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