Polytope of Type {4,243}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,243}*1944
if this polytope has a name.
Group : SmallGroup(1944,100)
Rank : 3
Schlafli Type : {4,243}
Number of vertices, edges, etc : 4, 486, 243
Order of s₀s₁s₂ : 243
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) :
   3-fold quotients : {4,81}*648
   9-fold quotients : {4,27}*216
   27-fold quotients : {4,9}*72
   81-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)
( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)
( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)
( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)
( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)
( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)
( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)
(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)
(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)
(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)
(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)
(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)
(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)
(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)
(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)
(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)
(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)
(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)
(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)
(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)
(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)
(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)
(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)
(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)
(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)
(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)
(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432)
(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)(446,448)
(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)(462,464)
(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)(478,480)
(481,483)(482,484)(485,487)(486,488)(489,491)(490,492)(493,495)(494,496)
(497,499)(498,500)(501,503)(502,504)(505,507)(506,508)(509,511)(510,512)
(513,515)(514,516)(517,519)(518,520)(521,523)(522,524)(525,527)(526,528)
(529,531)(530,532)(533,535)(534,536)(537,539)(538,540)(541,543)(542,544)
(545,547)(546,548)(549,551)(550,552)(553,555)(554,556)(557,559)(558,560)
(561,563)(562,564)(565,567)(566,568)(569,571)(570,572)(573,575)(574,576)
(577,579)(578,580)(581,583)(582,584)(585,587)(586,588)(589,591)(590,592)
(593,595)(594,596)(597,599)(598,600)(601,603)(602,604)(605,607)(606,608)
(609,611)(610,612)(613,615)(614,616)(617,619)(618,620)(621,623)(622,624)
(625,627)(626,628)(629,631)(630,632)(633,635)(634,636)(637,639)(638,640)
(641,643)(642,644)(645,647)(646,648)(649,651)(650,652)(653,655)(654,656)
(657,659)(658,660)(661,663)(662,664)(665,667)(666,668)(669,671)(670,672)
(673,675)(674,676)(677,679)(678,680)(681,683)(682,684)(685,687)(686,688)
(689,691)(690,692)(693,695)(694,696)(697,699)(698,700)(701,703)(702,704)
(705,707)(706,708)(709,711)(710,712)(713,715)(714,716)(717,719)(718,720)
(721,723)(722,724)(725,727)(726,728)(729,731)(730,732)(733,735)(734,736)
(737,739)(738,740)(741,743)(742,744)(745,747)(746,748)(749,751)(750,752)
(753,755)(754,756)(757,759)(758,760)(761,763)(762,764)(765,767)(766,768)
(769,771)(770,772)(773,775)(774,776)(777,779)(778,780)(781,783)(782,784)
(785,787)(786,788)(789,791)(790,792)(793,795)(794,796)(797,799)(798,800)
(801,803)(802,804)(805,807)(806,808)(809,811)(810,812)(813,815)(814,816)
(817,819)(818,820)(821,823)(822,824)(825,827)(826,828)(829,831)(830,832)
(833,835)(834,836)(837,839)(838,840)(841,843)(842,844)(845,847)(846,848)
(849,851)(850,852)(853,855)(854,856)(857,859)(858,860)(861,863)(862,864)
(865,867)(866,868)(869,871)(870,872)(873,875)(874,876)(877,879)(878,880)
(881,883)(882,884)(885,887)(886,888)(889,891)(890,892)(893,895)(894,896)
(897,899)(898,900)(901,903)(902,904)(905,907)(906,908)(909,911)(910,912)
(913,915)(914,916)(917,919)(918,920)(921,923)(922,924)(925,927)(926,928)
(929,931)(930,932)(933,935)(934,936)(937,939)(938,940)(941,943)(942,944)
(945,947)(946,948)(949,951)(950,952)(953,955)(954,956)(957,959)(958,960)
(961,963)(962,964)(965,967)(966,968)(969,971)(970,972);;
s1 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 33)( 14, 34)( 15, 36)
( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)
( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)( 43,104)
( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)( 51, 96)
( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)
( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)( 67, 80)
( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(109,321)(110,322)(111,324)
(112,323)(113,317)(114,318)(115,320)(116,319)(117,313)(118,314)(119,316)
(120,315)(121,309)(122,310)(123,312)(124,311)(125,305)(126,306)(127,308)
(128,307)(129,301)(130,302)(131,304)(132,303)(133,297)(134,298)(135,300)
(136,299)(137,293)(138,294)(139,296)(140,295)(141,289)(142,290)(143,292)
(144,291)(145,285)(146,286)(147,288)(148,287)(149,281)(150,282)(151,284)
(152,283)(153,277)(154,278)(155,280)(156,279)(157,273)(158,274)(159,276)
(160,275)(161,269)(162,270)(163,272)(164,271)(165,265)(166,266)(167,268)
(168,267)(169,261)(170,262)(171,264)(172,263)(173,257)(174,258)(175,260)
(176,259)(177,253)(178,254)(179,256)(180,255)(181,249)(182,250)(183,252)
(184,251)(185,245)(186,246)(187,248)(188,247)(189,241)(190,242)(191,244)
(192,243)(193,237)(194,238)(195,240)(196,239)(197,233)(198,234)(199,236)
(200,235)(201,229)(202,230)(203,232)(204,231)(205,225)(206,226)(207,228)
(208,227)(209,221)(210,222)(211,224)(212,223)(213,217)(214,218)(215,220)
(216,219)(325,969)(326,970)(327,972)(328,971)(329,965)(330,966)(331,968)
(332,967)(333,961)(334,962)(335,964)(336,963)(337,957)(338,958)(339,960)
(340,959)(341,953)(342,954)(343,956)(344,955)(345,949)(346,950)(347,952)
(348,951)(349,945)(350,946)(351,948)(352,947)(353,941)(354,942)(355,944)
(356,943)(357,937)(358,938)(359,940)(360,939)(361,933)(362,934)(363,936)
(364,935)(365,929)(366,930)(367,932)(368,931)(369,925)(370,926)(371,928)
(372,927)(373,921)(374,922)(375,924)(376,923)(377,917)(378,918)(379,920)
(380,919)(381,913)(382,914)(383,916)(384,915)(385,909)(386,910)(387,912)
(388,911)(389,905)(390,906)(391,908)(392,907)(393,901)(394,902)(395,904)
(396,903)(397,897)(398,898)(399,900)(400,899)(401,893)(402,894)(403,896)
(404,895)(405,889)(406,890)(407,892)(408,891)(409,885)(410,886)(411,888)
(412,887)(413,881)(414,882)(415,884)(416,883)(417,877)(418,878)(419,880)
(420,879)(421,873)(422,874)(423,876)(424,875)(425,869)(426,870)(427,872)
(428,871)(429,865)(430,866)(431,868)(432,867)(433,861)(434,862)(435,864)
(436,863)(437,857)(438,858)(439,860)(440,859)(441,853)(442,854)(443,856)
(444,855)(445,849)(446,850)(447,852)(448,851)(449,845)(450,846)(451,848)
(452,847)(453,841)(454,842)(455,844)(456,843)(457,837)(458,838)(459,840)
(460,839)(461,833)(462,834)(463,836)(464,835)(465,829)(466,830)(467,832)
(468,831)(469,825)(470,826)(471,828)(472,827)(473,821)(474,822)(475,824)
(476,823)(477,817)(478,818)(479,820)(480,819)(481,813)(482,814)(483,816)
(484,815)(485,809)(486,810)(487,812)(488,811)(489,805)(490,806)(491,808)
(492,807)(493,801)(494,802)(495,804)(496,803)(497,797)(498,798)(499,800)
(500,799)(501,793)(502,794)(503,796)(504,795)(505,789)(506,790)(507,792)
(508,791)(509,785)(510,786)(511,788)(512,787)(513,781)(514,782)(515,784)
(516,783)(517,777)(518,778)(519,780)(520,779)(521,773)(522,774)(523,776)
(524,775)(525,769)(526,770)(527,772)(528,771)(529,765)(530,766)(531,768)
(532,767)(533,761)(534,762)(535,764)(536,763)(537,757)(538,758)(539,760)
(540,759)(541,753)(542,754)(543,756)(544,755)(545,749)(546,750)(547,752)
(548,751)(549,745)(550,746)(551,748)(552,747)(553,741)(554,742)(555,744)
(556,743)(557,737)(558,738)(559,740)(560,739)(561,733)(562,734)(563,736)
(564,735)(565,729)(566,730)(567,732)(568,731)(569,725)(570,726)(571,728)
(572,727)(573,721)(574,722)(575,724)(576,723)(577,717)(578,718)(579,720)
(580,719)(581,713)(582,714)(583,716)(584,715)(585,709)(586,710)(587,712)
(588,711)(589,705)(590,706)(591,708)(592,707)(593,701)(594,702)(595,704)
(596,703)(597,697)(598,698)(599,700)(600,699)(601,693)(602,694)(603,696)
(604,695)(605,689)(606,690)(607,692)(608,691)(609,685)(610,686)(611,688)
(612,687)(613,681)(614,682)(615,684)(616,683)(617,677)(618,678)(619,680)
(620,679)(621,673)(622,674)(623,676)(624,675)(625,669)(626,670)(627,672)
(628,671)(629,665)(630,666)(631,668)(632,667)(633,661)(634,662)(635,664)
(636,663)(637,657)(638,658)(639,660)(640,659)(641,653)(642,654)(643,656)
(644,655)(645,649)(646,650)(647,652)(648,651);;
s2 := (  1,325)(  2,328)(  3,327)(  4,326)(  5,333)(  6,336)(  7,335)(  8,334)
(  9,329)( 10,332)( 11,331)( 12,330)( 13,357)( 14,360)( 15,359)( 16,358)
( 17,353)( 18,356)( 19,355)( 20,354)( 21,349)( 22,352)( 23,351)( 24,350)
( 25,345)( 26,348)( 27,347)( 28,346)( 29,341)( 30,344)( 31,343)( 32,342)
( 33,337)( 34,340)( 35,339)( 36,338)( 37,429)( 38,432)( 39,431)( 40,430)
( 41,425)( 42,428)( 43,427)( 44,426)( 45,421)( 46,424)( 47,423)( 48,422)
( 49,417)( 50,420)( 51,419)( 52,418)( 53,413)( 54,416)( 55,415)( 56,414)
( 57,409)( 58,412)( 59,411)( 60,410)( 61,405)( 62,408)( 63,407)( 64,406)
( 65,401)( 66,404)( 67,403)( 68,402)( 69,397)( 70,400)( 71,399)( 72,398)
( 73,393)( 74,396)( 75,395)( 76,394)( 77,389)( 78,392)( 79,391)( 80,390)
( 81,385)( 82,388)( 83,387)( 84,386)( 85,381)( 86,384)( 87,383)( 88,382)
( 89,377)( 90,380)( 91,379)( 92,378)( 93,373)( 94,376)( 95,375)( 96,374)
( 97,369)( 98,372)( 99,371)(100,370)(101,365)(102,368)(103,367)(104,366)
(105,361)(106,364)(107,363)(108,362)(109,645)(110,648)(111,647)(112,646)
(113,641)(114,644)(115,643)(116,642)(117,637)(118,640)(119,639)(120,638)
(121,633)(122,636)(123,635)(124,634)(125,629)(126,632)(127,631)(128,630)
(129,625)(130,628)(131,627)(132,626)(133,621)(134,624)(135,623)(136,622)
(137,617)(138,620)(139,619)(140,618)(141,613)(142,616)(143,615)(144,614)
(145,609)(146,612)(147,611)(148,610)(149,605)(150,608)(151,607)(152,606)
(153,601)(154,604)(155,603)(156,602)(157,597)(158,600)(159,599)(160,598)
(161,593)(162,596)(163,595)(164,594)(165,589)(166,592)(167,591)(168,590)
(169,585)(170,588)(171,587)(172,586)(173,581)(174,584)(175,583)(176,582)
(177,577)(178,580)(179,579)(180,578)(181,573)(182,576)(183,575)(184,574)
(185,569)(186,572)(187,571)(188,570)(189,565)(190,568)(191,567)(192,566)
(193,561)(194,564)(195,563)(196,562)(197,557)(198,560)(199,559)(200,558)
(201,553)(202,556)(203,555)(204,554)(205,549)(206,552)(207,551)(208,550)
(209,545)(210,548)(211,547)(212,546)(213,541)(214,544)(215,543)(216,542)
(217,537)(218,540)(219,539)(220,538)(221,533)(222,536)(223,535)(224,534)
(225,529)(226,532)(227,531)(228,530)(229,525)(230,528)(231,527)(232,526)
(233,521)(234,524)(235,523)(236,522)(237,517)(238,520)(239,519)(240,518)
(241,513)(242,516)(243,515)(244,514)(245,509)(246,512)(247,511)(248,510)
(249,505)(250,508)(251,507)(252,506)(253,501)(254,504)(255,503)(256,502)
(257,497)(258,500)(259,499)(260,498)(261,493)(262,496)(263,495)(264,494)
(265,489)(266,492)(267,491)(268,490)(269,485)(270,488)(271,487)(272,486)
(273,481)(274,484)(275,483)(276,482)(277,477)(278,480)(279,479)(280,478)
(281,473)(282,476)(283,475)(284,474)(285,469)(286,472)(287,471)(288,470)
(289,465)(290,468)(291,467)(292,466)(293,461)(294,464)(295,463)(296,462)
(297,457)(298,460)(299,459)(300,458)(301,453)(302,456)(303,455)(304,454)
(305,449)(306,452)(307,451)(308,450)(309,445)(310,448)(311,447)(312,446)
(313,441)(314,444)(315,443)(316,442)(317,437)(318,440)(319,439)(320,438)
(321,433)(322,436)(323,435)(324,434)(649,969)(650,972)(651,971)(652,970)
(653,965)(654,968)(655,967)(656,966)(657,961)(658,964)(659,963)(660,962)
(661,957)(662,960)(663,959)(664,958)(665,953)(666,956)(667,955)(668,954)
(669,949)(670,952)(671,951)(672,950)(673,945)(674,948)(675,947)(676,946)
(677,941)(678,944)(679,943)(680,942)(681,937)(682,940)(683,939)(684,938)
(685,933)(686,936)(687,935)(688,934)(689,929)(690,932)(691,931)(692,930)
(693,925)(694,928)(695,927)(696,926)(697,921)(698,924)(699,923)(700,922)
(701,917)(702,920)(703,919)(704,918)(705,913)(706,916)(707,915)(708,914)
(709,909)(710,912)(711,911)(712,910)(713,905)(714,908)(715,907)(716,906)
(717,901)(718,904)(719,903)(720,902)(721,897)(722,900)(723,899)(724,898)
(725,893)(726,896)(727,895)(728,894)(729,889)(730,892)(731,891)(732,890)
(733,885)(734,888)(735,887)(736,886)(737,881)(738,884)(739,883)(740,882)
(741,877)(742,880)(743,879)(744,878)(745,873)(746,876)(747,875)(748,874)
(749,869)(750,872)(751,871)(752,870)(753,865)(754,868)(755,867)(756,866)
(757,861)(758,864)(759,863)(760,862)(761,857)(762,860)(763,859)(764,858)
(765,853)(766,856)(767,855)(768,854)(769,849)(770,852)(771,851)(772,850)
(773,845)(774,848)(775,847)(776,846)(777,841)(778,844)(779,843)(780,842)
(781,837)(782,840)(783,839)(784,838)(785,833)(786,836)(787,835)(788,834)
(789,829)(790,832)(791,831)(792,830)(793,825)(794,828)(795,827)(796,826)
(797,821)(798,824)(799,823)(800,822)(801,817)(802,820)(803,819)(804,818)
(805,813)(806,816)(807,815)(808,814)(810,812);;
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*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(972)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)
( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)
( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)
( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)
( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)
( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)
( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)
(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)
(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)
(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)
(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)
(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)
(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)
(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)
(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)
(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)
(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)
(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)
(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)
(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)
(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)
(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)
(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)
(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)
(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)
(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)
(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)
(430,432)(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)
(446,448)(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)
(462,464)(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)
(478,480)(481,483)(482,484)(485,487)(486,488)(489,491)(490,492)(493,495)
(494,496)(497,499)(498,500)(501,503)(502,504)(505,507)(506,508)(509,511)
(510,512)(513,515)(514,516)(517,519)(518,520)(521,523)(522,524)(525,527)
(526,528)(529,531)(530,532)(533,535)(534,536)(537,539)(538,540)(541,543)
(542,544)(545,547)(546,548)(549,551)(550,552)(553,555)(554,556)(557,559)
(558,560)(561,563)(562,564)(565,567)(566,568)(569,571)(570,572)(573,575)
(574,576)(577,579)(578,580)(581,583)(582,584)(585,587)(586,588)(589,591)
(590,592)(593,595)(594,596)(597,599)(598,600)(601,603)(602,604)(605,607)
(606,608)(609,611)(610,612)(613,615)(614,616)(617,619)(618,620)(621,623)
(622,624)(625,627)(626,628)(629,631)(630,632)(633,635)(634,636)(637,639)
(638,640)(641,643)(642,644)(645,647)(646,648)(649,651)(650,652)(653,655)
(654,656)(657,659)(658,660)(661,663)(662,664)(665,667)(666,668)(669,671)
(670,672)(673,675)(674,676)(677,679)(678,680)(681,683)(682,684)(685,687)
(686,688)(689,691)(690,692)(693,695)(694,696)(697,699)(698,700)(701,703)
(702,704)(705,707)(706,708)(709,711)(710,712)(713,715)(714,716)(717,719)
(718,720)(721,723)(722,724)(725,727)(726,728)(729,731)(730,732)(733,735)
(734,736)(737,739)(738,740)(741,743)(742,744)(745,747)(746,748)(749,751)
(750,752)(753,755)(754,756)(757,759)(758,760)(761,763)(762,764)(765,767)
(766,768)(769,771)(770,772)(773,775)(774,776)(777,779)(778,780)(781,783)
(782,784)(785,787)(786,788)(789,791)(790,792)(793,795)(794,796)(797,799)
(798,800)(801,803)(802,804)(805,807)(806,808)(809,811)(810,812)(813,815)
(814,816)(817,819)(818,820)(821,823)(822,824)(825,827)(826,828)(829,831)
(830,832)(833,835)(834,836)(837,839)(838,840)(841,843)(842,844)(845,847)
(846,848)(849,851)(850,852)(853,855)(854,856)(857,859)(858,860)(861,863)
(862,864)(865,867)(866,868)(869,871)(870,872)(873,875)(874,876)(877,879)
(878,880)(881,883)(882,884)(885,887)(886,888)(889,891)(890,892)(893,895)
(894,896)(897,899)(898,900)(901,903)(902,904)(905,907)(906,908)(909,911)
(910,912)(913,915)(914,916)(917,919)(918,920)(921,923)(922,924)(925,927)
(926,928)(929,931)(930,932)(933,935)(934,936)(937,939)(938,940)(941,943)
(942,944)(945,947)(946,948)(949,951)(950,952)(953,955)(954,956)(957,959)
(958,960)(961,963)(962,964)(965,967)(966,968)(969,971)(970,972);
s1 := Sym(972)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 33)( 14, 34)
( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)
( 23, 28)( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)
( 43,104)( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)
( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)
( 59, 88)( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)
( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(109,321)(110,322)
(111,324)(112,323)(113,317)(114,318)(115,320)(116,319)(117,313)(118,314)
(119,316)(120,315)(121,309)(122,310)(123,312)(124,311)(125,305)(126,306)
(127,308)(128,307)(129,301)(130,302)(131,304)(132,303)(133,297)(134,298)
(135,300)(136,299)(137,293)(138,294)(139,296)(140,295)(141,289)(142,290)
(143,292)(144,291)(145,285)(146,286)(147,288)(148,287)(149,281)(150,282)
(151,284)(152,283)(153,277)(154,278)(155,280)(156,279)(157,273)(158,274)
(159,276)(160,275)(161,269)(162,270)(163,272)(164,271)(165,265)(166,266)
(167,268)(168,267)(169,261)(170,262)(171,264)(172,263)(173,257)(174,258)
(175,260)(176,259)(177,253)(178,254)(179,256)(180,255)(181,249)(182,250)
(183,252)(184,251)(185,245)(186,246)(187,248)(188,247)(189,241)(190,242)
(191,244)(192,243)(193,237)(194,238)(195,240)(196,239)(197,233)(198,234)
(199,236)(200,235)(201,229)(202,230)(203,232)(204,231)(205,225)(206,226)
(207,228)(208,227)(209,221)(210,222)(211,224)(212,223)(213,217)(214,218)
(215,220)(216,219)(325,969)(326,970)(327,972)(328,971)(329,965)(330,966)
(331,968)(332,967)(333,961)(334,962)(335,964)(336,963)(337,957)(338,958)
(339,960)(340,959)(341,953)(342,954)(343,956)(344,955)(345,949)(346,950)
(347,952)(348,951)(349,945)(350,946)(351,948)(352,947)(353,941)(354,942)
(355,944)(356,943)(357,937)(358,938)(359,940)(360,939)(361,933)(362,934)
(363,936)(364,935)(365,929)(366,930)(367,932)(368,931)(369,925)(370,926)
(371,928)(372,927)(373,921)(374,922)(375,924)(376,923)(377,917)(378,918)
(379,920)(380,919)(381,913)(382,914)(383,916)(384,915)(385,909)(386,910)
(387,912)(388,911)(389,905)(390,906)(391,908)(392,907)(393,901)(394,902)
(395,904)(396,903)(397,897)(398,898)(399,900)(400,899)(401,893)(402,894)
(403,896)(404,895)(405,889)(406,890)(407,892)(408,891)(409,885)(410,886)
(411,888)(412,887)(413,881)(414,882)(415,884)(416,883)(417,877)(418,878)
(419,880)(420,879)(421,873)(422,874)(423,876)(424,875)(425,869)(426,870)
(427,872)(428,871)(429,865)(430,866)(431,868)(432,867)(433,861)(434,862)
(435,864)(436,863)(437,857)(438,858)(439,860)(440,859)(441,853)(442,854)
(443,856)(444,855)(445,849)(446,850)(447,852)(448,851)(449,845)(450,846)
(451,848)(452,847)(453,841)(454,842)(455,844)(456,843)(457,837)(458,838)
(459,840)(460,839)(461,833)(462,834)(463,836)(464,835)(465,829)(466,830)
(467,832)(468,831)(469,825)(470,826)(471,828)(472,827)(473,821)(474,822)
(475,824)(476,823)(477,817)(478,818)(479,820)(480,819)(481,813)(482,814)
(483,816)(484,815)(485,809)(486,810)(487,812)(488,811)(489,805)(490,806)
(491,808)(492,807)(493,801)(494,802)(495,804)(496,803)(497,797)(498,798)
(499,800)(500,799)(501,793)(502,794)(503,796)(504,795)(505,789)(506,790)
(507,792)(508,791)(509,785)(510,786)(511,788)(512,787)(513,781)(514,782)
(515,784)(516,783)(517,777)(518,778)(519,780)(520,779)(521,773)(522,774)
(523,776)(524,775)(525,769)(526,770)(527,772)(528,771)(529,765)(530,766)
(531,768)(532,767)(533,761)(534,762)(535,764)(536,763)(537,757)(538,758)
(539,760)(540,759)(541,753)(542,754)(543,756)(544,755)(545,749)(546,750)
(547,752)(548,751)(549,745)(550,746)(551,748)(552,747)(553,741)(554,742)
(555,744)(556,743)(557,737)(558,738)(559,740)(560,739)(561,733)(562,734)
(563,736)(564,735)(565,729)(566,730)(567,732)(568,731)(569,725)(570,726)
(571,728)(572,727)(573,721)(574,722)(575,724)(576,723)(577,717)(578,718)
(579,720)(580,719)(581,713)(582,714)(583,716)(584,715)(585,709)(586,710)
(587,712)(588,711)(589,705)(590,706)(591,708)(592,707)(593,701)(594,702)
(595,704)(596,703)(597,697)(598,698)(599,700)(600,699)(601,693)(602,694)
(603,696)(604,695)(605,689)(606,690)(607,692)(608,691)(609,685)(610,686)
(611,688)(612,687)(613,681)(614,682)(615,684)(616,683)(617,677)(618,678)
(619,680)(620,679)(621,673)(622,674)(623,676)(624,675)(625,669)(626,670)
(627,672)(628,671)(629,665)(630,666)(631,668)(632,667)(633,661)(634,662)
(635,664)(636,663)(637,657)(638,658)(639,660)(640,659)(641,653)(642,654)
(643,656)(644,655)(645,649)(646,650)(647,652)(648,651);
s2 := Sym(972)!(  1,325)(  2,328)(  3,327)(  4,326)(  5,333)(  6,336)(  7,335)
(  8,334)(  9,329)( 10,332)( 11,331)( 12,330)( 13,357)( 14,360)( 15,359)
( 16,358)( 17,353)( 18,356)( 19,355)( 20,354)( 21,349)( 22,352)( 23,351)
( 24,350)( 25,345)( 26,348)( 27,347)( 28,346)( 29,341)( 30,344)( 31,343)
( 32,342)( 33,337)( 34,340)( 35,339)( 36,338)( 37,429)( 38,432)( 39,431)
( 40,430)( 41,425)( 42,428)( 43,427)( 44,426)( 45,421)( 46,424)( 47,423)
( 48,422)( 49,417)( 50,420)( 51,419)( 52,418)( 53,413)( 54,416)( 55,415)
( 56,414)( 57,409)( 58,412)( 59,411)( 60,410)( 61,405)( 62,408)( 63,407)
( 64,406)( 65,401)( 66,404)( 67,403)( 68,402)( 69,397)( 70,400)( 71,399)
( 72,398)( 73,393)( 74,396)( 75,395)( 76,394)( 77,389)( 78,392)( 79,391)
( 80,390)( 81,385)( 82,388)( 83,387)( 84,386)( 85,381)( 86,384)( 87,383)
( 88,382)( 89,377)( 90,380)( 91,379)( 92,378)( 93,373)( 94,376)( 95,375)
( 96,374)( 97,369)( 98,372)( 99,371)(100,370)(101,365)(102,368)(103,367)
(104,366)(105,361)(106,364)(107,363)(108,362)(109,645)(110,648)(111,647)
(112,646)(113,641)(114,644)(115,643)(116,642)(117,637)(118,640)(119,639)
(120,638)(121,633)(122,636)(123,635)(124,634)(125,629)(126,632)(127,631)
(128,630)(129,625)(130,628)(131,627)(132,626)(133,621)(134,624)(135,623)
(136,622)(137,617)(138,620)(139,619)(140,618)(141,613)(142,616)(143,615)
(144,614)(145,609)(146,612)(147,611)(148,610)(149,605)(150,608)(151,607)
(152,606)(153,601)(154,604)(155,603)(156,602)(157,597)(158,600)(159,599)
(160,598)(161,593)(162,596)(163,595)(164,594)(165,589)(166,592)(167,591)
(168,590)(169,585)(170,588)(171,587)(172,586)(173,581)(174,584)(175,583)
(176,582)(177,577)(178,580)(179,579)(180,578)(181,573)(182,576)(183,575)
(184,574)(185,569)(186,572)(187,571)(188,570)(189,565)(190,568)(191,567)
(192,566)(193,561)(194,564)(195,563)(196,562)(197,557)(198,560)(199,559)
(200,558)(201,553)(202,556)(203,555)(204,554)(205,549)(206,552)(207,551)
(208,550)(209,545)(210,548)(211,547)(212,546)(213,541)(214,544)(215,543)
(216,542)(217,537)(218,540)(219,539)(220,538)(221,533)(222,536)(223,535)
(224,534)(225,529)(226,532)(227,531)(228,530)(229,525)(230,528)(231,527)
(232,526)(233,521)(234,524)(235,523)(236,522)(237,517)(238,520)(239,519)
(240,518)(241,513)(242,516)(243,515)(244,514)(245,509)(246,512)(247,511)
(248,510)(249,505)(250,508)(251,507)(252,506)(253,501)(254,504)(255,503)
(256,502)(257,497)(258,500)(259,499)(260,498)(261,493)(262,496)(263,495)
(264,494)(265,489)(266,492)(267,491)(268,490)(269,485)(270,488)(271,487)
(272,486)(273,481)(274,484)(275,483)(276,482)(277,477)(278,480)(279,479)
(280,478)(281,473)(282,476)(283,475)(284,474)(285,469)(286,472)(287,471)
(288,470)(289,465)(290,468)(291,467)(292,466)(293,461)(294,464)(295,463)
(296,462)(297,457)(298,460)(299,459)(300,458)(301,453)(302,456)(303,455)
(304,454)(305,449)(306,452)(307,451)(308,450)(309,445)(310,448)(311,447)
(312,446)(313,441)(314,444)(315,443)(316,442)(317,437)(318,440)(319,439)
(320,438)(321,433)(322,436)(323,435)(324,434)(649,969)(650,972)(651,971)
(652,970)(653,965)(654,968)(655,967)(656,966)(657,961)(658,964)(659,963)
(660,962)(661,957)(662,960)(663,959)(664,958)(665,953)(666,956)(667,955)
(668,954)(669,949)(670,952)(671,951)(672,950)(673,945)(674,948)(675,947)
(676,946)(677,941)(678,944)(679,943)(680,942)(681,937)(682,940)(683,939)
(684,938)(685,933)(686,936)(687,935)(688,934)(689,929)(690,932)(691,931)
(692,930)(693,925)(694,928)(695,927)(696,926)(697,921)(698,924)(699,923)
(700,922)(701,917)(702,920)(703,919)(704,918)(705,913)(706,916)(707,915)
(708,914)(709,909)(710,912)(711,911)(712,910)(713,905)(714,908)(715,907)
(716,906)(717,901)(718,904)(719,903)(720,902)(721,897)(722,900)(723,899)
(724,898)(725,893)(726,896)(727,895)(728,894)(729,889)(730,892)(731,891)
(732,890)(733,885)(734,888)(735,887)(736,886)(737,881)(738,884)(739,883)
(740,882)(741,877)(742,880)(743,879)(744,878)(745,873)(746,876)(747,875)
(748,874)(749,869)(750,872)(751,871)(752,870)(753,865)(754,868)(755,867)
(756,866)(757,861)(758,864)(759,863)(760,862)(761,857)(762,860)(763,859)
(764,858)(765,853)(766,856)(767,855)(768,854)(769,849)(770,852)(771,851)
(772,850)(773,845)(774,848)(775,847)(776,846)(777,841)(778,844)(779,843)
(780,842)(781,837)(782,840)(783,839)(784,838)(785,833)(786,836)(787,835)
(788,834)(789,829)(790,832)(791,831)(792,830)(793,825)(794,828)(795,827)
(796,826)(797,821)(798,824)(799,823)(800,822)(801,817)(802,820)(803,819)
(804,818)(805,813)(806,816)(807,815)(808,814)(810,812);
poly := sub<Sym(972)|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*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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