Polytope of Type {240,4}

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