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Polytope of Type {8,57}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,57}*1824
if this polytope has a name.
Group : SmallGroup(1824,1077)
Rank : 3
Schlafli Type : {8,57}
Number of vertices, edges, etc : 16, 456, 114
Order of s0s1s2 : 228
Order of s0s1s2s1 : 8
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-fold quotients : {4,57}*456
   8-fold quotients : {2,57}*228
   19-fold quotients : {8,3}*96
   24-fold quotients : {2,19}*76
   38-fold quotients : {4,3}*48
   76-fold quotients : {4,3}*24
   152-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,461)(  2,462)(  3,464)(  4,463)(  5,458)(  6,457)(  7,459)(  8,460)
(  9,469)( 10,470)( 11,472)( 12,471)( 13,466)( 14,465)( 15,467)( 16,468)
( 17,477)( 18,478)( 19,480)( 20,479)( 21,474)( 22,473)( 23,475)( 24,476)
( 25,485)( 26,486)( 27,488)( 28,487)( 29,482)( 30,481)( 31,483)( 32,484)
( 33,493)( 34,494)( 35,496)( 36,495)( 37,490)( 38,489)( 39,491)( 40,492)
( 41,501)( 42,502)( 43,504)( 44,503)( 45,498)( 46,497)( 47,499)( 48,500)
( 49,509)( 50,510)( 51,512)( 52,511)( 53,506)( 54,505)( 55,507)( 56,508)
( 57,517)( 58,518)( 59,520)( 60,519)( 61,514)( 62,513)( 63,515)( 64,516)
( 65,525)( 66,526)( 67,528)( 68,527)( 69,522)( 70,521)( 71,523)( 72,524)
( 73,533)( 74,534)( 75,536)( 76,535)( 77,530)( 78,529)( 79,531)( 80,532)
( 81,541)( 82,542)( 83,544)( 84,543)( 85,538)( 86,537)( 87,539)( 88,540)
( 89,549)( 90,550)( 91,552)( 92,551)( 93,546)( 94,545)( 95,547)( 96,548)
( 97,557)( 98,558)( 99,560)(100,559)(101,554)(102,553)(103,555)(104,556)
(105,565)(106,566)(107,568)(108,567)(109,562)(110,561)(111,563)(112,564)
(113,573)(114,574)(115,576)(116,575)(117,570)(118,569)(119,571)(120,572)
(121,581)(122,582)(123,584)(124,583)(125,578)(126,577)(127,579)(128,580)
(129,589)(130,590)(131,592)(132,591)(133,586)(134,585)(135,587)(136,588)
(137,597)(138,598)(139,600)(140,599)(141,594)(142,593)(143,595)(144,596)
(145,605)(146,606)(147,608)(148,607)(149,602)(150,601)(151,603)(152,604)
(153,613)(154,614)(155,616)(156,615)(157,610)(158,609)(159,611)(160,612)
(161,621)(162,622)(163,624)(164,623)(165,618)(166,617)(167,619)(168,620)
(169,629)(170,630)(171,632)(172,631)(173,626)(174,625)(175,627)(176,628)
(177,637)(178,638)(179,640)(180,639)(181,634)(182,633)(183,635)(184,636)
(185,645)(186,646)(187,648)(188,647)(189,642)(190,641)(191,643)(192,644)
(193,653)(194,654)(195,656)(196,655)(197,650)(198,649)(199,651)(200,652)
(201,661)(202,662)(203,664)(204,663)(205,658)(206,657)(207,659)(208,660)
(209,669)(210,670)(211,672)(212,671)(213,666)(214,665)(215,667)(216,668)
(217,677)(218,678)(219,680)(220,679)(221,674)(222,673)(223,675)(224,676)
(225,685)(226,686)(227,688)(228,687)(229,682)(230,681)(231,683)(232,684)
(233,693)(234,694)(235,696)(236,695)(237,690)(238,689)(239,691)(240,692)
(241,701)(242,702)(243,704)(244,703)(245,698)(246,697)(247,699)(248,700)
(249,709)(250,710)(251,712)(252,711)(253,706)(254,705)(255,707)(256,708)
(257,717)(258,718)(259,720)(260,719)(261,714)(262,713)(263,715)(264,716)
(265,725)(266,726)(267,728)(268,727)(269,722)(270,721)(271,723)(272,724)
(273,733)(274,734)(275,736)(276,735)(277,730)(278,729)(279,731)(280,732)
(281,741)(282,742)(283,744)(284,743)(285,738)(286,737)(287,739)(288,740)
(289,749)(290,750)(291,752)(292,751)(293,746)(294,745)(295,747)(296,748)
(297,757)(298,758)(299,760)(300,759)(301,754)(302,753)(303,755)(304,756)
(305,765)(306,766)(307,768)(308,767)(309,762)(310,761)(311,763)(312,764)
(313,773)(314,774)(315,776)(316,775)(317,770)(318,769)(319,771)(320,772)
(321,781)(322,782)(323,784)(324,783)(325,778)(326,777)(327,779)(328,780)
(329,789)(330,790)(331,792)(332,791)(333,786)(334,785)(335,787)(336,788)
(337,797)(338,798)(339,800)(340,799)(341,794)(342,793)(343,795)(344,796)
(345,805)(346,806)(347,808)(348,807)(349,802)(350,801)(351,803)(352,804)
(353,813)(354,814)(355,816)(356,815)(357,810)(358,809)(359,811)(360,812)
(361,821)(362,822)(363,824)(364,823)(365,818)(366,817)(367,819)(368,820)
(369,829)(370,830)(371,832)(372,831)(373,826)(374,825)(375,827)(376,828)
(377,837)(378,838)(379,840)(380,839)(381,834)(382,833)(383,835)(384,836)
(385,845)(386,846)(387,848)(388,847)(389,842)(390,841)(391,843)(392,844)
(393,853)(394,854)(395,856)(396,855)(397,850)(398,849)(399,851)(400,852)
(401,861)(402,862)(403,864)(404,863)(405,858)(406,857)(407,859)(408,860)
(409,869)(410,870)(411,872)(412,871)(413,866)(414,865)(415,867)(416,868)
(417,877)(418,878)(419,880)(420,879)(421,874)(422,873)(423,875)(424,876)
(425,885)(426,886)(427,888)(428,887)(429,882)(430,881)(431,883)(432,884)
(433,893)(434,894)(435,896)(436,895)(437,890)(438,889)(439,891)(440,892)
(441,901)(442,902)(443,904)(444,903)(445,898)(446,897)(447,899)(448,900)
(449,909)(450,910)(451,912)(452,911)(453,906)(454,905)(455,907)(456,908);;
s1 := (  3,  4)(  5,  7)(  6,  8)(  9,145)( 10,146)( 11,148)( 12,147)( 13,151)
( 14,152)( 15,149)( 16,150)( 17,137)( 18,138)( 19,140)( 20,139)( 21,143)
( 22,144)( 23,141)( 24,142)( 25,129)( 26,130)( 27,132)( 28,131)( 29,135)
( 30,136)( 31,133)( 32,134)( 33,121)( 34,122)( 35,124)( 36,123)( 37,127)
( 38,128)( 39,125)( 40,126)( 41,113)( 42,114)( 43,116)( 44,115)( 45,119)
( 46,120)( 47,117)( 48,118)( 49,105)( 50,106)( 51,108)( 52,107)( 53,111)
( 54,112)( 55,109)( 56,110)( 57, 97)( 58, 98)( 59,100)( 60, 99)( 61,103)
( 62,104)( 63,101)( 64,102)( 65, 89)( 66, 90)( 67, 92)( 68, 91)( 69, 95)
( 70, 96)( 71, 93)( 72, 94)( 73, 81)( 74, 82)( 75, 84)( 76, 83)( 77, 87)
( 78, 88)( 79, 85)( 80, 86)(153,305)(154,306)(155,308)(156,307)(157,311)
(158,312)(159,309)(160,310)(161,449)(162,450)(163,452)(164,451)(165,455)
(166,456)(167,453)(168,454)(169,441)(170,442)(171,444)(172,443)(173,447)
(174,448)(175,445)(176,446)(177,433)(178,434)(179,436)(180,435)(181,439)
(182,440)(183,437)(184,438)(185,425)(186,426)(187,428)(188,427)(189,431)
(190,432)(191,429)(192,430)(193,417)(194,418)(195,420)(196,419)(197,423)
(198,424)(199,421)(200,422)(201,409)(202,410)(203,412)(204,411)(205,415)
(206,416)(207,413)(208,414)(209,401)(210,402)(211,404)(212,403)(213,407)
(214,408)(215,405)(216,406)(217,393)(218,394)(219,396)(220,395)(221,399)
(222,400)(223,397)(224,398)(225,385)(226,386)(227,388)(228,387)(229,391)
(230,392)(231,389)(232,390)(233,377)(234,378)(235,380)(236,379)(237,383)
(238,384)(239,381)(240,382)(241,369)(242,370)(243,372)(244,371)(245,375)
(246,376)(247,373)(248,374)(249,361)(250,362)(251,364)(252,363)(253,367)
(254,368)(255,365)(256,366)(257,353)(258,354)(259,356)(260,355)(261,359)
(262,360)(263,357)(264,358)(265,345)(266,346)(267,348)(268,347)(269,351)
(270,352)(271,349)(272,350)(273,337)(274,338)(275,340)(276,339)(277,343)
(278,344)(279,341)(280,342)(281,329)(282,330)(283,332)(284,331)(285,335)
(286,336)(287,333)(288,334)(289,321)(290,322)(291,324)(292,323)(293,327)
(294,328)(295,325)(296,326)(297,313)(298,314)(299,316)(300,315)(301,319)
(302,320)(303,317)(304,318)(457,458)(461,464)(462,463)(465,602)(466,601)
(467,603)(468,604)(469,608)(470,607)(471,606)(472,605)(473,594)(474,593)
(475,595)(476,596)(477,600)(478,599)(479,598)(480,597)(481,586)(482,585)
(483,587)(484,588)(485,592)(486,591)(487,590)(488,589)(489,578)(490,577)
(491,579)(492,580)(493,584)(494,583)(495,582)(496,581)(497,570)(498,569)
(499,571)(500,572)(501,576)(502,575)(503,574)(504,573)(505,562)(506,561)
(507,563)(508,564)(509,568)(510,567)(511,566)(512,565)(513,554)(514,553)
(515,555)(516,556)(517,560)(518,559)(519,558)(520,557)(521,546)(522,545)
(523,547)(524,548)(525,552)(526,551)(527,550)(528,549)(529,538)(530,537)
(531,539)(532,540)(533,544)(534,543)(535,542)(536,541)(609,762)(610,761)
(611,763)(612,764)(613,768)(614,767)(615,766)(616,765)(617,906)(618,905)
(619,907)(620,908)(621,912)(622,911)(623,910)(624,909)(625,898)(626,897)
(627,899)(628,900)(629,904)(630,903)(631,902)(632,901)(633,890)(634,889)
(635,891)(636,892)(637,896)(638,895)(639,894)(640,893)(641,882)(642,881)
(643,883)(644,884)(645,888)(646,887)(647,886)(648,885)(649,874)(650,873)
(651,875)(652,876)(653,880)(654,879)(655,878)(656,877)(657,866)(658,865)
(659,867)(660,868)(661,872)(662,871)(663,870)(664,869)(665,858)(666,857)
(667,859)(668,860)(669,864)(670,863)(671,862)(672,861)(673,850)(674,849)
(675,851)(676,852)(677,856)(678,855)(679,854)(680,853)(681,842)(682,841)
(683,843)(684,844)(685,848)(686,847)(687,846)(688,845)(689,834)(690,833)
(691,835)(692,836)(693,840)(694,839)(695,838)(696,837)(697,826)(698,825)
(699,827)(700,828)(701,832)(702,831)(703,830)(704,829)(705,818)(706,817)
(707,819)(708,820)(709,824)(710,823)(711,822)(712,821)(713,810)(714,809)
(715,811)(716,812)(717,816)(718,815)(719,814)(720,813)(721,802)(722,801)
(723,803)(724,804)(725,808)(726,807)(727,806)(728,805)(729,794)(730,793)
(731,795)(732,796)(733,800)(734,799)(735,798)(736,797)(737,786)(738,785)
(739,787)(740,788)(741,792)(742,791)(743,790)(744,789)(745,778)(746,777)
(747,779)(748,780)(749,784)(750,783)(751,782)(752,781)(753,770)(754,769)
(755,771)(756,772)(757,776)(758,775)(759,774)(760,773);;
s2 := (  1,161)(  2,162)(  3,167)(  4,168)(  5,166)(  6,165)(  7,163)(  8,164)
(  9,153)( 10,154)( 11,159)( 12,160)( 13,158)( 14,157)( 15,155)( 16,156)
( 17,297)( 18,298)( 19,303)( 20,304)( 21,302)( 22,301)( 23,299)( 24,300)
( 25,289)( 26,290)( 27,295)( 28,296)( 29,294)( 30,293)( 31,291)( 32,292)
( 33,281)( 34,282)( 35,287)( 36,288)( 37,286)( 38,285)( 39,283)( 40,284)
( 41,273)( 42,274)( 43,279)( 44,280)( 45,278)( 46,277)( 47,275)( 48,276)
( 49,265)( 50,266)( 51,271)( 52,272)( 53,270)( 54,269)( 55,267)( 56,268)
( 57,257)( 58,258)( 59,263)( 60,264)( 61,262)( 62,261)( 63,259)( 64,260)
( 65,249)( 66,250)( 67,255)( 68,256)( 69,254)( 70,253)( 71,251)( 72,252)
( 73,241)( 74,242)( 75,247)( 76,248)( 77,246)( 78,245)( 79,243)( 80,244)
( 81,233)( 82,234)( 83,239)( 84,240)( 85,238)( 86,237)( 87,235)( 88,236)
( 89,225)( 90,226)( 91,231)( 92,232)( 93,230)( 94,229)( 95,227)( 96,228)
( 97,217)( 98,218)( 99,223)(100,224)(101,222)(102,221)(103,219)(104,220)
(105,209)(106,210)(107,215)(108,216)(109,214)(110,213)(111,211)(112,212)
(113,201)(114,202)(115,207)(116,208)(117,206)(118,205)(119,203)(120,204)
(121,193)(122,194)(123,199)(124,200)(125,198)(126,197)(127,195)(128,196)
(129,185)(130,186)(131,191)(132,192)(133,190)(134,189)(135,187)(136,188)
(137,177)(138,178)(139,183)(140,184)(141,182)(142,181)(143,179)(144,180)
(145,169)(146,170)(147,175)(148,176)(149,174)(150,173)(151,171)(152,172)
(305,313)(306,314)(307,319)(308,320)(309,318)(310,317)(311,315)(312,316)
(321,449)(322,450)(323,455)(324,456)(325,454)(326,453)(327,451)(328,452)
(329,441)(330,442)(331,447)(332,448)(333,446)(334,445)(335,443)(336,444)
(337,433)(338,434)(339,439)(340,440)(341,438)(342,437)(343,435)(344,436)
(345,425)(346,426)(347,431)(348,432)(349,430)(350,429)(351,427)(352,428)
(353,417)(354,418)(355,423)(356,424)(357,422)(358,421)(359,419)(360,420)
(361,409)(362,410)(363,415)(364,416)(365,414)(366,413)(367,411)(368,412)
(369,401)(370,402)(371,407)(372,408)(373,406)(374,405)(375,403)(376,404)
(377,393)(378,394)(379,399)(380,400)(381,398)(382,397)(383,395)(384,396)
(387,391)(388,392)(389,390)(457,618)(458,617)(459,624)(460,623)(461,621)
(462,622)(463,620)(464,619)(465,610)(466,609)(467,616)(468,615)(469,613)
(470,614)(471,612)(472,611)(473,754)(474,753)(475,760)(476,759)(477,757)
(478,758)(479,756)(480,755)(481,746)(482,745)(483,752)(484,751)(485,749)
(486,750)(487,748)(488,747)(489,738)(490,737)(491,744)(492,743)(493,741)
(494,742)(495,740)(496,739)(497,730)(498,729)(499,736)(500,735)(501,733)
(502,734)(503,732)(504,731)(505,722)(506,721)(507,728)(508,727)(509,725)
(510,726)(511,724)(512,723)(513,714)(514,713)(515,720)(516,719)(517,717)
(518,718)(519,716)(520,715)(521,706)(522,705)(523,712)(524,711)(525,709)
(526,710)(527,708)(528,707)(529,698)(530,697)(531,704)(532,703)(533,701)
(534,702)(535,700)(536,699)(537,690)(538,689)(539,696)(540,695)(541,693)
(542,694)(543,692)(544,691)(545,682)(546,681)(547,688)(548,687)(549,685)
(550,686)(551,684)(552,683)(553,674)(554,673)(555,680)(556,679)(557,677)
(558,678)(559,676)(560,675)(561,666)(562,665)(563,672)(564,671)(565,669)
(566,670)(567,668)(568,667)(569,658)(570,657)(571,664)(572,663)(573,661)
(574,662)(575,660)(576,659)(577,650)(578,649)(579,656)(580,655)(581,653)
(582,654)(583,652)(584,651)(585,642)(586,641)(587,648)(588,647)(589,645)
(590,646)(591,644)(592,643)(593,634)(594,633)(595,640)(596,639)(597,637)
(598,638)(599,636)(600,635)(601,626)(602,625)(603,632)(604,631)(605,629)
(606,630)(607,628)(608,627)(761,770)(762,769)(763,776)(764,775)(765,773)
(766,774)(767,772)(768,771)(777,906)(778,905)(779,912)(780,911)(781,909)
(782,910)(783,908)(784,907)(785,898)(786,897)(787,904)(788,903)(789,901)
(790,902)(791,900)(792,899)(793,890)(794,889)(795,896)(796,895)(797,893)
(798,894)(799,892)(800,891)(801,882)(802,881)(803,888)(804,887)(805,885)
(806,886)(807,884)(808,883)(809,874)(810,873)(811,880)(812,879)(813,877)
(814,878)(815,876)(816,875)(817,866)(818,865)(819,872)(820,871)(821,869)
(822,870)(823,868)(824,867)(825,858)(826,857)(827,864)(828,863)(829,861)
(830,862)(831,860)(832,859)(833,850)(834,849)(835,856)(836,855)(837,853)
(838,854)(839,852)(840,851)(841,842)(843,848)(844,847);;
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*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(912)!(  1,461)(  2,462)(  3,464)(  4,463)(  5,458)(  6,457)(  7,459)
(  8,460)(  9,469)( 10,470)( 11,472)( 12,471)( 13,466)( 14,465)( 15,467)
( 16,468)( 17,477)( 18,478)( 19,480)( 20,479)( 21,474)( 22,473)( 23,475)
( 24,476)( 25,485)( 26,486)( 27,488)( 28,487)( 29,482)( 30,481)( 31,483)
( 32,484)( 33,493)( 34,494)( 35,496)( 36,495)( 37,490)( 38,489)( 39,491)
( 40,492)( 41,501)( 42,502)( 43,504)( 44,503)( 45,498)( 46,497)( 47,499)
( 48,500)( 49,509)( 50,510)( 51,512)( 52,511)( 53,506)( 54,505)( 55,507)
( 56,508)( 57,517)( 58,518)( 59,520)( 60,519)( 61,514)( 62,513)( 63,515)
( 64,516)( 65,525)( 66,526)( 67,528)( 68,527)( 69,522)( 70,521)( 71,523)
( 72,524)( 73,533)( 74,534)( 75,536)( 76,535)( 77,530)( 78,529)( 79,531)
( 80,532)( 81,541)( 82,542)( 83,544)( 84,543)( 85,538)( 86,537)( 87,539)
( 88,540)( 89,549)( 90,550)( 91,552)( 92,551)( 93,546)( 94,545)( 95,547)
( 96,548)( 97,557)( 98,558)( 99,560)(100,559)(101,554)(102,553)(103,555)
(104,556)(105,565)(106,566)(107,568)(108,567)(109,562)(110,561)(111,563)
(112,564)(113,573)(114,574)(115,576)(116,575)(117,570)(118,569)(119,571)
(120,572)(121,581)(122,582)(123,584)(124,583)(125,578)(126,577)(127,579)
(128,580)(129,589)(130,590)(131,592)(132,591)(133,586)(134,585)(135,587)
(136,588)(137,597)(138,598)(139,600)(140,599)(141,594)(142,593)(143,595)
(144,596)(145,605)(146,606)(147,608)(148,607)(149,602)(150,601)(151,603)
(152,604)(153,613)(154,614)(155,616)(156,615)(157,610)(158,609)(159,611)
(160,612)(161,621)(162,622)(163,624)(164,623)(165,618)(166,617)(167,619)
(168,620)(169,629)(170,630)(171,632)(172,631)(173,626)(174,625)(175,627)
(176,628)(177,637)(178,638)(179,640)(180,639)(181,634)(182,633)(183,635)
(184,636)(185,645)(186,646)(187,648)(188,647)(189,642)(190,641)(191,643)
(192,644)(193,653)(194,654)(195,656)(196,655)(197,650)(198,649)(199,651)
(200,652)(201,661)(202,662)(203,664)(204,663)(205,658)(206,657)(207,659)
(208,660)(209,669)(210,670)(211,672)(212,671)(213,666)(214,665)(215,667)
(216,668)(217,677)(218,678)(219,680)(220,679)(221,674)(222,673)(223,675)
(224,676)(225,685)(226,686)(227,688)(228,687)(229,682)(230,681)(231,683)
(232,684)(233,693)(234,694)(235,696)(236,695)(237,690)(238,689)(239,691)
(240,692)(241,701)(242,702)(243,704)(244,703)(245,698)(246,697)(247,699)
(248,700)(249,709)(250,710)(251,712)(252,711)(253,706)(254,705)(255,707)
(256,708)(257,717)(258,718)(259,720)(260,719)(261,714)(262,713)(263,715)
(264,716)(265,725)(266,726)(267,728)(268,727)(269,722)(270,721)(271,723)
(272,724)(273,733)(274,734)(275,736)(276,735)(277,730)(278,729)(279,731)
(280,732)(281,741)(282,742)(283,744)(284,743)(285,738)(286,737)(287,739)
(288,740)(289,749)(290,750)(291,752)(292,751)(293,746)(294,745)(295,747)
(296,748)(297,757)(298,758)(299,760)(300,759)(301,754)(302,753)(303,755)
(304,756)(305,765)(306,766)(307,768)(308,767)(309,762)(310,761)(311,763)
(312,764)(313,773)(314,774)(315,776)(316,775)(317,770)(318,769)(319,771)
(320,772)(321,781)(322,782)(323,784)(324,783)(325,778)(326,777)(327,779)
(328,780)(329,789)(330,790)(331,792)(332,791)(333,786)(334,785)(335,787)
(336,788)(337,797)(338,798)(339,800)(340,799)(341,794)(342,793)(343,795)
(344,796)(345,805)(346,806)(347,808)(348,807)(349,802)(350,801)(351,803)
(352,804)(353,813)(354,814)(355,816)(356,815)(357,810)(358,809)(359,811)
(360,812)(361,821)(362,822)(363,824)(364,823)(365,818)(366,817)(367,819)
(368,820)(369,829)(370,830)(371,832)(372,831)(373,826)(374,825)(375,827)
(376,828)(377,837)(378,838)(379,840)(380,839)(381,834)(382,833)(383,835)
(384,836)(385,845)(386,846)(387,848)(388,847)(389,842)(390,841)(391,843)
(392,844)(393,853)(394,854)(395,856)(396,855)(397,850)(398,849)(399,851)
(400,852)(401,861)(402,862)(403,864)(404,863)(405,858)(406,857)(407,859)
(408,860)(409,869)(410,870)(411,872)(412,871)(413,866)(414,865)(415,867)
(416,868)(417,877)(418,878)(419,880)(420,879)(421,874)(422,873)(423,875)
(424,876)(425,885)(426,886)(427,888)(428,887)(429,882)(430,881)(431,883)
(432,884)(433,893)(434,894)(435,896)(436,895)(437,890)(438,889)(439,891)
(440,892)(441,901)(442,902)(443,904)(444,903)(445,898)(446,897)(447,899)
(448,900)(449,909)(450,910)(451,912)(452,911)(453,906)(454,905)(455,907)
(456,908);
s1 := Sym(912)!(  3,  4)(  5,  7)(  6,  8)(  9,145)( 10,146)( 11,148)( 12,147)
( 13,151)( 14,152)( 15,149)( 16,150)( 17,137)( 18,138)( 19,140)( 20,139)
( 21,143)( 22,144)( 23,141)( 24,142)( 25,129)( 26,130)( 27,132)( 28,131)
( 29,135)( 30,136)( 31,133)( 32,134)( 33,121)( 34,122)( 35,124)( 36,123)
( 37,127)( 38,128)( 39,125)( 40,126)( 41,113)( 42,114)( 43,116)( 44,115)
( 45,119)( 46,120)( 47,117)( 48,118)( 49,105)( 50,106)( 51,108)( 52,107)
( 53,111)( 54,112)( 55,109)( 56,110)( 57, 97)( 58, 98)( 59,100)( 60, 99)
( 61,103)( 62,104)( 63,101)( 64,102)( 65, 89)( 66, 90)( 67, 92)( 68, 91)
( 69, 95)( 70, 96)( 71, 93)( 72, 94)( 73, 81)( 74, 82)( 75, 84)( 76, 83)
( 77, 87)( 78, 88)( 79, 85)( 80, 86)(153,305)(154,306)(155,308)(156,307)
(157,311)(158,312)(159,309)(160,310)(161,449)(162,450)(163,452)(164,451)
(165,455)(166,456)(167,453)(168,454)(169,441)(170,442)(171,444)(172,443)
(173,447)(174,448)(175,445)(176,446)(177,433)(178,434)(179,436)(180,435)
(181,439)(182,440)(183,437)(184,438)(185,425)(186,426)(187,428)(188,427)
(189,431)(190,432)(191,429)(192,430)(193,417)(194,418)(195,420)(196,419)
(197,423)(198,424)(199,421)(200,422)(201,409)(202,410)(203,412)(204,411)
(205,415)(206,416)(207,413)(208,414)(209,401)(210,402)(211,404)(212,403)
(213,407)(214,408)(215,405)(216,406)(217,393)(218,394)(219,396)(220,395)
(221,399)(222,400)(223,397)(224,398)(225,385)(226,386)(227,388)(228,387)
(229,391)(230,392)(231,389)(232,390)(233,377)(234,378)(235,380)(236,379)
(237,383)(238,384)(239,381)(240,382)(241,369)(242,370)(243,372)(244,371)
(245,375)(246,376)(247,373)(248,374)(249,361)(250,362)(251,364)(252,363)
(253,367)(254,368)(255,365)(256,366)(257,353)(258,354)(259,356)(260,355)
(261,359)(262,360)(263,357)(264,358)(265,345)(266,346)(267,348)(268,347)
(269,351)(270,352)(271,349)(272,350)(273,337)(274,338)(275,340)(276,339)
(277,343)(278,344)(279,341)(280,342)(281,329)(282,330)(283,332)(284,331)
(285,335)(286,336)(287,333)(288,334)(289,321)(290,322)(291,324)(292,323)
(293,327)(294,328)(295,325)(296,326)(297,313)(298,314)(299,316)(300,315)
(301,319)(302,320)(303,317)(304,318)(457,458)(461,464)(462,463)(465,602)
(466,601)(467,603)(468,604)(469,608)(470,607)(471,606)(472,605)(473,594)
(474,593)(475,595)(476,596)(477,600)(478,599)(479,598)(480,597)(481,586)
(482,585)(483,587)(484,588)(485,592)(486,591)(487,590)(488,589)(489,578)
(490,577)(491,579)(492,580)(493,584)(494,583)(495,582)(496,581)(497,570)
(498,569)(499,571)(500,572)(501,576)(502,575)(503,574)(504,573)(505,562)
(506,561)(507,563)(508,564)(509,568)(510,567)(511,566)(512,565)(513,554)
(514,553)(515,555)(516,556)(517,560)(518,559)(519,558)(520,557)(521,546)
(522,545)(523,547)(524,548)(525,552)(526,551)(527,550)(528,549)(529,538)
(530,537)(531,539)(532,540)(533,544)(534,543)(535,542)(536,541)(609,762)
(610,761)(611,763)(612,764)(613,768)(614,767)(615,766)(616,765)(617,906)
(618,905)(619,907)(620,908)(621,912)(622,911)(623,910)(624,909)(625,898)
(626,897)(627,899)(628,900)(629,904)(630,903)(631,902)(632,901)(633,890)
(634,889)(635,891)(636,892)(637,896)(638,895)(639,894)(640,893)(641,882)
(642,881)(643,883)(644,884)(645,888)(646,887)(647,886)(648,885)(649,874)
(650,873)(651,875)(652,876)(653,880)(654,879)(655,878)(656,877)(657,866)
(658,865)(659,867)(660,868)(661,872)(662,871)(663,870)(664,869)(665,858)
(666,857)(667,859)(668,860)(669,864)(670,863)(671,862)(672,861)(673,850)
(674,849)(675,851)(676,852)(677,856)(678,855)(679,854)(680,853)(681,842)
(682,841)(683,843)(684,844)(685,848)(686,847)(687,846)(688,845)(689,834)
(690,833)(691,835)(692,836)(693,840)(694,839)(695,838)(696,837)(697,826)
(698,825)(699,827)(700,828)(701,832)(702,831)(703,830)(704,829)(705,818)
(706,817)(707,819)(708,820)(709,824)(710,823)(711,822)(712,821)(713,810)
(714,809)(715,811)(716,812)(717,816)(718,815)(719,814)(720,813)(721,802)
(722,801)(723,803)(724,804)(725,808)(726,807)(727,806)(728,805)(729,794)
(730,793)(731,795)(732,796)(733,800)(734,799)(735,798)(736,797)(737,786)
(738,785)(739,787)(740,788)(741,792)(742,791)(743,790)(744,789)(745,778)
(746,777)(747,779)(748,780)(749,784)(750,783)(751,782)(752,781)(753,770)
(754,769)(755,771)(756,772)(757,776)(758,775)(759,774)(760,773);
s2 := Sym(912)!(  1,161)(  2,162)(  3,167)(  4,168)(  5,166)(  6,165)(  7,163)
(  8,164)(  9,153)( 10,154)( 11,159)( 12,160)( 13,158)( 14,157)( 15,155)
( 16,156)( 17,297)( 18,298)( 19,303)( 20,304)( 21,302)( 22,301)( 23,299)
( 24,300)( 25,289)( 26,290)( 27,295)( 28,296)( 29,294)( 30,293)( 31,291)
( 32,292)( 33,281)( 34,282)( 35,287)( 36,288)( 37,286)( 38,285)( 39,283)
( 40,284)( 41,273)( 42,274)( 43,279)( 44,280)( 45,278)( 46,277)( 47,275)
( 48,276)( 49,265)( 50,266)( 51,271)( 52,272)( 53,270)( 54,269)( 55,267)
( 56,268)( 57,257)( 58,258)( 59,263)( 60,264)( 61,262)( 62,261)( 63,259)
( 64,260)( 65,249)( 66,250)( 67,255)( 68,256)( 69,254)( 70,253)( 71,251)
( 72,252)( 73,241)( 74,242)( 75,247)( 76,248)( 77,246)( 78,245)( 79,243)
( 80,244)( 81,233)( 82,234)( 83,239)( 84,240)( 85,238)( 86,237)( 87,235)
( 88,236)( 89,225)( 90,226)( 91,231)( 92,232)( 93,230)( 94,229)( 95,227)
( 96,228)( 97,217)( 98,218)( 99,223)(100,224)(101,222)(102,221)(103,219)
(104,220)(105,209)(106,210)(107,215)(108,216)(109,214)(110,213)(111,211)
(112,212)(113,201)(114,202)(115,207)(116,208)(117,206)(118,205)(119,203)
(120,204)(121,193)(122,194)(123,199)(124,200)(125,198)(126,197)(127,195)
(128,196)(129,185)(130,186)(131,191)(132,192)(133,190)(134,189)(135,187)
(136,188)(137,177)(138,178)(139,183)(140,184)(141,182)(142,181)(143,179)
(144,180)(145,169)(146,170)(147,175)(148,176)(149,174)(150,173)(151,171)
(152,172)(305,313)(306,314)(307,319)(308,320)(309,318)(310,317)(311,315)
(312,316)(321,449)(322,450)(323,455)(324,456)(325,454)(326,453)(327,451)
(328,452)(329,441)(330,442)(331,447)(332,448)(333,446)(334,445)(335,443)
(336,444)(337,433)(338,434)(339,439)(340,440)(341,438)(342,437)(343,435)
(344,436)(345,425)(346,426)(347,431)(348,432)(349,430)(350,429)(351,427)
(352,428)(353,417)(354,418)(355,423)(356,424)(357,422)(358,421)(359,419)
(360,420)(361,409)(362,410)(363,415)(364,416)(365,414)(366,413)(367,411)
(368,412)(369,401)(370,402)(371,407)(372,408)(373,406)(374,405)(375,403)
(376,404)(377,393)(378,394)(379,399)(380,400)(381,398)(382,397)(383,395)
(384,396)(387,391)(388,392)(389,390)(457,618)(458,617)(459,624)(460,623)
(461,621)(462,622)(463,620)(464,619)(465,610)(466,609)(467,616)(468,615)
(469,613)(470,614)(471,612)(472,611)(473,754)(474,753)(475,760)(476,759)
(477,757)(478,758)(479,756)(480,755)(481,746)(482,745)(483,752)(484,751)
(485,749)(486,750)(487,748)(488,747)(489,738)(490,737)(491,744)(492,743)
(493,741)(494,742)(495,740)(496,739)(497,730)(498,729)(499,736)(500,735)
(501,733)(502,734)(503,732)(504,731)(505,722)(506,721)(507,728)(508,727)
(509,725)(510,726)(511,724)(512,723)(513,714)(514,713)(515,720)(516,719)
(517,717)(518,718)(519,716)(520,715)(521,706)(522,705)(523,712)(524,711)
(525,709)(526,710)(527,708)(528,707)(529,698)(530,697)(531,704)(532,703)
(533,701)(534,702)(535,700)(536,699)(537,690)(538,689)(539,696)(540,695)
(541,693)(542,694)(543,692)(544,691)(545,682)(546,681)(547,688)(548,687)
(549,685)(550,686)(551,684)(552,683)(553,674)(554,673)(555,680)(556,679)
(557,677)(558,678)(559,676)(560,675)(561,666)(562,665)(563,672)(564,671)
(565,669)(566,670)(567,668)(568,667)(569,658)(570,657)(571,664)(572,663)
(573,661)(574,662)(575,660)(576,659)(577,650)(578,649)(579,656)(580,655)
(581,653)(582,654)(583,652)(584,651)(585,642)(586,641)(587,648)(588,647)
(589,645)(590,646)(591,644)(592,643)(593,634)(594,633)(595,640)(596,639)
(597,637)(598,638)(599,636)(600,635)(601,626)(602,625)(603,632)(604,631)
(605,629)(606,630)(607,628)(608,627)(761,770)(762,769)(763,776)(764,775)
(765,773)(766,774)(767,772)(768,771)(777,906)(778,905)(779,912)(780,911)
(781,909)(782,910)(783,908)(784,907)(785,898)(786,897)(787,904)(788,903)
(789,901)(790,902)(791,900)(792,899)(793,890)(794,889)(795,896)(796,895)
(797,893)(798,894)(799,892)(800,891)(801,882)(802,881)(803,888)(804,887)
(805,885)(806,886)(807,884)(808,883)(809,874)(810,873)(811,880)(812,879)
(813,877)(814,878)(815,876)(816,875)(817,866)(818,865)(819,872)(820,871)
(821,869)(822,870)(823,868)(824,867)(825,858)(826,857)(827,864)(828,863)
(829,861)(830,862)(831,860)(832,859)(833,850)(834,849)(835,856)(836,855)
(837,853)(838,854)(839,852)(840,851)(841,842)(843,848)(844,847);
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*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 >; 
 
References : None.
to this polytope