Polytope of Type {117,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {117,4}*1872
if this polytope has a name.
Group : SmallGroup(1872,542)
Rank : 3
Schlafli Type : {117,4}
Number of vertices, edges, etc : 234, 468, 8
Order of s0s1s2 : 234
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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) :
2-fold quotients : {117,4}*936
3-fold quotients : {39,4}*624
4-fold quotients : {117,2}*468
6-fold quotients : {39,4}*312
12-fold quotients : {39,2}*156
13-fold quotients : {9,4}*144
26-fold quotients : {9,4}*72
36-fold quotients : {13,2}*52
39-fold quotients : {3,4}*48
52-fold quotients : {9,2}*36
78-fold quotients : {3,4}*24
156-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13,145)( 14,146)( 15,148)
( 16,147)( 17,153)( 18,154)( 19,156)( 20,155)( 21,149)( 22,150)( 23,152)
( 24,151)( 25,133)( 26,134)( 27,136)( 28,135)( 29,141)( 30,142)( 31,144)
( 32,143)( 33,137)( 34,138)( 35,140)( 36,139)( 37,121)( 38,122)( 39,124)
( 40,123)( 41,129)( 42,130)( 43,132)( 44,131)( 45,125)( 46,126)( 47,128)
( 48,127)( 49,109)( 50,110)( 51,112)( 52,111)( 53,117)( 54,118)( 55,120)
( 56,119)( 57,113)( 58,114)( 59,116)( 60,115)( 61, 97)( 62, 98)( 63,100)
( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)( 70,102)( 71,104)
( 72,103)( 73, 85)( 74, 86)( 75, 88)( 76, 87)( 77, 93)( 78, 94)( 79, 96)
( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)(157,321)(158,322)(159,324)
(160,323)(161,317)(162,318)(163,320)(164,319)(165,313)(166,314)(167,316)
(168,315)(169,465)(170,466)(171,468)(172,467)(173,461)(174,462)(175,464)
(176,463)(177,457)(178,458)(179,460)(180,459)(181,453)(182,454)(183,456)
(184,455)(185,449)(186,450)(187,452)(188,451)(189,445)(190,446)(191,448)
(192,447)(193,441)(194,442)(195,444)(196,443)(197,437)(198,438)(199,440)
(200,439)(201,433)(202,434)(203,436)(204,435)(205,429)(206,430)(207,432)
(208,431)(209,425)(210,426)(211,428)(212,427)(213,421)(214,422)(215,424)
(216,423)(217,417)(218,418)(219,420)(220,419)(221,413)(222,414)(223,416)
(224,415)(225,409)(226,410)(227,412)(228,411)(229,405)(230,406)(231,408)
(232,407)(233,401)(234,402)(235,404)(236,403)(237,397)(238,398)(239,400)
(240,399)(241,393)(242,394)(243,396)(244,395)(245,389)(246,390)(247,392)
(248,391)(249,385)(250,386)(251,388)(252,387)(253,381)(254,382)(255,384)
(256,383)(257,377)(258,378)(259,380)(260,379)(261,373)(262,374)(263,376)
(264,375)(265,369)(266,370)(267,372)(268,371)(269,365)(270,366)(271,368)
(272,367)(273,361)(274,362)(275,364)(276,363)(277,357)(278,358)(279,360)
(280,359)(281,353)(282,354)(283,356)(284,355)(285,349)(286,350)(287,352)
(288,351)(289,345)(290,346)(291,348)(292,347)(293,341)(294,342)(295,344)
(296,343)(297,337)(298,338)(299,340)(300,339)(301,333)(302,334)(303,336)
(304,335)(305,329)(306,330)(307,332)(308,331)(309,325)(310,326)(311,328)
(312,327)(471,472)(473,477)(474,478)(475,480)(476,479)(481,613)(482,614)
(483,616)(484,615)(485,621)(486,622)(487,624)(488,623)(489,617)(490,618)
(491,620)(492,619)(493,601)(494,602)(495,604)(496,603)(497,609)(498,610)
(499,612)(500,611)(501,605)(502,606)(503,608)(504,607)(505,589)(506,590)
(507,592)(508,591)(509,597)(510,598)(511,600)(512,599)(513,593)(514,594)
(515,596)(516,595)(517,577)(518,578)(519,580)(520,579)(521,585)(522,586)
(523,588)(524,587)(525,581)(526,582)(527,584)(528,583)(529,565)(530,566)
(531,568)(532,567)(533,573)(534,574)(535,576)(536,575)(537,569)(538,570)
(539,572)(540,571)(541,553)(542,554)(543,556)(544,555)(545,561)(546,562)
(547,564)(548,563)(549,557)(550,558)(551,560)(552,559)(625,789)(626,790)
(627,792)(628,791)(629,785)(630,786)(631,788)(632,787)(633,781)(634,782)
(635,784)(636,783)(637,933)(638,934)(639,936)(640,935)(641,929)(642,930)
(643,932)(644,931)(645,925)(646,926)(647,928)(648,927)(649,921)(650,922)
(651,924)(652,923)(653,917)(654,918)(655,920)(656,919)(657,913)(658,914)
(659,916)(660,915)(661,909)(662,910)(663,912)(664,911)(665,905)(666,906)
(667,908)(668,907)(669,901)(670,902)(671,904)(672,903)(673,897)(674,898)
(675,900)(676,899)(677,893)(678,894)(679,896)(680,895)(681,889)(682,890)
(683,892)(684,891)(685,885)(686,886)(687,888)(688,887)(689,881)(690,882)
(691,884)(692,883)(693,877)(694,878)(695,880)(696,879)(697,873)(698,874)
(699,876)(700,875)(701,869)(702,870)(703,872)(704,871)(705,865)(706,866)
(707,868)(708,867)(709,861)(710,862)(711,864)(712,863)(713,857)(714,858)
(715,860)(716,859)(717,853)(718,854)(719,856)(720,855)(721,849)(722,850)
(723,852)(724,851)(725,845)(726,846)(727,848)(728,847)(729,841)(730,842)
(731,844)(732,843)(733,837)(734,838)(735,840)(736,839)(737,833)(738,834)
(739,836)(740,835)(741,829)(742,830)(743,832)(744,831)(745,825)(746,826)
(747,828)(748,827)(749,821)(750,822)(751,824)(752,823)(753,817)(754,818)
(755,820)(756,819)(757,813)(758,814)(759,816)(760,815)(761,809)(762,810)
(763,812)(764,811)(765,805)(766,806)(767,808)(768,807)(769,801)(770,802)
(771,804)(772,803)(773,797)(774,798)(775,800)(776,799)(777,793)(778,794)
(779,796)(780,795);;
s1 := ( 1,169)( 2,172)( 3,171)( 4,170)( 5,177)( 6,180)( 7,179)( 8,178)
( 9,173)( 10,176)( 11,175)( 12,174)( 13,157)( 14,160)( 15,159)( 16,158)
( 17,165)( 18,168)( 19,167)( 20,166)( 21,161)( 22,164)( 23,163)( 24,162)
( 25,301)( 26,304)( 27,303)( 28,302)( 29,309)( 30,312)( 31,311)( 32,310)
( 33,305)( 34,308)( 35,307)( 36,306)( 37,289)( 38,292)( 39,291)( 40,290)
( 41,297)( 42,300)( 43,299)( 44,298)( 45,293)( 46,296)( 47,295)( 48,294)
( 49,277)( 50,280)( 51,279)( 52,278)( 53,285)( 54,288)( 55,287)( 56,286)
( 57,281)( 58,284)( 59,283)( 60,282)( 61,265)( 62,268)( 63,267)( 64,266)
( 65,273)( 66,276)( 67,275)( 68,274)( 69,269)( 70,272)( 71,271)( 72,270)
( 73,253)( 74,256)( 75,255)( 76,254)( 77,261)( 78,264)( 79,263)( 80,262)
( 81,257)( 82,260)( 83,259)( 84,258)( 85,241)( 86,244)( 87,243)( 88,242)
( 89,249)( 90,252)( 91,251)( 92,250)( 93,245)( 94,248)( 95,247)( 96,246)
( 97,229)( 98,232)( 99,231)(100,230)(101,237)(102,240)(103,239)(104,238)
(105,233)(106,236)(107,235)(108,234)(109,217)(110,220)(111,219)(112,218)
(113,225)(114,228)(115,227)(116,226)(117,221)(118,224)(119,223)(120,222)
(121,205)(122,208)(123,207)(124,206)(125,213)(126,216)(127,215)(128,214)
(129,209)(130,212)(131,211)(132,210)(133,193)(134,196)(135,195)(136,194)
(137,201)(138,204)(139,203)(140,202)(141,197)(142,200)(143,199)(144,198)
(145,181)(146,184)(147,183)(148,182)(149,189)(150,192)(151,191)(152,190)
(153,185)(154,188)(155,187)(156,186)(313,333)(314,336)(315,335)(316,334)
(317,329)(318,332)(319,331)(320,330)(321,325)(322,328)(323,327)(324,326)
(337,465)(338,468)(339,467)(340,466)(341,461)(342,464)(343,463)(344,462)
(345,457)(346,460)(347,459)(348,458)(349,453)(350,456)(351,455)(352,454)
(353,449)(354,452)(355,451)(356,450)(357,445)(358,448)(359,447)(360,446)
(361,441)(362,444)(363,443)(364,442)(365,437)(366,440)(367,439)(368,438)
(369,433)(370,436)(371,435)(372,434)(373,429)(374,432)(375,431)(376,430)
(377,425)(378,428)(379,427)(380,426)(381,421)(382,424)(383,423)(384,422)
(385,417)(386,420)(387,419)(388,418)(389,413)(390,416)(391,415)(392,414)
(393,409)(394,412)(395,411)(396,410)(397,405)(398,408)(399,407)(400,406)
(402,404)(469,637)(470,640)(471,639)(472,638)(473,645)(474,648)(475,647)
(476,646)(477,641)(478,644)(479,643)(480,642)(481,625)(482,628)(483,627)
(484,626)(485,633)(486,636)(487,635)(488,634)(489,629)(490,632)(491,631)
(492,630)(493,769)(494,772)(495,771)(496,770)(497,777)(498,780)(499,779)
(500,778)(501,773)(502,776)(503,775)(504,774)(505,757)(506,760)(507,759)
(508,758)(509,765)(510,768)(511,767)(512,766)(513,761)(514,764)(515,763)
(516,762)(517,745)(518,748)(519,747)(520,746)(521,753)(522,756)(523,755)
(524,754)(525,749)(526,752)(527,751)(528,750)(529,733)(530,736)(531,735)
(532,734)(533,741)(534,744)(535,743)(536,742)(537,737)(538,740)(539,739)
(540,738)(541,721)(542,724)(543,723)(544,722)(545,729)(546,732)(547,731)
(548,730)(549,725)(550,728)(551,727)(552,726)(553,709)(554,712)(555,711)
(556,710)(557,717)(558,720)(559,719)(560,718)(561,713)(562,716)(563,715)
(564,714)(565,697)(566,700)(567,699)(568,698)(569,705)(570,708)(571,707)
(572,706)(573,701)(574,704)(575,703)(576,702)(577,685)(578,688)(579,687)
(580,686)(581,693)(582,696)(583,695)(584,694)(585,689)(586,692)(587,691)
(588,690)(589,673)(590,676)(591,675)(592,674)(593,681)(594,684)(595,683)
(596,682)(597,677)(598,680)(599,679)(600,678)(601,661)(602,664)(603,663)
(604,662)(605,669)(606,672)(607,671)(608,670)(609,665)(610,668)(611,667)
(612,666)(613,649)(614,652)(615,651)(616,650)(617,657)(618,660)(619,659)
(620,658)(621,653)(622,656)(623,655)(624,654)(781,801)(782,804)(783,803)
(784,802)(785,797)(786,800)(787,799)(788,798)(789,793)(790,796)(791,795)
(792,794)(805,933)(806,936)(807,935)(808,934)(809,929)(810,932)(811,931)
(812,930)(813,925)(814,928)(815,927)(816,926)(817,921)(818,924)(819,923)
(820,922)(821,917)(822,920)(823,919)(824,918)(825,913)(826,916)(827,915)
(828,914)(829,909)(830,912)(831,911)(832,910)(833,905)(834,908)(835,907)
(836,906)(837,901)(838,904)(839,903)(840,902)(841,897)(842,900)(843,899)
(844,898)(845,893)(846,896)(847,895)(848,894)(849,889)(850,892)(851,891)
(852,890)(853,885)(854,888)(855,887)(856,886)(857,881)(858,884)(859,883)
(860,882)(861,877)(862,880)(863,879)(864,878)(865,873)(866,876)(867,875)
(868,874)(870,872);;
s2 := ( 1,470)( 2,469)( 3,472)( 4,471)( 5,474)( 6,473)( 7,476)( 8,475)
( 9,478)( 10,477)( 11,480)( 12,479)( 13,482)( 14,481)( 15,484)( 16,483)
( 17,486)( 18,485)( 19,488)( 20,487)( 21,490)( 22,489)( 23,492)( 24,491)
( 25,494)( 26,493)( 27,496)( 28,495)( 29,498)( 30,497)( 31,500)( 32,499)
( 33,502)( 34,501)( 35,504)( 36,503)( 37,506)( 38,505)( 39,508)( 40,507)
( 41,510)( 42,509)( 43,512)( 44,511)( 45,514)( 46,513)( 47,516)( 48,515)
( 49,518)( 50,517)( 51,520)( 52,519)( 53,522)( 54,521)( 55,524)( 56,523)
( 57,526)( 58,525)( 59,528)( 60,527)( 61,530)( 62,529)( 63,532)( 64,531)
( 65,534)( 66,533)( 67,536)( 68,535)( 69,538)( 70,537)( 71,540)( 72,539)
( 73,542)( 74,541)( 75,544)( 76,543)( 77,546)( 78,545)( 79,548)( 80,547)
( 81,550)( 82,549)( 83,552)( 84,551)( 85,554)( 86,553)( 87,556)( 88,555)
( 89,558)( 90,557)( 91,560)( 92,559)( 93,562)( 94,561)( 95,564)( 96,563)
( 97,566)( 98,565)( 99,568)(100,567)(101,570)(102,569)(103,572)(104,571)
(105,574)(106,573)(107,576)(108,575)(109,578)(110,577)(111,580)(112,579)
(113,582)(114,581)(115,584)(116,583)(117,586)(118,585)(119,588)(120,587)
(121,590)(122,589)(123,592)(124,591)(125,594)(126,593)(127,596)(128,595)
(129,598)(130,597)(131,600)(132,599)(133,602)(134,601)(135,604)(136,603)
(137,606)(138,605)(139,608)(140,607)(141,610)(142,609)(143,612)(144,611)
(145,614)(146,613)(147,616)(148,615)(149,618)(150,617)(151,620)(152,619)
(153,622)(154,621)(155,624)(156,623)(157,626)(158,625)(159,628)(160,627)
(161,630)(162,629)(163,632)(164,631)(165,634)(166,633)(167,636)(168,635)
(169,638)(170,637)(171,640)(172,639)(173,642)(174,641)(175,644)(176,643)
(177,646)(178,645)(179,648)(180,647)(181,650)(182,649)(183,652)(184,651)
(185,654)(186,653)(187,656)(188,655)(189,658)(190,657)(191,660)(192,659)
(193,662)(194,661)(195,664)(196,663)(197,666)(198,665)(199,668)(200,667)
(201,670)(202,669)(203,672)(204,671)(205,674)(206,673)(207,676)(208,675)
(209,678)(210,677)(211,680)(212,679)(213,682)(214,681)(215,684)(216,683)
(217,686)(218,685)(219,688)(220,687)(221,690)(222,689)(223,692)(224,691)
(225,694)(226,693)(227,696)(228,695)(229,698)(230,697)(231,700)(232,699)
(233,702)(234,701)(235,704)(236,703)(237,706)(238,705)(239,708)(240,707)
(241,710)(242,709)(243,712)(244,711)(245,714)(246,713)(247,716)(248,715)
(249,718)(250,717)(251,720)(252,719)(253,722)(254,721)(255,724)(256,723)
(257,726)(258,725)(259,728)(260,727)(261,730)(262,729)(263,732)(264,731)
(265,734)(266,733)(267,736)(268,735)(269,738)(270,737)(271,740)(272,739)
(273,742)(274,741)(275,744)(276,743)(277,746)(278,745)(279,748)(280,747)
(281,750)(282,749)(283,752)(284,751)(285,754)(286,753)(287,756)(288,755)
(289,758)(290,757)(291,760)(292,759)(293,762)(294,761)(295,764)(296,763)
(297,766)(298,765)(299,768)(300,767)(301,770)(302,769)(303,772)(304,771)
(305,774)(306,773)(307,776)(308,775)(309,778)(310,777)(311,780)(312,779)
(313,782)(314,781)(315,784)(316,783)(317,786)(318,785)(319,788)(320,787)
(321,790)(322,789)(323,792)(324,791)(325,794)(326,793)(327,796)(328,795)
(329,798)(330,797)(331,800)(332,799)(333,802)(334,801)(335,804)(336,803)
(337,806)(338,805)(339,808)(340,807)(341,810)(342,809)(343,812)(344,811)
(345,814)(346,813)(347,816)(348,815)(349,818)(350,817)(351,820)(352,819)
(353,822)(354,821)(355,824)(356,823)(357,826)(358,825)(359,828)(360,827)
(361,830)(362,829)(363,832)(364,831)(365,834)(366,833)(367,836)(368,835)
(369,838)(370,837)(371,840)(372,839)(373,842)(374,841)(375,844)(376,843)
(377,846)(378,845)(379,848)(380,847)(381,850)(382,849)(383,852)(384,851)
(385,854)(386,853)(387,856)(388,855)(389,858)(390,857)(391,860)(392,859)
(393,862)(394,861)(395,864)(396,863)(397,866)(398,865)(399,868)(400,867)
(401,870)(402,869)(403,872)(404,871)(405,874)(406,873)(407,876)(408,875)
(409,878)(410,877)(411,880)(412,879)(413,882)(414,881)(415,884)(416,883)
(417,886)(418,885)(419,888)(420,887)(421,890)(422,889)(423,892)(424,891)
(425,894)(426,893)(427,896)(428,895)(429,898)(430,897)(431,900)(432,899)
(433,902)(434,901)(435,904)(436,903)(437,906)(438,905)(439,908)(440,907)
(441,910)(442,909)(443,912)(444,911)(445,914)(446,913)(447,916)(448,915)
(449,918)(450,917)(451,920)(452,919)(453,922)(454,921)(455,924)(456,923)
(457,926)(458,925)(459,928)(460,927)(461,930)(462,929)(463,932)(464,931)
(465,934)(466,933)(467,936)(468,935);;
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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(936)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13,145)( 14,146)
( 15,148)( 16,147)( 17,153)( 18,154)( 19,156)( 20,155)( 21,149)( 22,150)
( 23,152)( 24,151)( 25,133)( 26,134)( 27,136)( 28,135)( 29,141)( 30,142)
( 31,144)( 32,143)( 33,137)( 34,138)( 35,140)( 36,139)( 37,121)( 38,122)
( 39,124)( 40,123)( 41,129)( 42,130)( 43,132)( 44,131)( 45,125)( 46,126)
( 47,128)( 48,127)( 49,109)( 50,110)( 51,112)( 52,111)( 53,117)( 54,118)
( 55,120)( 56,119)( 57,113)( 58,114)( 59,116)( 60,115)( 61, 97)( 62, 98)
( 63,100)( 64, 99)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)( 70,102)
( 71,104)( 72,103)( 73, 85)( 74, 86)( 75, 88)( 76, 87)( 77, 93)( 78, 94)
( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)(157,321)(158,322)
(159,324)(160,323)(161,317)(162,318)(163,320)(164,319)(165,313)(166,314)
(167,316)(168,315)(169,465)(170,466)(171,468)(172,467)(173,461)(174,462)
(175,464)(176,463)(177,457)(178,458)(179,460)(180,459)(181,453)(182,454)
(183,456)(184,455)(185,449)(186,450)(187,452)(188,451)(189,445)(190,446)
(191,448)(192,447)(193,441)(194,442)(195,444)(196,443)(197,437)(198,438)
(199,440)(200,439)(201,433)(202,434)(203,436)(204,435)(205,429)(206,430)
(207,432)(208,431)(209,425)(210,426)(211,428)(212,427)(213,421)(214,422)
(215,424)(216,423)(217,417)(218,418)(219,420)(220,419)(221,413)(222,414)
(223,416)(224,415)(225,409)(226,410)(227,412)(228,411)(229,405)(230,406)
(231,408)(232,407)(233,401)(234,402)(235,404)(236,403)(237,397)(238,398)
(239,400)(240,399)(241,393)(242,394)(243,396)(244,395)(245,389)(246,390)
(247,392)(248,391)(249,385)(250,386)(251,388)(252,387)(253,381)(254,382)
(255,384)(256,383)(257,377)(258,378)(259,380)(260,379)(261,373)(262,374)
(263,376)(264,375)(265,369)(266,370)(267,372)(268,371)(269,365)(270,366)
(271,368)(272,367)(273,361)(274,362)(275,364)(276,363)(277,357)(278,358)
(279,360)(280,359)(281,353)(282,354)(283,356)(284,355)(285,349)(286,350)
(287,352)(288,351)(289,345)(290,346)(291,348)(292,347)(293,341)(294,342)
(295,344)(296,343)(297,337)(298,338)(299,340)(300,339)(301,333)(302,334)
(303,336)(304,335)(305,329)(306,330)(307,332)(308,331)(309,325)(310,326)
(311,328)(312,327)(471,472)(473,477)(474,478)(475,480)(476,479)(481,613)
(482,614)(483,616)(484,615)(485,621)(486,622)(487,624)(488,623)(489,617)
(490,618)(491,620)(492,619)(493,601)(494,602)(495,604)(496,603)(497,609)
(498,610)(499,612)(500,611)(501,605)(502,606)(503,608)(504,607)(505,589)
(506,590)(507,592)(508,591)(509,597)(510,598)(511,600)(512,599)(513,593)
(514,594)(515,596)(516,595)(517,577)(518,578)(519,580)(520,579)(521,585)
(522,586)(523,588)(524,587)(525,581)(526,582)(527,584)(528,583)(529,565)
(530,566)(531,568)(532,567)(533,573)(534,574)(535,576)(536,575)(537,569)
(538,570)(539,572)(540,571)(541,553)(542,554)(543,556)(544,555)(545,561)
(546,562)(547,564)(548,563)(549,557)(550,558)(551,560)(552,559)(625,789)
(626,790)(627,792)(628,791)(629,785)(630,786)(631,788)(632,787)(633,781)
(634,782)(635,784)(636,783)(637,933)(638,934)(639,936)(640,935)(641,929)
(642,930)(643,932)(644,931)(645,925)(646,926)(647,928)(648,927)(649,921)
(650,922)(651,924)(652,923)(653,917)(654,918)(655,920)(656,919)(657,913)
(658,914)(659,916)(660,915)(661,909)(662,910)(663,912)(664,911)(665,905)
(666,906)(667,908)(668,907)(669,901)(670,902)(671,904)(672,903)(673,897)
(674,898)(675,900)(676,899)(677,893)(678,894)(679,896)(680,895)(681,889)
(682,890)(683,892)(684,891)(685,885)(686,886)(687,888)(688,887)(689,881)
(690,882)(691,884)(692,883)(693,877)(694,878)(695,880)(696,879)(697,873)
(698,874)(699,876)(700,875)(701,869)(702,870)(703,872)(704,871)(705,865)
(706,866)(707,868)(708,867)(709,861)(710,862)(711,864)(712,863)(713,857)
(714,858)(715,860)(716,859)(717,853)(718,854)(719,856)(720,855)(721,849)
(722,850)(723,852)(724,851)(725,845)(726,846)(727,848)(728,847)(729,841)
(730,842)(731,844)(732,843)(733,837)(734,838)(735,840)(736,839)(737,833)
(738,834)(739,836)(740,835)(741,829)(742,830)(743,832)(744,831)(745,825)
(746,826)(747,828)(748,827)(749,821)(750,822)(751,824)(752,823)(753,817)
(754,818)(755,820)(756,819)(757,813)(758,814)(759,816)(760,815)(761,809)
(762,810)(763,812)(764,811)(765,805)(766,806)(767,808)(768,807)(769,801)
(770,802)(771,804)(772,803)(773,797)(774,798)(775,800)(776,799)(777,793)
(778,794)(779,796)(780,795);
s1 := Sym(936)!( 1,169)( 2,172)( 3,171)( 4,170)( 5,177)( 6,180)( 7,179)
( 8,178)( 9,173)( 10,176)( 11,175)( 12,174)( 13,157)( 14,160)( 15,159)
( 16,158)( 17,165)( 18,168)( 19,167)( 20,166)( 21,161)( 22,164)( 23,163)
( 24,162)( 25,301)( 26,304)( 27,303)( 28,302)( 29,309)( 30,312)( 31,311)
( 32,310)( 33,305)( 34,308)( 35,307)( 36,306)( 37,289)( 38,292)( 39,291)
( 40,290)( 41,297)( 42,300)( 43,299)( 44,298)( 45,293)( 46,296)( 47,295)
( 48,294)( 49,277)( 50,280)( 51,279)( 52,278)( 53,285)( 54,288)( 55,287)
( 56,286)( 57,281)( 58,284)( 59,283)( 60,282)( 61,265)( 62,268)( 63,267)
( 64,266)( 65,273)( 66,276)( 67,275)( 68,274)( 69,269)( 70,272)( 71,271)
( 72,270)( 73,253)( 74,256)( 75,255)( 76,254)( 77,261)( 78,264)( 79,263)
( 80,262)( 81,257)( 82,260)( 83,259)( 84,258)( 85,241)( 86,244)( 87,243)
( 88,242)( 89,249)( 90,252)( 91,251)( 92,250)( 93,245)( 94,248)( 95,247)
( 96,246)( 97,229)( 98,232)( 99,231)(100,230)(101,237)(102,240)(103,239)
(104,238)(105,233)(106,236)(107,235)(108,234)(109,217)(110,220)(111,219)
(112,218)(113,225)(114,228)(115,227)(116,226)(117,221)(118,224)(119,223)
(120,222)(121,205)(122,208)(123,207)(124,206)(125,213)(126,216)(127,215)
(128,214)(129,209)(130,212)(131,211)(132,210)(133,193)(134,196)(135,195)
(136,194)(137,201)(138,204)(139,203)(140,202)(141,197)(142,200)(143,199)
(144,198)(145,181)(146,184)(147,183)(148,182)(149,189)(150,192)(151,191)
(152,190)(153,185)(154,188)(155,187)(156,186)(313,333)(314,336)(315,335)
(316,334)(317,329)(318,332)(319,331)(320,330)(321,325)(322,328)(323,327)
(324,326)(337,465)(338,468)(339,467)(340,466)(341,461)(342,464)(343,463)
(344,462)(345,457)(346,460)(347,459)(348,458)(349,453)(350,456)(351,455)
(352,454)(353,449)(354,452)(355,451)(356,450)(357,445)(358,448)(359,447)
(360,446)(361,441)(362,444)(363,443)(364,442)(365,437)(366,440)(367,439)
(368,438)(369,433)(370,436)(371,435)(372,434)(373,429)(374,432)(375,431)
(376,430)(377,425)(378,428)(379,427)(380,426)(381,421)(382,424)(383,423)
(384,422)(385,417)(386,420)(387,419)(388,418)(389,413)(390,416)(391,415)
(392,414)(393,409)(394,412)(395,411)(396,410)(397,405)(398,408)(399,407)
(400,406)(402,404)(469,637)(470,640)(471,639)(472,638)(473,645)(474,648)
(475,647)(476,646)(477,641)(478,644)(479,643)(480,642)(481,625)(482,628)
(483,627)(484,626)(485,633)(486,636)(487,635)(488,634)(489,629)(490,632)
(491,631)(492,630)(493,769)(494,772)(495,771)(496,770)(497,777)(498,780)
(499,779)(500,778)(501,773)(502,776)(503,775)(504,774)(505,757)(506,760)
(507,759)(508,758)(509,765)(510,768)(511,767)(512,766)(513,761)(514,764)
(515,763)(516,762)(517,745)(518,748)(519,747)(520,746)(521,753)(522,756)
(523,755)(524,754)(525,749)(526,752)(527,751)(528,750)(529,733)(530,736)
(531,735)(532,734)(533,741)(534,744)(535,743)(536,742)(537,737)(538,740)
(539,739)(540,738)(541,721)(542,724)(543,723)(544,722)(545,729)(546,732)
(547,731)(548,730)(549,725)(550,728)(551,727)(552,726)(553,709)(554,712)
(555,711)(556,710)(557,717)(558,720)(559,719)(560,718)(561,713)(562,716)
(563,715)(564,714)(565,697)(566,700)(567,699)(568,698)(569,705)(570,708)
(571,707)(572,706)(573,701)(574,704)(575,703)(576,702)(577,685)(578,688)
(579,687)(580,686)(581,693)(582,696)(583,695)(584,694)(585,689)(586,692)
(587,691)(588,690)(589,673)(590,676)(591,675)(592,674)(593,681)(594,684)
(595,683)(596,682)(597,677)(598,680)(599,679)(600,678)(601,661)(602,664)
(603,663)(604,662)(605,669)(606,672)(607,671)(608,670)(609,665)(610,668)
(611,667)(612,666)(613,649)(614,652)(615,651)(616,650)(617,657)(618,660)
(619,659)(620,658)(621,653)(622,656)(623,655)(624,654)(781,801)(782,804)
(783,803)(784,802)(785,797)(786,800)(787,799)(788,798)(789,793)(790,796)
(791,795)(792,794)(805,933)(806,936)(807,935)(808,934)(809,929)(810,932)
(811,931)(812,930)(813,925)(814,928)(815,927)(816,926)(817,921)(818,924)
(819,923)(820,922)(821,917)(822,920)(823,919)(824,918)(825,913)(826,916)
(827,915)(828,914)(829,909)(830,912)(831,911)(832,910)(833,905)(834,908)
(835,907)(836,906)(837,901)(838,904)(839,903)(840,902)(841,897)(842,900)
(843,899)(844,898)(845,893)(846,896)(847,895)(848,894)(849,889)(850,892)
(851,891)(852,890)(853,885)(854,888)(855,887)(856,886)(857,881)(858,884)
(859,883)(860,882)(861,877)(862,880)(863,879)(864,878)(865,873)(866,876)
(867,875)(868,874)(870,872);
s2 := Sym(936)!( 1,470)( 2,469)( 3,472)( 4,471)( 5,474)( 6,473)( 7,476)
( 8,475)( 9,478)( 10,477)( 11,480)( 12,479)( 13,482)( 14,481)( 15,484)
( 16,483)( 17,486)( 18,485)( 19,488)( 20,487)( 21,490)( 22,489)( 23,492)
( 24,491)( 25,494)( 26,493)( 27,496)( 28,495)( 29,498)( 30,497)( 31,500)
( 32,499)( 33,502)( 34,501)( 35,504)( 36,503)( 37,506)( 38,505)( 39,508)
( 40,507)( 41,510)( 42,509)( 43,512)( 44,511)( 45,514)( 46,513)( 47,516)
( 48,515)( 49,518)( 50,517)( 51,520)( 52,519)( 53,522)( 54,521)( 55,524)
( 56,523)( 57,526)( 58,525)( 59,528)( 60,527)( 61,530)( 62,529)( 63,532)
( 64,531)( 65,534)( 66,533)( 67,536)( 68,535)( 69,538)( 70,537)( 71,540)
( 72,539)( 73,542)( 74,541)( 75,544)( 76,543)( 77,546)( 78,545)( 79,548)
( 80,547)( 81,550)( 82,549)( 83,552)( 84,551)( 85,554)( 86,553)( 87,556)
( 88,555)( 89,558)( 90,557)( 91,560)( 92,559)( 93,562)( 94,561)( 95,564)
( 96,563)( 97,566)( 98,565)( 99,568)(100,567)(101,570)(102,569)(103,572)
(104,571)(105,574)(106,573)(107,576)(108,575)(109,578)(110,577)(111,580)
(112,579)(113,582)(114,581)(115,584)(116,583)(117,586)(118,585)(119,588)
(120,587)(121,590)(122,589)(123,592)(124,591)(125,594)(126,593)(127,596)
(128,595)(129,598)(130,597)(131,600)(132,599)(133,602)(134,601)(135,604)
(136,603)(137,606)(138,605)(139,608)(140,607)(141,610)(142,609)(143,612)
(144,611)(145,614)(146,613)(147,616)(148,615)(149,618)(150,617)(151,620)
(152,619)(153,622)(154,621)(155,624)(156,623)(157,626)(158,625)(159,628)
(160,627)(161,630)(162,629)(163,632)(164,631)(165,634)(166,633)(167,636)
(168,635)(169,638)(170,637)(171,640)(172,639)(173,642)(174,641)(175,644)
(176,643)(177,646)(178,645)(179,648)(180,647)(181,650)(182,649)(183,652)
(184,651)(185,654)(186,653)(187,656)(188,655)(189,658)(190,657)(191,660)
(192,659)(193,662)(194,661)(195,664)(196,663)(197,666)(198,665)(199,668)
(200,667)(201,670)(202,669)(203,672)(204,671)(205,674)(206,673)(207,676)
(208,675)(209,678)(210,677)(211,680)(212,679)(213,682)(214,681)(215,684)
(216,683)(217,686)(218,685)(219,688)(220,687)(221,690)(222,689)(223,692)
(224,691)(225,694)(226,693)(227,696)(228,695)(229,698)(230,697)(231,700)
(232,699)(233,702)(234,701)(235,704)(236,703)(237,706)(238,705)(239,708)
(240,707)(241,710)(242,709)(243,712)(244,711)(245,714)(246,713)(247,716)
(248,715)(249,718)(250,717)(251,720)(252,719)(253,722)(254,721)(255,724)
(256,723)(257,726)(258,725)(259,728)(260,727)(261,730)(262,729)(263,732)
(264,731)(265,734)(266,733)(267,736)(268,735)(269,738)(270,737)(271,740)
(272,739)(273,742)(274,741)(275,744)(276,743)(277,746)(278,745)(279,748)
(280,747)(281,750)(282,749)(283,752)(284,751)(285,754)(286,753)(287,756)
(288,755)(289,758)(290,757)(291,760)(292,759)(293,762)(294,761)(295,764)
(296,763)(297,766)(298,765)(299,768)(300,767)(301,770)(302,769)(303,772)
(304,771)(305,774)(306,773)(307,776)(308,775)(309,778)(310,777)(311,780)
(312,779)(313,782)(314,781)(315,784)(316,783)(317,786)(318,785)(319,788)
(320,787)(321,790)(322,789)(323,792)(324,791)(325,794)(326,793)(327,796)
(328,795)(329,798)(330,797)(331,800)(332,799)(333,802)(334,801)(335,804)
(336,803)(337,806)(338,805)(339,808)(340,807)(341,810)(342,809)(343,812)
(344,811)(345,814)(346,813)(347,816)(348,815)(349,818)(350,817)(351,820)
(352,819)(353,822)(354,821)(355,824)(356,823)(357,826)(358,825)(359,828)
(360,827)(361,830)(362,829)(363,832)(364,831)(365,834)(366,833)(367,836)
(368,835)(369,838)(370,837)(371,840)(372,839)(373,842)(374,841)(375,844)
(376,843)(377,846)(378,845)(379,848)(380,847)(381,850)(382,849)(383,852)
(384,851)(385,854)(386,853)(387,856)(388,855)(389,858)(390,857)(391,860)
(392,859)(393,862)(394,861)(395,864)(396,863)(397,866)(398,865)(399,868)
(400,867)(401,870)(402,869)(403,872)(404,871)(405,874)(406,873)(407,876)
(408,875)(409,878)(410,877)(411,880)(412,879)(413,882)(414,881)(415,884)
(416,883)(417,886)(418,885)(419,888)(420,887)(421,890)(422,889)(423,892)
(424,891)(425,894)(426,893)(427,896)(428,895)(429,898)(430,897)(431,900)
(432,899)(433,902)(434,901)(435,904)(436,903)(437,906)(438,905)(439,908)
(440,907)(441,910)(442,909)(443,912)(444,911)(445,914)(446,913)(447,916)
(448,915)(449,918)(450,917)(451,920)(452,919)(453,922)(454,921)(455,924)
(456,923)(457,926)(458,925)(459,928)(460,927)(461,930)(462,929)(463,932)
(464,931)(465,934)(466,933)(467,936)(468,935);
poly := sub<Sym(936)|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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope