,677)(147,678)(148,679)(149,680)(150,681)(151,682)(152,683)
(153,684)(154,685)(155,686)(156,687)(157,688)(158,689)(159,690)(160,691)
(161,692)(162,693)(163,694)(164,695)(165,696)(166,697)(167,698)(168,699)
(169,700)(170,701)(171,702)(172,703)(173,704)(174,705)(175,706)(176,707)
(177,708)(178,591)(179,592)(180,593)(181,594)(182,595)(183,596)(184,597)
(185,598)(186,599)(187,600)(188,601)(189,602)(190,603)(191,604)(192,605)
(193,606)(194,607)(195,608)(196,609)(197,610)(198,611)(199,612)(200,613)
(201,614)(202,615)(203,616)(204,617)(205,618)(206,619)(207,620)(208,621)
(209,622)(210,623)(211,624)(212,625)(213,626)(214,627)(215,628)(216,629)
(217,630)(218,631)(219,632)(220,633)(221,634)(222,635)(223,636)(224,637)
(225,638)(226,639)(227,640)(228,641)(229,642)(230,643)(231,644)(232,645)
(233,646)(234,647)(235,648)(236,649)(237,709)(238,710)(239,711)(240,712)
(241,713)(242,714)(243,715)(244,716)(245,717)(246,718)(247,719)(248,720)
(249,721)(250,722)(251,723)(252,724)(253,725)(254,726)(255,727)(256,728)
(257,729)(258,730)(259,731)(260,732)(261,733)(262,734)(263,735)(264,736)
(265,737)(266,738)(267,739)(268,740)(269,741)(270,742)(271,743)(272,744)
(273,745)(274,746)(275,747)(276,748)(277,749)(278,750)(279,751)(280,752)
(281,753)(282,754)(283,755)(284,756)(285,757)(286,758)(287,759)(288,760)
(289,761)(290,762)(291,763)(292,764)(293,765)(294,766)(295,767)(296,768)
(297,769)(298,770)(299,771)(300,772)(301,773)(302,774)(303,775)(304,776)
(305,777)(306,778)(307,779)(308,780)(309,781)(310,782)(311,783)(312,784)
(313,785)(314,786)(315,787)(316,788)(317,789)(318,790)(319,791)(320,792)
(321,793)(322,794)(323,795)(324,796)(325,797)(326,798)(327,799)(328,800)
(329,801)(330,802)(331,803)(332,804)(333,805)(334,806)(335,807)(336,808)
(337,809)(338,810)(339,811)(340,812)(341,813)(342,814)(343,815)(344,816)
(345,817)(346,818)(347,819)(348,820)(349,821)(350,822)(351,823)(352,824)
(353,825)(354,826)(355,886)(356,887)(357,888)(358,889)(359,890)(360,891)
(361,892)(362,893)(363,894)(364,895)(365,896)(366,897)(367,898)(368,899)
(369,900)(370,901)(371,902)(372,903)(373,904)(374,905)(375,906)(376,907)
(377,908)(378,909)(379,910)(380,911)(381,912)(382,913)(383,914)(384,915)
(385,916)(386,917)(387,918)(388,919)(389,920)(390,921)(391,922)(392,923)
(393,924)(394,925)(395,926)(396,927)(397,928)(398,929)(399,930)(400,931)
(401,932)(402,933)(403,934)(404,935)(405,936)(406,937)(407,938)(408,939)
(409,940)(410,941)(411,942)(412,943)(413,944)(414,827)(415,828)(416,829)
(417,830)(418,831)(419,832)(420,833)(421,834)(422,835)(423,836)(424,837)
(425,838)(426,839)(427,840)(428,841)(429,842)(430,843)(431,844)(432,845)
(433,846)(434,847)(435,848)(436,849)(437,850)(438,851)(439,852)(440,853)
(441,854)(442,855)(443,856)(444,857)(445,858)(446,859)(447,860)(448,861)
(449,862)(450,863)(451,864)(452,865)(453,866)(454,867)(455,868)(456,869)
(457,870)(458,871)(459,872)(460,873)(461,874)(462,875)(463,876)(464,877)
(465,878)(466,879)(467,880)(468,881)(469,882)(470,883)(471,884)(472,885);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(944)!( 1,237)( 2,295)( 3,294)( 4,293)( 5,292)( 6,291)( 7,290)
( 8,289)( 9,288)( 10,287)( 11,286)( 12,285)( 13,284)( 14,283)( 15,282)
( 16,281)( 17,280)( 18,279)( 19,278)( 20,277)( 21,276)( 22,275)( 23,274)
( 24,273)( 25,272)( 26,271)( 27,270)( 28,269)( 29,268)( 30,267)( 31,266)
( 32,265)( 33,264)( 34,263)( 35,262)( 36,261)( 37,260)( 38,259)( 39,258)
( 40,257)( 41,256)( 42,255)( 43,254)( 44,253)( 45,252)( 46,251)( 47,250)
( 48,249)( 49,248)( 50,247)( 51,246)( 52,245)( 53,244)( 54,243)( 55,242)
( 56,241)( 57,240)( 58,239)( 59,238)( 60,296)( 61,354)( 62,353)( 63,352)
( 64,351)( 65,350)( 66,349)( 67,348)( 68,347)( 69,346)( 70,345)( 71,344)
( 72,343)( 73,342)( 74,341)( 75,340)( 76,339)( 77,338)( 78,337)( 79,336)
( 80,335)( 81,334)( 82,333)( 83,332)( 84,331)( 85,330)( 86,329)( 87,328)
( 88,327)( 89,326)( 90,325)( 91,324)( 92,323)( 93,322)( 94,321)( 95,320)
( 96,319)( 97,318)( 98,317)( 99,316)(100,315)(101,314)(102,313)(103,312)
(104,311)(105,310)(106,309)(107,308)(108,307)(109,306)(110,305)(111,304)
(112,303)(113,302)(114,301)(115,300)(116,299)(117,298)(118,297)(119,355)
(120,413)(121,412)(122,411)(123,410)(124,409)(125,408)(126,407)(127,406)
(128,405)(129,404)(130,403)(131,402)(132,401)(133,400)(134,399)(135,398)
(136,397)(137,396)(138,395)(139,394)(140,393)(141,392)(142,391)(143,390)
(144,389)(145,388)(146,387)(147,386)(148,385)(149,384)(150,383)(151,382)
(152,381)(153,380)(154,379)(155,378)(156,377)(157,376)(158,375)(159,374)
(160,373)(161,372)(162,371)(163,370)(164,369)(165,368)(166,367)(167,366)
(168,365)(169,364)(170,363)(171,362)(172,361)(173,360)(174,359)(175,358)
(176,357)(177,356)(178,414)(179,472)(180,471)(181,470)(182,469)(183,468)
(184,467)(185,466)(186,465)(187,464)(188,463)(189,462)(190,461)(191,460)
(192,459)(193,458)(194,457)(195,456)(196,455)(197,454)(198,453)(199,452)
(200,451)(201,450)(202,449)(203,448)(204,447)(205,446)(206,445)(207,444)
(208,443)(209,442)(210,441)(211,440)(212,439)(213,438)(214,437)(215,436)
(216,435)(217,434)(218,433)(219,432)(220,431)(221,430)(222,429)(223,428)
(224,427)(225,426)(226,425)(227,424)(228,423)(229,422)(230,421)(231,420)
(232,419)(233,418)(234,417)(235,416)(236,415)(473,709)(474,767)(475,766)
(476,765)(477,764)(478,763)(479,762)(480,761)(481,760)(482,759)(483,758)
(484,757)(485,756)(486,755)(487,754)(488,753)(489,752)(490,751)(491,750)
(492,749)(493,748)(494,747)(495,746)(496,745)(497,744)(498,743)(499,742)
(500,741)(501,740)(502,739)(503,738)(504,737)(505,736)(506,735)(507,734)
(508,733)(509,732)(510,731)(511,730)(512,729)(513,728)(514,727)(515,726)
(516,725)(517,724)(518,723)(519,722)(520,721)(521,720)(522,719)(523,718)
(524,717)(525,716)(526,715)(527,714)(528,713)(529,712)(530,711)(531,710)
(532,768)(533,826)(534,825)(535,824)(536,823)(537,822)(538,821)(539,820)
(540,819)(541,818)(542,817)(543,816)(544,815)(545,814)(546,813)(547,812)
(548,811)(549,810)(550,809)(551,808)(552,807)(553,806)(554,805)(555,804)
(556,803)(557,802)(558,801)(559,800)(560,799)(561,798)(562,797)(563,796)
(564,795)(565,794)(566,793)(567,792)(568,791)(569,790)(570,789)(571,788)
(572,787)(573,786)(574,785)(575,784)(576,783)(577,782)(578,781)(579,780)
(580,779)(581,778)(582,777)(583,776)(584,775)(585,774)(586,773)(587,772)
(588,771)(589,770)(590,769)(591,827)(592,885)(593,884)(594,883)(595,882)
(596,881)(597,880)(598,879)(599,878)(600,877)(601,876)(602,875)(603,874)
(604,873)(605,872)(606,871)(607,870)(608,869)(609,868)(610,867)(611,866)
(612,865)(613,864)(614,863)(615,862)(616,861)(617,860)(618,859)(619,858)
(620,857)(621,856)(622,855)(623,854)(624,853)(625,852)(626,851)(627,850)
(628,849)(629,848)(630,847)(631,846)(632,845)(633,844)(634,843)(635,842)
(636,841)(637,840)(638,839)(639,838)(640,837)(641,836)(642,835)(643,834)
(644,833)(645,832)(646,831)(647,830)(648,829)(649,828)(650,886)(651,944)
(652,943)(653,942)(654,941)(655,940)(656,939)(657,938)(658,937)(659,936)
(660,935)(661,934)(662,933)(663,932)(664,931)(665,930)(666,929)(667,928)
(668,927)(669,926)(670,925)(671,924)(672,923)(673,922)(674,921)(675,920)
(676,919)(677,918)(678,917)(679,916)(680,915)(681,914)(682,913)(683,912)
(684,911)(685,910)(686,909)(687,908)(688,907)(689,906)(690,905)(691,904)
(692,903)(693,902)(694,901)(695,900)(696,899)(697,898)(698,897)(699,896)
(700,895)(701,894)(702,893)(703,892)(704,891)(705,890)(706,889)(707,888)
(708,887);
s1 := Sym(944)!( 1,238)( 2,237)( 3,295)( 4,294)( 5,293)( 6,292)( 7,291)
( 8,290)( 9,289)( 10,288)( 11,287)( 12,286)( 13,285)( 14,284)( 15,283)
( 16,282)( 17,281)( 18,280)( 19,279)( 20,278)( 21,277)( 22,276)( 23,275)
( 24,274)( 25,273)( 26,272)( 27,271)( 28,270)( 29,269)( 30,268)( 31,267)
( 32,266)( 33,265)( 34,264)( 35,263)( 36,262)( 37,261)( 38,260)( 39,259)
( 40,258)( 41,257)( 42,256)( 43,255)( 44,254)( 45,253)( 46,252)( 47,251)
( 48,250)( 49,249)( 50,248)( 51,247)( 52,246)( 53,245)( 54,244)( 55,243)
( 56,242)( 57,241)( 58,240)( 59,239)( 60,297)( 61,296)( 62,354)( 63,353)
( 64,352)( 65,351)( 66,350)( 67,349)( 68,348)( 69,347)( 70,346)( 71,345)
( 72,344)( 73,343)( 74,342)( 75,341)( 76,340)( 77,339)( 78,338)( 79,337)
( 80,336)( 81,335)( 82,334)( 83,333)( 84,332)( 85,331)( 86,330)( 87,329)
( 88,328)( 89,327)( 90,326)( 91,325)( 92,324)( 93,323)( 94,322)( 95,321)
( 96,320)( 97,319)( 98,318)( 99,317)(100,316)(101,315)(102,314)(103,313)
(104,312)(105,311)(106,310)(107,309)(108,308)(109,307)(110,306)(111,305)
(112,304)(113,303)(114,302)(115,301)(116,300)(117,299)(118,298)(119,415)
(120,414)(121,472)(122,471)(123,470)(124,469)(125,468)(126,467)(127,466)
(128,465)(129,464)(130,463)(131,462)(132,461)(133,460)(134,459)(135,458)
(136,457)(137,456)(138,455)(139,454)(140,453)(141,452)(142,451)(143,450)
(144,449)(145,448)(146,447)(147,446)(148,445)(149,444)(150,443)(151,442)
(152,441)(153,440)(154,439)(155,438)(156,437)(157,436)(158,435)(159,434)
(160,433)(161,432)(162,431)(163,430)(164,429)(165,428)(166,427)(167,426)
(168,425)(169,424)(170,423)(171,422)(172,421)(173,420)(174,419)(175,418)
(176,417)(177,416)(178,356)(179,355)(180,413)(181,412)(182,411)(183,410)
(184,409)(185,408)(186,407)(187,406)(188,405)(189,404)(190,403)(191,402)
(192,401)(193,400)(194,399)(195,398)(196,397)(197,396)(198,395)(199,394)
(200,393)(201,392)(202,391)(203,390)(204,389)(205,388)(206,387)(207,386)
(208,385)(209,384)(210,383)(211,382)(212,381)(213,380)(214,379)(215,378)
(216,377)(217,376)(218,375)(219,374)(220,373)(221,372)(222,371)(223,370)
(224,369)(225,368)(226,367)(227,366)(228,365)(229,364)(230,363)(231,362)
(232,361)(233,360)(234,359)(235,358)(236,357)(473,828)(474,827)(475,885)
(476,884)(477,883)(478,882)(479,881)(480,880)(481,879)(482,878)(483,877)
(484,876)(485,875)(486,874)(487,873)(488,872)(489,871)(490,870)(491,869)
(492,868)(493,867)(494,866)(495,865)(496,864)(497,863)(498,862)(499,861)
(500,860)(501,859)(502,858)(503,857)(504,856)(505,855)(506,854)(507,853)
(508,852)(509,851)(510,850)(511,849)(512,848)(513,847)(514,846)(515,845)
(516,844)(517,843)(518,842)(519,841)(520,840)(521,839)(522,838)(523,837)
(524,836)(525,835)(526,834)(527,833)(528,832)(529,831)(530,830)(531,829)
(532,887)(533,886)(534,944)(535,943)(536,942)(537,941)(538,940)(539,939)
(540,938)(541,937)(542,936)(543,935)(544,934)(545,933)(546,932)(547,931)
(548,930)(549,929)(550,928)(551,927)(552,926)(553,925)(554,924)(555,923)
(556,922)(557,921)(558,920)(559,919)(560,918)(561,917)(562,916)(563,915)
(564,914)(565,913)(566,912)(567,911)(568,910)(569,909)(570,908)(571,907)
(572,906)(573,905)(574,904)(575,903)(576,902)(577,901)(578,900)(579,899)
(580,898)(581,897)(582,896)(583,895)(584,894)(585,893)(586,892)(587,891)
(588,890)(589,889)(590,888)(591,710)(592,709)(593,767)(594,766)(595,765)
(596,764)(597,763)(598,762)(599,761)(600,760)(601,759)(602,758)(603,757)
(604,756)(605,755)(606,754)(607,753)(608,752)(609,751)(610,750)(611,749)
(612,748)(613,747)(614,746)(615,745)(616,744)(617,743)(618,742)(619,741)
(620,740)(621,739)(622,738)(623,737)(624,736)(625,735)(626,734)(627,733)
(628,732)(629,731)(630,730)(631,729)(632,728)(633,727)(634,726)(635,725)
(636,724)(637,723)(638,722)(639,721)(640,720)(641,719)(642,718)(643,717)
(644,716)(645,715)(646,714)(647,713)(648,712)(649,711)(650,769)(651,768)
(652,826)(653,825)(654,824)(655,823)(656,822)(657,821)(658,820)(659,819)
(660,818)(661,817)(662,816)(663,815)(664,814)(665,813)(666,812)(667,811)
(668,810)(669,809)(670,808)(671,807)(672,806)(673,805)(674,804)(675,803)
(676,802)(677,801)(678,800)(679,799)(680,798)(681,797)(682,796)(683,795)
(684,794)(685,793)(686,792)(687,791)(688,790)(689,789)(690,788)(691,787)
(692,786)(693,785)(694,784)(695,783)(696,782)(697,781)(698,780)(699,779)
(700,778)(701,777)(702,776)(703,775)(704,774)(705,773)(706,772)(707,771)
(708,770);
s2 := Sym(944)!( 1,473)( 2,474)( 3,475)( 4,476)( 5,477)( 6,478)( 7,479)
( 8,480)( 9,481)( 10,482)( 11,483)( 12,484)( 13,485)( 14,486)( 15,487)
( 16,488)( 17,489)( 18,490)( 19,491)( 20,492)( 21,493)( 22,494)( 23,495)
( 24,496)( 25,497)( 26,498)( 27,499)( 28,500)( 29,501)( 30,502)( 31,503)
( 32,504)( 33,505)( 34,506)( 35,507)( 36,508)( 37,509)( 38,510)( 39,511)
( 40,512)( 41,513)( 42,514)( 43,515)( 44,516)( 45,517)( 46,518)( 47,519)
( 48,520)( 49,521)( 50,522)( 51,523)( 52,524)( 53,525)( 54,526)( 55,527)
( 56,528)( 57,529)( 58,530)( 59,531)( 60,532)( 61,533)( 62,534)( 63,535)
( 64,536)( 65,537)( 66,538)( 67,539)( 68,540)( 69,541)( 70,542)( 71,543)
( 72,544)( 73,545)( 74,546)( 75,547)( 76,548)( 77,549)( 78,550)( 79,551)
( 80,552)( 81,553)( 82,554)( 83,555)( 84,556)( 85,557)( 86,558)( 87,559)
( 88,560)( 89,561)( 90,562)( 91,563)( 92,564)( 93,565)( 94,566)( 95,567)
( 96,568)( 97,569)( 98,570)( 99,571)(100,572)(101,573)(102,574)(103,575)
(104,576)(105,577)(106,578)(107,579)(108,580)(109,581)(110,582)(111,583)
(112,584)(113,585)(114,586)(115,587)(116,588)(117,589)(118,590)(119,650)
(120,651)(121,652)(122,653)(123,654)(124,655)(125,656)(126,657)(127,658)
(128,659)(129,660)(130,661)(131,662)(132,663)(133,664)(134,665)(135,666)
(136,667)(137,668)(138,669)(139,670)(140,671)(141,672)(142,673)(143,674)
(144,675)(145,676)(146,677)(147,678)(148,679)(149,680)(150,681)(151,682)
(152,683)(153,684)(154,685)(155,686)(156,687)(157,688)(158,689)(159,690)
(160,691)(161,692)(162,693)(163,694)(164,695)(165,696)(166,697)(167,698)
(168,699)(169,700)(170,701)(171,702)(172,703)(173,704)(174,705)(175,706)
(176,707)(177,708)(178,591)(179,592)(180,593)(181,594)(182,595)(183,596)
(184,597)(185,598)(186,599)(187,600)(188,601)(189,602)(190,603)(191,604)
(192,605)(193,606)(194,607)(195,608)(196,609)(197,610)(198,611)(199,612)
(200,613)(201,614)(202,615)(203,616)(204,617)(205,618)(206,619)(207,620)
(208,621)(209,622)(210,623)(211,624)(212,625)(213,626)(214,627)(215,628)
(216,629)(217,630)(218,631)(219,632)(220,633)(221,634)(222,635)(223,636)
(224,637)(225,638)(226,639)(227,640)(228,641)(229,642)(230,643)(231,644)
(232,645)(233,646)(234,647)(235,648)(236,649)(237,709)(238,710)(239,711)
(240,712)(241,713)(242,714)(243,715)(244,716)(245,717)(246,718)(247,719)
(248,720)(249,721)(250,722)(251,723)(252,724)(253,725)(254,726)(255,727)
(256,728)(257,729)(258,730)(259,731)(260,732)(261,733)(262,734)(263,735)
(264,736)(265,737)(266,738)(267,739)(268,740)(269,741)(270,742)(271,743)
(272,744)(273,745)(274,746)(275,747)(276,748)(277,749)(278,750)(279,751)
(280,752)(281,753)(282,754)(283,755)(284,756)(285,757)(286,758)(287,759)
(288,760)(289,761)(290,762)(291,763)(292,764)(293,765)(294,766)(295,767)
(296,768)(297,769)(298,770)(299,771)(300,772)(301,773)(302,774)(303,775)
(304,776)(305,777)(306,778)(307,779)(308,780)(309,781)(310,782)(311,783)
(312,784)(313,785)(314,786)(315,787)(316,788)(317,789)(318,790)(319,791)
(320,792)(321,793)(322,794)(323,795)(324,796)(325,797)(326,798)(327,799)
(328,800)(329,801)(330,802)(331,803)(332,804)(333,805)(334,806)(335,807)
(336,808)(337,809)(338,810)(339,811)(340,812)(341,813)(342,814)(343,815)
(344,816)(345,817)(346,818)(347,819)(348,820)(349,821)(350,822)(351,823)
(352,824)(353,825)(354,826)(355,886)(356,887)(357,888)(358,889)(359,890)
(360,891)(361,892)(362,893)(363,894)(364,895)(365,896)(366,897)(367,898)
(368,899)(369,900)(370,901)(371,902)(372,903)(373,904)(374,905)(375,906)
(376,907)(377,908)(378,909)(379,910)(380,911)(381,912)(382,913)(383,914)
(384,915)(385,916)(386,917)(387,918)(388,919)(389,920)(390,921)(391,922)
(392,923)(393,924)(394,925)(395,926)(396,927)(397,928)(398,929)(399,930)
(400,931)(401,932)(402,933)(403,934)(404,935)(405,936)(406,937)(407,938)
(408,939)(409,940)(410,941)(411,942)(412,943)(413,944)(414,827)(415,828)
(416,829)(417,830)(418,831)(419,832)(420,833)(421,834)(422,835)(423,836)
(424,837)(425,838)(426,839)(427,840)(428,841)(429,842)(430,843)(431,844)
(432,845)(433,846)(434,847)(435,848)(436,849)(437,850)(438,851)(439,852)
(440,853)(441,854)(442,855)(443,856)(444,857)(445,858)(446,859)(447,860)
(448,861)(449,862)(450,863)(451,864)(452,865)(453,866)(454,867)(455,868)
(456,869)(457,870)(458,871)(459,872)(460,873)(461,874)(462,875)(463,876)
(464,877)(465,878)(466,879)(467,880)(468,881)(469,882)(470,883)(471,884)
(472,885);
poly := sub<Sym(944)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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