Polytope of Type {4,240}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope