Polytope of Type {4,240}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,240}*1920d
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}*384d
   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, 63)(  2, 64)(  3, 61)(  4, 62)(  5, 67)(  6, 68)(  7, 65)(  8, 66)
(  9, 71)( 10, 72)( 11, 69)( 12, 70)( 13, 75)( 14, 76)( 15, 73)( 16, 74)
( 17, 79)( 18, 80)( 19, 77)( 20, 78)( 21, 83)( 22, 84)( 23, 81)( 24, 82)
( 25, 87)( 26, 88)( 27, 85)( 28, 86)( 29, 91)( 30, 92)( 31, 89)( 32, 90)
( 33, 95)( 34, 96)( 35, 93)( 36, 94)( 37, 99)( 38,100)( 39, 97)( 40, 98)
( 41,103)( 42,104)( 43,101)( 44,102)( 45,107)( 46,108)( 47,105)( 48,106)
( 49,111)( 50,112)( 51,109)( 52,110)( 53,115)( 54,116)( 55,113)( 56,114)
( 57,119)( 58,120)( 59,117)( 60,118)(121,183)(122,184)(123,181)(124,182)
(125,187)(126,188)(127,185)(128,186)(129,191)(130,192)(131,189)(132,190)
(133,195)(134,196)(135,193)(136,194)(137,199)(138,200)(139,197)(140,198)
(141,203)(142,204)(143,201)(144,202)(145,207)(146,208)(147,205)(148,206)
(149,211)(150,212)(151,209)(152,210)(153,215)(154,216)(155,213)(156,214)
(157,219)(158,220)(159,217)(160,218)(161,223)(162,224)(163,221)(164,222)
(165,227)(166,228)(167,225)(168,226)(169,231)(170,232)(171,229)(172,230)
(173,235)(174,236)(175,233)(176,234)(177,239)(178,240)(179,237)(180,238)
(241,303)(242,304)(243,301)(244,302)(245,307)(246,308)(247,305)(248,306)
(249,311)(250,312)(251,309)(252,310)(253,315)(254,316)(255,313)(256,314)
(257,319)(258,320)(259,317)(260,318)(261,323)(262,324)(263,321)(264,322)
(265,327)(266,328)(267,325)(268,326)(269,331)(270,332)(271,329)(272,330)
(273,335)(274,336)(275,333)(276,334)(277,339)(278,340)(279,337)(280,338)
(281,343)(282,344)(283,341)(284,342)(285,347)(286,348)(287,345)(288,346)
(289,351)(290,352)(291,349)(292,350)(293,355)(294,356)(295,353)(296,354)
(297,359)(298,360)(299,357)(300,358)(361,423)(362,424)(363,421)(364,422)
(365,427)(366,428)(367,425)(368,426)(369,431)(370,432)(371,429)(372,430)
(373,435)(374,436)(375,433)(376,434)(377,439)(378,440)(379,437)(380,438)
(381,443)(382,444)(383,441)(384,442)(385,447)(386,448)(387,445)(388,446)
(389,451)(390,452)(391,449)(392,450)(393,455)(394,456)(395,453)(396,454)
(397,459)(398,460)(399,457)(400,458)(401,463)(402,464)(403,461)(404,462)
(405,467)(406,468)(407,465)(408,466)(409,471)(410,472)(411,469)(412,470)
(413,475)(414,476)(415,473)(416,474)(417,479)(418,480)(419,477)(420,478)
(481,543)(482,544)(483,541)(484,542)(485,547)(486,548)(487,545)(488,546)
(489,551)(490,552)(491,549)(492,550)(493,555)(494,556)(495,553)(496,554)
(497,559)(498,560)(499,557)(500,558)(501,563)(502,564)(503,561)(504,562)
(505,567)(506,568)(507,565)(508,566)(509,571)(510,572)(511,569)(512,570)
(513,575)(514,576)(515,573)(516,574)(517,579)(518,580)(519,577)(520,578)
(521,583)(522,584)(523,581)(524,582)(525,587)(526,588)(527,585)(528,586)
(529,591)(530,592)(531,589)(532,590)(533,595)(534,596)(535,593)(536,594)
(537,599)(538,600)(539,597)(540,598)(601,663)(602,664)(603,661)(604,662)
(605,667)(606,668)(607,665)(608,666)(609,671)(610,672)(611,669)(612,670)
(613,675)(614,676)(615,673)(616,674)(617,679)(618,680)(619,677)(620,678)
(621,683)(622,684)(623,681)(624,682)(625,687)(626,688)(627,685)(628,686)
(629,691)(630,692)(631,689)(632,690)(633,695)(634,696)(635,693)(636,694)
(637,699)(638,700)(639,697)(640,698)(641,703)(642,704)(643,701)(644,702)
(645,707)(646,708)(647,705)(648,706)(649,711)(650,712)(651,709)(652,710)
(653,715)(654,716)(655,713)(656,714)(657,719)(658,720)(659,717)(660,718)
(721,783)(722,784)(723,781)(724,782)(725,787)(726,788)(727,785)(728,786)
(729,791)(730,792)(731,789)(732,790)(733,795)(734,796)(735,793)(736,794)
(737,799)(738,800)(739,797)(740,798)(741,803)(742,804)(743,801)(744,802)
(745,807)(746,808)(747,805)(748,806)(749,811)(750,812)(751,809)(752,810)
(753,815)(754,816)(755,813)(756,814)(757,819)(758,820)(759,817)(760,818)
(761,823)(762,824)(763,821)(764,822)(765,827)(766,828)(767,825)(768,826)
(769,831)(770,832)(771,829)(772,830)(773,835)(774,836)(775,833)(776,834)
(777,839)(778,840)(779,837)(780,838)(841,903)(842,904)(843,901)(844,902)
(845,907)(846,908)(847,905)(848,906)(849,911)(850,912)(851,909)(852,910)
(853,915)(854,916)(855,913)(856,914)(857,919)(858,920)(859,917)(860,918)
(861,923)(862,924)(863,921)(864,922)(865,927)(866,928)(867,925)(868,926)
(869,931)(870,932)(871,929)(872,930)(873,935)(874,936)(875,933)(876,934)
(877,939)(878,940)(879,937)(880,938)(881,943)(882,944)(883,941)(884,942)
(885,947)(886,948)(887,945)(888,946)(889,951)(890,952)(891,949)(892,950)
(893,955)(894,956)(895,953)(896,954)(897,959)(898,960)(899,957)(900,958);;
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*s2*s1*s0*s1*s2*s1*s2*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*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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, 63)(  2, 64)(  3, 61)(  4, 62)(  5, 67)(  6, 68)(  7, 65)
(  8, 66)(  9, 71)( 10, 72)( 11, 69)( 12, 70)( 13, 75)( 14, 76)( 15, 73)
( 16, 74)( 17, 79)( 18, 80)( 19, 77)( 20, 78)( 21, 83)( 22, 84)( 23, 81)
( 24, 82)( 25, 87)( 26, 88)( 27, 85)( 28, 86)( 29, 91)( 30, 92)( 31, 89)
( 32, 90)( 33, 95)( 34, 96)( 35, 93)( 36, 94)( 37, 99)( 38,100)( 39, 97)
( 40, 98)( 41,103)( 42,104)( 43,101)( 44,102)( 45,107)( 46,108)( 47,105)
( 48,106)( 49,111)( 50,112)( 51,109)( 52,110)( 53,115)( 54,116)( 55,113)
( 56,114)( 57,119)( 58,120)( 59,117)( 60,118)(121,183)(122,184)(123,181)
(124,182)(125,187)(126,188)(127,185)(128,186)(129,191)(130,192)(131,189)
(132,190)(133,195)(134,196)(135,193)(136,194)(137,199)(138,200)(139,197)
(140,198)(141,203)(142,204)(143,201)(144,202)(145,207)(146,208)(147,205)
(148,206)(149,211)(150,212)(151,209)(152,210)(153,215)(154,216)(155,213)
(156,214)(157,219)(158,220)(159,217)(160,218)(161,223)(162,224)(163,221)
(164,222)(165,227)(166,228)(167,225)(168,226)(169,231)(170,232)(171,229)
(172,230)(173,235)(174,236)(175,233)(176,234)(177,239)(178,240)(179,237)
(180,238)(241,303)(242,304)(243,301)(244,302)(245,307)(246,308)(247,305)
(248,306)(249,311)(250,312)(251,309)(252,310)(253,315)(254,316)(255,313)
(256,314)(257,319)(258,320)(259,317)(260,318)(261,323)(262,324)(263,321)
(264,322)(265,327)(266,328)(267,325)(268,326)(269,331)(270,332)(271,329)
(272,330)(273,335)(274,336)(275,333)(276,334)(277,339)(278,340)(279,337)
(280,338)(281,343)(282,344)(283,341)(284,342)(285,347)(286,348)(287,345)
(288,346)(289,351)(290,352)(291,349)(292,350)(293,355)(294,356)(295,353)
(296,354)(297,359)(298,360)(299,357)(300,358)(361,423)(362,424)(363,421)
(364,422)(365,427)(366,428)(367,425)(368,426)(369,431)(370,432)(371,429)
(372,430)(373,435)(374,436)(375,433)(376,434)(377,439)(378,440)(379,437)
(380,438)(381,443)(382,444)(383,441)(384,442)(385,447)(386,448)(387,445)
(388,446)(389,451)(390,452)(391,449)(392,450)(393,455)(394,456)(395,453)
(396,454)(397,459)(398,460)(399,457)(400,458)(401,463)(402,464)(403,461)
(404,462)(405,467)(406,468)(407,465)(408,466)(409,471)(410,472)(411,469)
(412,470)(413,475)(414,476)(415,473)(416,474)(417,479)(418,480)(419,477)
(420,478)(481,543)(482,544)(483,541)(484,542)(485,547)(486,548)(487,545)
(488,546)(489,551)(490,552)(491,549)(492,550)(493,555)(494,556)(495,553)
(496,554)(497,559)(498,560)(499,557)(500,558)(501,563)(502,564)(503,561)
(504,562)(505,567)(506,568)(507,565)(508,566)(509,571)(510,572)(511,569)
(512,570)(513,575)(514,576)(515,573)(516,574)(517,579)(518,580)(519,577)
(520,578)(521,583)(522,584)(523,581)(524,582)(525,587)(526,588)(527,585)
(528,586)(529,591)(530,592)(531,589)(532,590)(533,595)(534,596)(535,593)
(536,594)(537,599)(538,600)(539,597)(540,598)(601,663)(602,664)(603,661)
(604,662)(605,667)(606,668)(607,665)(608,666)(609,671)(610,672)(611,669)
(612,670)(613,675)(614,676)(615,673)(616,674)(617,679)(618,680)(619,677)
(620,678)(621,683)(622,684)(623,681)(624,682)(625,687)(626,688)(627,685)
(628,686)(629,691)(630,692)(631,689)(632,690)(633,695)(634,696)(635,693)
(636,694)(637,699)(638,700)(639,697)(640,698)(641,703)(642,704)(643,701)
(644,702)(645,707)(646,708)(647,705)(648,706)(649,711)(650,712)(651,709)
(652,710)(653,715)(654,716)(655,713)(656,714)(657,719)(658,720)(659,717)
(660,718)(721,783)(722,784)(723,781)(724,782)(725,787)(726,788)(727,785)
(728,786)(729,791)(730,792)(731,789)(732,790)(733,795)(734,796)(735,793)
(736,794)(737,799)(738,800)(739,797)(740,798)(741,803)(742,804)(743,801)
(744,802)(745,807)(746,808)(747,805)(748,806)(749,811)(750,812)(751,809)
(752,810)(753,815)(754,816)(755,813)(756,814)(757,819)(758,820)(759,817)
(760,818)(761,823)(762,824)(763,821)(764,822)(765,827)(766,828)(767,825)
(768,826)(769,831)(770,832)(771,829)(772,830)(773,835)(774,836)(775,833)
(776,834)(777,839)(778,840)(779,837)(780,838)(841,903)(842,904)(843,901)
(844,902)(845,907)(846,908)(847,905)(848,906)(849,911)(850,912)(851,909)
(852,910)(853,915)(854,916)(855,913)(856,914)(857,919)(858,920)(859,917)
(860,918)(861,923)(862,924)(863,921)(864,922)(865,927)(866,928)(867,925)
(868,926)(869,931)(870,932)(871,929)(872,930)(873,935)(874,936)(875,933)
(876,934)(877,939)(878,940)(879,937)(880,938)(881,943)(882,944)(883,941)
(884,942)(885,947)(886,948)(887,945)(888,946)(889,951)(890,952)(891,949)
(892,950)(893,955)(894,956)(895,953)(896,954)(897,959)(898,960)(899,957)
(900,958);
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*s2*s1*s0*s1*s2*s1*s2*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*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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