Polytope of Type {4,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,60}*1920e
if this polytope has a name.
Group : SmallGroup(1920,239568)
Rank : 3
Schlafli Type : {4,60}
Number of vertices, edges, etc : 16, 480, 240
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {4,30}*960b
   4-fold quotients : {4,30}*480
   5-fold quotients : {4,12}*384e
   8-fold quotients : {4,30}*240a, {4,15}*240, {4,30}*240b, {4,30}*240c
   10-fold quotients : {4,6}*192b
   16-fold quotients : {4,15}*120, {2,30}*120
   20-fold quotients : {4,6}*96
   24-fold quotients : {4,10}*80
   32-fold quotients : {2,15}*60
   40-fold quotients : {4,6}*48a, {4,3}*48, {4,6}*48b, {4,6}*48c
   48-fold quotients : {2,10}*40
   80-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {2,5}*20
   120-fold quotients : {4,2}*16
   160-fold quotients : {2,3}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope