Polytope of Type {4,228}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,228}*1824c
if this polytope has a name.
Group : SmallGroup(1824,1071)
Rank : 3
Schlafli Type : {4,228}
Number of vertices, edges, etc : 4, 456, 228
Order of s₀s₁s₂ : 228
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {4,114}*912b
   4-fold quotients : {4,57}*456
   19-fold quotients : {4,12}*96c
   38-fold quotients : {4,6}*48c
   76-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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