Polytope of Type {4,114}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,114}*1824
if this polytope has a name.
Group : SmallGroup(1824,1247)
Rank : 3
Schlafli Type : {4,114}
Number of vertices, edges, etc : 8, 456, 228
Order of s₀s₁s₂ : 114
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,57}*912, {4,114}*912b, {4,114}*912c
   4-fold quotients : {4,57}*456, {2,114}*456
   8-fold quotients : {2,57}*228
   12-fold quotients : {2,38}*152
   19-fold quotients : {4,6}*96
   24-fold quotients : {2,19}*76
   38-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   76-fold quotients : {4,3}*24, {2,6}*24
   152-fold quotients : {2,3}*12
   228-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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