Polytope of Type {8,118}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,118}*1888
Also Known As : {8,118|2}. if this polytope has another name.
Group : SmallGroup(1888,155)
Rank : 3
Schlafli Type : {8,118}
Number of vertices, edges, etc : 8, 472, 118
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 : {4,118}*944
   4-fold quotients : {2,118}*472
   8-fold quotients : {2,59}*236
   59-fold quotients : {8,2}*32
   118-fold quotients : {4,2}*16
   236-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope