Polytope of Type {4,226}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,226}*1808
Also Known As : {4,226|2}. if this polytope has another name.
Group : SmallGroup(1808,34)
Rank : 3
Schlafli Type : {4,226}
Number of vertices, edges, etc : 4, 452, 226
Order of s₀s₁s₂ : 452
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 : {2,226}*904
   4-fold quotients : {2,113}*452
   113-fold quotients : {4,2}*16
   226-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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