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Polytope of Type {4,9}

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