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# Polytope of Type {9,4}

Atlas Canonical Name : {9,4}*1944
if this polytope has a name.
Group : SmallGroup(1944,3453)
Rank : 3
Schlafli Type : {9,4}
Number of vertices, edges, etc : 243, 486, 108
Order of s0s1s2 : 9
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {9,4}*648
27-fold quotients : {9,4}*72
81-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (  2,  3)(  4, 19)(  5, 21)(  6, 20)(  7, 10)(  8, 12)(  9, 11)( 13, 25)
( 14, 27)( 15, 26)( 17, 18)( 23, 24)( 28, 55)( 29, 57)( 30, 56)( 31, 73)
( 32, 75)( 33, 74)( 34, 64)( 35, 66)( 36, 65)( 37, 61)( 38, 63)( 39, 62)
( 40, 79)( 41, 81)( 42, 80)( 43, 70)( 44, 72)( 45, 71)( 46, 58)( 47, 60)
( 48, 59)( 49, 76)( 50, 78)( 51, 77)( 52, 67)( 53, 69)( 54, 68)( 83, 84)
( 85,100)( 86,102)( 87,101)( 88, 91)( 89, 93)( 90, 92)( 94,106)( 95,108)
( 96,107)( 98, 99)(104,105)(109,217)(110,219)(111,218)(112,235)(113,237)
(114,236)(115,226)(116,228)(117,227)(118,223)(119,225)(120,224)(121,241)
(122,243)(123,242)(124,232)(125,234)(126,233)(127,220)(128,222)(129,221)
(130,238)(131,240)(132,239)(133,229)(134,231)(135,230)(136,271)(137,273)
(138,272)(139,289)(140,291)(141,290)(142,280)(143,282)(144,281)(145,277)
(146,279)(147,278)(148,295)(149,297)(150,296)(151,286)(152,288)(153,287)
(154,274)(155,276)(156,275)(157,292)(158,294)(159,293)(160,283)(161,285)
(162,284)(163,244)(164,246)(165,245)(166,262)(167,264)(168,263)(169,253)
(170,255)(171,254)(172,250)(173,252)(174,251)(175,268)(176,270)(177,269)
(178,259)(179,261)(180,260)(181,247)(182,249)(183,248)(184,265)(185,267)
(186,266)(187,256)(188,258)(189,257)(190,298)(191,300)(192,299)(193,316)
(194,318)(195,317)(196,307)(197,309)(198,308)(199,304)(200,306)(201,305)
(202,322)(203,324)(204,323)(205,313)(206,315)(207,314)(208,301)(209,303)
(210,302)(211,319)(212,321)(213,320)(214,310)(215,312)(216,311)(325,865)
(326,867)(327,866)(328,883)(329,885)(330,884)(331,874)(332,876)(333,875)
(334,871)(335,873)(336,872)(337,889)(338,891)(339,890)(340,880)(341,882)
(342,881)(343,868)(344,870)(345,869)(346,886)(347,888)(348,887)(349,877)
(350,879)(351,878)(352,919)(353,921)(354,920)(355,937)(356,939)(357,938)
(358,928)(359,930)(360,929)(361,925)(362,927)(363,926)(364,943)(365,945)
(366,944)(367,934)(368,936)(369,935)(370,922)(371,924)(372,923)(373,940)
(374,942)(375,941)(376,931)(377,933)(378,932)(379,892)(380,894)(381,893)
(382,910)(383,912)(384,911)(385,901)(386,903)(387,902)(388,898)(389,900)
(390,899)(391,916)(392,918)(393,917)(394,907)(395,909)(396,908)(397,895)
(398,897)(399,896)(400,913)(401,915)(402,914)(403,904)(404,906)(405,905)
(406,946)(407,948)(408,947)(409,964)(410,966)(411,965)(412,955)(413,957)
(414,956)(415,952)(416,954)(417,953)(418,970)(419,972)(420,971)(421,961)
(422,963)(423,962)(424,949)(425,951)(426,950)(427,967)(428,969)(429,968)
(430,958)(431,960)(432,959)(433,757)(434,759)(435,758)(436,775)(437,777)
(438,776)(439,766)(440,768)(441,767)(442,763)(443,765)(444,764)(445,781)
(446,783)(447,782)(448,772)(449,774)(450,773)(451,760)(452,762)(453,761)
(454,778)(455,780)(456,779)(457,769)(458,771)(459,770)(460,811)(461,813)
(462,812)(463,829)(464,831)(465,830)(466,820)(467,822)(468,821)(469,817)
(470,819)(471,818)(472,835)(473,837)(474,836)(475,826)(476,828)(477,827)
(478,814)(479,816)(480,815)(481,832)(482,834)(483,833)(484,823)(485,825)
(486,824)(487,784)(488,786)(489,785)(490,802)(491,804)(492,803)(493,793)
(494,795)(495,794)(496,790)(497,792)(498,791)(499,808)(500,810)(501,809)
(502,799)(503,801)(504,800)(505,787)(506,789)(507,788)(508,805)(509,807)
(510,806)(511,796)(512,798)(513,797)(514,838)(515,840)(516,839)(517,856)
(518,858)(519,857)(520,847)(521,849)(522,848)(523,844)(524,846)(525,845)
(526,862)(527,864)(528,863)(529,853)(530,855)(531,854)(532,841)(533,843)
(534,842)(535,859)(536,861)(537,860)(538,850)(539,852)(540,851)(541,649)
(542,651)(543,650)(544,667)(545,669)(546,668)(547,658)(548,660)(549,659)
(550,655)(551,657)(552,656)(553,673)(554,675)(555,674)(556,664)(557,666)
(558,665)(559,652)(560,654)(561,653)(562,670)(563,672)(564,671)(565,661)
(566,663)(567,662)(568,703)(569,705)(570,704)(571,721)(572,723)(573,722)
(574,712)(575,714)(576,713)(577,709)(578,711)(579,710)(580,727)(581,729)
(582,728)(583,718)(584,720)(585,719)(586,706)(587,708)(588,707)(589,724)
(590,726)(591,725)(592,715)(593,717)(594,716)(595,676)(596,678)(597,677)
(598,694)(599,696)(600,695)(601,685)(602,687)(603,686)(604,682)(605,684)
(606,683)(607,700)(608,702)(609,701)(610,691)(611,693)(612,692)(613,679)
(614,681)(615,680)(616,697)(617,699)(618,698)(619,688)(620,690)(621,689)
(622,730)(623,732)(624,731)(625,748)(626,750)(627,749)(628,739)(629,741)
(630,740)(631,736)(632,738)(633,737)(634,754)(635,756)(636,755)(637,745)
(638,747)(639,746)(640,733)(641,735)(642,734)(643,751)(644,753)(645,752)
(646,742)(647,744)(648,743);;
s1 := (  1,334)(  2,340)(  3,337)(  4,336)(  5,342)(  6,339)(  7,335)(  8,341)
(  9,338)( 10,325)( 11,331)( 12,328)( 13,327)( 14,333)( 15,330)( 16,326)
( 17,332)( 18,329)( 19,343)( 20,349)( 21,346)( 22,345)( 23,351)( 24,348)
( 25,344)( 26,350)( 27,347)( 28,361)( 29,367)( 30,364)( 31,363)( 32,369)
( 33,366)( 34,362)( 35,368)( 36,365)( 37,352)( 38,358)( 39,355)( 40,354)
( 41,360)( 42,357)( 43,353)( 44,359)( 45,356)( 46,370)( 47,376)( 48,373)
( 49,372)( 50,378)( 51,375)( 52,371)( 53,377)( 54,374)( 55,415)( 56,421)
( 57,418)( 58,417)( 59,423)( 60,420)( 61,416)( 62,422)( 63,419)( 64,406)
( 65,412)( 66,409)( 67,408)( 68,414)( 69,411)( 70,407)( 71,413)( 72,410)
( 73,424)( 74,430)( 75,427)( 76,426)( 77,432)( 78,429)( 79,425)( 80,431)
( 81,428)( 82,388)( 83,394)( 84,391)( 85,390)( 86,396)( 87,393)( 88,389)
( 89,395)( 90,392)( 91,379)( 92,385)( 93,382)( 94,381)( 95,387)( 96,384)
( 97,380)( 98,386)( 99,383)(100,397)(101,403)(102,400)(103,399)(104,405)
(105,402)(106,398)(107,404)(108,401)(109,550)(110,556)(111,553)(112,552)
(113,558)(114,555)(115,551)(116,557)(117,554)(118,541)(119,547)(120,544)
(121,543)(122,549)(123,546)(124,542)(125,548)(126,545)(127,559)(128,565)
(129,562)(130,561)(131,567)(132,564)(133,560)(134,566)(135,563)(136,577)
(137,583)(138,580)(139,579)(140,585)(141,582)(142,578)(143,584)(144,581)
(145,568)(146,574)(147,571)(148,570)(149,576)(150,573)(151,569)(152,575)
(153,572)(154,586)(155,592)(156,589)(157,588)(158,594)(159,591)(160,587)
(161,593)(162,590)(163,631)(164,637)(165,634)(166,633)(167,639)(168,636)
(169,632)(170,638)(171,635)(172,622)(173,628)(174,625)(175,624)(176,630)
(177,627)(178,623)(179,629)(180,626)(181,640)(182,646)(183,643)(184,642)
(185,648)(186,645)(187,641)(188,647)(189,644)(190,604)(191,610)(192,607)
(193,606)(194,612)(195,609)(196,605)(197,611)(198,608)(199,595)(200,601)
(201,598)(202,597)(203,603)(204,600)(205,596)(206,602)(207,599)(208,613)
(209,619)(210,616)(211,615)(212,621)(213,618)(214,614)(215,620)(216,617)
(217,442)(218,448)(219,445)(220,444)(221,450)(222,447)(223,443)(224,449)
(225,446)(226,433)(227,439)(228,436)(229,435)(230,441)(231,438)(232,434)
(233,440)(234,437)(235,451)(236,457)(237,454)(238,453)(239,459)(240,456)
(241,452)(242,458)(243,455)(244,469)(245,475)(246,472)(247,471)(248,477)
(249,474)(250,470)(251,476)(252,473)(253,460)(254,466)(255,463)(256,462)
(257,468)(258,465)(259,461)(260,467)(261,464)(262,478)(263,484)(264,481)
(265,480)(266,486)(267,483)(268,479)(269,485)(270,482)(271,523)(272,529)
(273,526)(274,525)(275,531)(276,528)(277,524)(278,530)(279,527)(280,514)
(281,520)(282,517)(283,516)(284,522)(285,519)(286,515)(287,521)(288,518)
(289,532)(290,538)(291,535)(292,534)(293,540)(294,537)(295,533)(296,539)
(297,536)(298,496)(299,502)(300,499)(301,498)(302,504)(303,501)(304,497)
(305,503)(306,500)(307,487)(308,493)(309,490)(310,489)(311,495)(312,492)
(313,488)(314,494)(315,491)(316,505)(317,511)(318,508)(319,507)(320,513)
(321,510)(322,506)(323,512)(324,509)(649,874)(650,880)(651,877)(652,876)
(653,882)(654,879)(655,875)(656,881)(657,878)(658,865)(659,871)(660,868)
(661,867)(662,873)(663,870)(664,866)(665,872)(666,869)(667,883)(668,889)
(669,886)(670,885)(671,891)(672,888)(673,884)(674,890)(675,887)(676,901)
(677,907)(678,904)(679,903)(680,909)(681,906)(682,902)(683,908)(684,905)
(685,892)(686,898)(687,895)(688,894)(689,900)(690,897)(691,893)(692,899)
(693,896)(694,910)(695,916)(696,913)(697,912)(698,918)(699,915)(700,911)
(701,917)(702,914)(703,955)(704,961)(705,958)(706,957)(707,963)(708,960)
(709,956)(710,962)(711,959)(712,946)(713,952)(714,949)(715,948)(716,954)
(717,951)(718,947)(719,953)(720,950)(721,964)(722,970)(723,967)(724,966)
(725,972)(726,969)(727,965)(728,971)(729,968)(730,928)(731,934)(732,931)
(733,930)(734,936)(735,933)(736,929)(737,935)(738,932)(739,919)(740,925)
(741,922)(742,921)(743,927)(744,924)(745,920)(746,926)(747,923)(748,937)
(749,943)(750,940)(751,939)(752,945)(753,942)(754,938)(755,944)(756,941)
(757,766)(758,772)(759,769)(760,768)(761,774)(762,771)(763,767)(764,773)
(765,770)(776,781)(777,778)(779,783)(784,793)(785,799)(786,796)(787,795)
(788,801)(789,798)(790,794)(791,800)(792,797)(803,808)(804,805)(806,810)
(811,847)(812,853)(813,850)(814,849)(815,855)(816,852)(817,848)(818,854)
(819,851)(820,838)(821,844)(822,841)(823,840)(824,846)(825,843)(826,839)
(827,845)(828,842)(829,856)(830,862)(831,859)(832,858)(833,864)(834,861)
(835,857)(836,863)(837,860);;
s2 := (  1, 97)(  2, 98)(  3, 99)(  4, 94)(  5, 95)(  6, 96)(  7, 91)(  8, 92)
(  9, 93)( 10, 88)( 11, 89)( 12, 90)( 13, 85)( 14, 86)( 15, 87)( 16, 82)
( 17, 83)( 18, 84)( 19,106)( 20,107)( 21,108)( 22,103)( 23,104)( 24,105)
( 25,100)( 26,101)( 27,102)( 28, 70)( 29, 71)( 30, 72)( 31, 67)( 32, 68)
( 33, 69)( 34, 64)( 35, 65)( 36, 66)( 37, 61)( 38, 62)( 39, 63)( 40, 58)
( 41, 59)( 42, 60)( 43, 55)( 44, 56)( 45, 57)( 46, 79)( 47, 80)( 48, 81)
( 49, 76)( 50, 77)( 51, 78)( 52, 73)( 53, 74)( 54, 75)(109,205)(110,206)
(111,207)(112,202)(113,203)(114,204)(115,199)(116,200)(117,201)(118,196)
(119,197)(120,198)(121,193)(122,194)(123,195)(124,190)(125,191)(126,192)
(127,214)(128,215)(129,216)(130,211)(131,212)(132,213)(133,208)(134,209)
(135,210)(136,178)(137,179)(138,180)(139,175)(140,176)(141,177)(142,172)
(143,173)(144,174)(145,169)(146,170)(147,171)(148,166)(149,167)(150,168)
(151,163)(152,164)(153,165)(154,187)(155,188)(156,189)(157,184)(158,185)
(159,186)(160,181)(161,182)(162,183)(217,313)(218,314)(219,315)(220,310)
(221,311)(222,312)(223,307)(224,308)(225,309)(226,304)(227,305)(228,306)
(229,301)(230,302)(231,303)(232,298)(233,299)(234,300)(235,322)(236,323)
(237,324)(238,319)(239,320)(240,321)(241,316)(242,317)(243,318)(244,286)
(245,287)(246,288)(247,283)(248,284)(249,285)(250,280)(251,281)(252,282)
(253,277)(254,278)(255,279)(256,274)(257,275)(258,276)(259,271)(260,272)
(261,273)(262,295)(263,296)(264,297)(265,292)(266,293)(267,294)(268,289)
(269,290)(270,291)(325,421)(326,422)(327,423)(328,418)(329,419)(330,420)
(331,415)(332,416)(333,417)(334,412)(335,413)(336,414)(337,409)(338,410)
(339,411)(340,406)(341,407)(342,408)(343,430)(344,431)(345,432)(346,427)
(347,428)(348,429)(349,424)(350,425)(351,426)(352,394)(353,395)(354,396)
(355,391)(356,392)(357,393)(358,388)(359,389)(360,390)(361,385)(362,386)
(363,387)(364,382)(365,383)(366,384)(367,379)(368,380)(369,381)(370,403)
(371,404)(372,405)(373,400)(374,401)(375,402)(376,397)(377,398)(378,399)
(433,529)(434,530)(435,531)(436,526)(437,527)(438,528)(439,523)(440,524)
(441,525)(442,520)(443,521)(444,522)(445,517)(446,518)(447,519)(448,514)
(449,515)(450,516)(451,538)(452,539)(453,540)(454,535)(455,536)(456,537)
(457,532)(458,533)(459,534)(460,502)(461,503)(462,504)(463,499)(464,500)
(465,501)(466,496)(467,497)(468,498)(469,493)(470,494)(471,495)(472,490)
(473,491)(474,492)(475,487)(476,488)(477,489)(478,511)(479,512)(480,513)
(481,508)(482,509)(483,510)(484,505)(485,506)(486,507)(541,637)(542,638)
(543,639)(544,634)(545,635)(546,636)(547,631)(548,632)(549,633)(550,628)
(551,629)(552,630)(553,625)(554,626)(555,627)(556,622)(557,623)(558,624)
(559,646)(560,647)(561,648)(562,643)(563,644)(564,645)(565,640)(566,641)
(567,642)(568,610)(569,611)(570,612)(571,607)(572,608)(573,609)(574,604)
(575,605)(576,606)(577,601)(578,602)(579,603)(580,598)(581,599)(582,600)
(583,595)(584,596)(585,597)(586,619)(587,620)(588,621)(589,616)(590,617)
(591,618)(592,613)(593,614)(594,615)(649,745)(650,746)(651,747)(652,742)
(653,743)(654,744)(655,739)(656,740)(657,741)(658,736)(659,737)(660,738)
(661,733)(662,734)(663,735)(664,730)(665,731)(666,732)(667,754)(668,755)
(669,756)(670,751)(671,752)(672,753)(673,748)(674,749)(675,750)(676,718)
(677,719)(678,720)(679,715)(680,716)(681,717)(682,712)(683,713)(684,714)
(685,709)(686,710)(687,711)(688,706)(689,707)(690,708)(691,703)(692,704)
(693,705)(694,727)(695,728)(696,729)(697,724)(698,725)(699,726)(700,721)
(701,722)(702,723)(757,853)(758,854)(759,855)(760,850)(761,851)(762,852)
(763,847)(764,848)(765,849)(766,844)(767,845)(768,846)(769,841)(770,842)
(771,843)(772,838)(773,839)(774,840)(775,862)(776,863)(777,864)(778,859)
(779,860)(780,861)(781,856)(782,857)(783,858)(784,826)(785,827)(786,828)
(787,823)(788,824)(789,825)(790,820)(791,821)(792,822)(793,817)(794,818)
(795,819)(796,814)(797,815)(798,816)(799,811)(800,812)(801,813)(802,835)
(803,836)(804,837)(805,832)(806,833)(807,834)(808,829)(809,830)(810,831)
(865,961)(866,962)(867,963)(868,958)(869,959)(870,960)(871,955)(872,956)
(873,957)(874,952)(875,953)(876,954)(877,949)(878,950)(879,951)(880,946)
(881,947)(882,948)(883,970)(884,971)(885,972)(886,967)(887,968)(888,969)
(889,964)(890,965)(891,966)(892,934)(893,935)(894,936)(895,931)(896,932)
(897,933)(898,928)(899,929)(900,930)(901,925)(902,926)(903,927)(904,922)
(905,923)(906,924)(907,919)(908,920)(909,921)(910,943)(911,944)(912,945)
(913,940)(914,941)(915,942)(916,937)(917,938)(918,939);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1,
s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2 ];;
poly := F / rels;;

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

References : None.
to this polytope