Polytope of Type {240,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {240,4}*1920c
if this polytope has a name.
Group : SmallGroup(1920,237648)
Rank : 3
Schlafli Type : {240,4}
Number of vertices, edges, etc : 240, 480, 4
Order of s₀s₁s₂ : 240
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
   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) :
   2-fold quotients : {120,4}*960c
   4-fold quotients : {60,4}*480b
   5-fold quotients : {48,4}*384c
   8-fold quotients : {30,4}*240b
   10-fold quotients : {24,4}*192c
   16-fold quotients : {15,4}*120
   20-fold quotients : {12,4}*96b
   40-fold quotients : {6,4}*48c
   80-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope