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# Polytope of Type {8,120}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,120}*1920d
if this polytope has a name.
Group : SmallGroup(1920,16585)
Rank : 3
Schlafli Type : {8,120}
Number of vertices, edges, etc : 8, 480, 120
Order of s0s1s2 : 120
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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}*960b, {8,60}*960b
3-fold quotients : {8,40}*640c
4-fold quotients : {4,60}*480a
5-fold quotients : {8,24}*384c
6-fold quotients : {4,40}*320b, {8,20}*320b
8-fold quotients : {2,60}*240, {4,30}*240a
10-fold quotients : {4,24}*192b, {8,12}*192b
12-fold quotients : {4,20}*160
15-fold quotients : {8,8}*128d
16-fold quotients : {2,30}*120
20-fold quotients : {4,12}*96a
24-fold quotients : {2,20}*80, {4,10}*80
30-fold quotients : {4,8}*64b, {8,4}*64b
32-fold quotients : {2,15}*60
40-fold quotients : {2,12}*48, {4,6}*48a
48-fold quotients : {2,10}*40
60-fold quotients : {4,4}*32
80-fold quotients : {2,6}*24
96-fold quotients : {2,5}*20
120-fold quotients : {2,4}*16, {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 := (  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,486)(  7,487)(  8,488)
(  9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)
( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)( 24,504)
( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,511)( 32,512)
( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)( 40,520)
( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)( 48,528)
( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)( 56,536)
( 57,537)( 58,538)( 59,539)( 60,540)( 61,556)( 62,557)( 63,558)( 64,559)
( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)( 72,567)
( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)( 80,545)
( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)( 88,553)
( 89,554)( 90,555)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,591)
( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)(104,599)
(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)(112,577)
(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)(120,585)
(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)(128,638)
(129,639)(130,640)(131,641)(132,642)(133,643)(134,644)(135,645)(136,646)
(137,647)(138,648)(139,649)(140,650)(141,651)(142,652)(143,653)(144,654)
(145,655)(146,656)(147,657)(148,658)(149,659)(150,660)(151,601)(152,602)
(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)(160,610)
(161,611)(162,612)(163,613)(164,614)(165,615)(166,616)(167,617)(168,618)
(169,619)(170,620)(171,621)(172,622)(173,623)(174,624)(175,625)(176,626)
(177,627)(178,628)(179,629)(180,630)(181,706)(182,707)(183,708)(184,709)
(185,710)(186,711)(187,712)(188,713)(189,714)(190,715)(191,716)(192,717)
(193,718)(194,719)(195,720)(196,691)(197,692)(198,693)(199,694)(200,695)
(201,696)(202,697)(203,698)(204,699)(205,700)(206,701)(207,702)(208,703)
(209,704)(210,705)(211,676)(212,677)(213,678)(214,679)(215,680)(216,681)
(217,682)(218,683)(219,684)(220,685)(221,686)(222,687)(223,688)(224,689)
(225,690)(226,661)(227,662)(228,663)(229,664)(230,665)(231,666)(232,667)
(233,668)(234,669)(235,670)(236,671)(237,672)(238,673)(239,674)(240,675)
(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)(248,728)
(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)(256,736)
(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)(264,744)
(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,751)(272,752)
(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)(280,760)
(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)(288,768)
(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)(296,776)
(297,777)(298,778)(299,779)(300,780)(301,796)(302,797)(303,798)(304,799)
(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)(312,807)
(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)(320,785)
(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)(328,793)
(329,794)(330,795)(331,826)(332,827)(333,828)(334,829)(335,830)(336,831)
(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)(344,839)
(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)(352,817)
(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)(360,825)
(361,871)(362,872)(363,873)(364,874)(365,875)(366,876)(367,877)(368,878)
(369,879)(370,880)(371,881)(372,882)(373,883)(374,884)(375,885)(376,886)
(377,887)(378,888)(379,889)(380,890)(381,891)(382,892)(383,893)(384,894)
(385,895)(386,896)(387,897)(388,898)(389,899)(390,900)(391,841)(392,842)
(393,843)(394,844)(395,845)(396,846)(397,847)(398,848)(399,849)(400,850)
(401,851)(402,852)(403,853)(404,854)(405,855)(406,856)(407,857)(408,858)
(409,859)(410,860)(411,861)(412,862)(413,863)(414,864)(415,865)(416,866)
(417,867)(418,868)(419,869)(420,870)(421,946)(422,947)(423,948)(424,949)
(425,950)(426,951)(427,952)(428,953)(429,954)(430,955)(431,956)(432,957)
(433,958)(434,959)(435,960)(436,931)(437,932)(438,933)(439,934)(440,935)
(441,936)(442,937)(443,938)(444,939)(445,940)(446,941)(447,942)(448,943)
(449,944)(450,945)(451,916)(452,917)(453,918)(454,919)(455,920)(456,921)
(457,922)(458,923)(459,924)(460,925)(461,926)(462,927)(463,928)(464,929)
(465,930)(466,901)(467,902)(468,903)(469,904)(470,905)(471,906)(472,907)
(473,908)(474,909)(475,910)(476,911)(477,912)(478,913)(479,914)(480,915);;
s1 := (  2,  5)(  3,  4)(  6, 11)(  7, 15)(  8, 14)(  9, 13)( 10, 12)( 17, 20)
( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)
( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)
( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 61,106)( 62,110)( 63,109)( 64,108)
( 65,107)( 66,116)( 67,120)( 68,119)( 69,118)( 70,117)( 71,111)( 72,115)
( 73,114)( 74,113)( 75,112)( 76, 91)( 77, 95)( 78, 94)( 79, 93)( 80, 92)
( 81,101)( 82,105)( 83,104)( 84,103)( 85,102)( 86, 96)( 87,100)( 88, 99)
( 89, 98)( 90, 97)(121,151)(122,155)(123,154)(124,153)(125,152)(126,161)
(127,165)(128,164)(129,163)(130,162)(131,156)(132,160)(133,159)(134,158)
(135,157)(136,166)(137,170)(138,169)(139,168)(140,167)(141,176)(142,180)
(143,179)(144,178)(145,177)(146,171)(147,175)(148,174)(149,173)(150,172)
(181,196)(182,200)(183,199)(184,198)(185,197)(186,206)(187,210)(188,209)
(189,208)(190,207)(191,201)(192,205)(193,204)(194,203)(195,202)(211,226)
(212,230)(213,229)(214,228)(215,227)(216,236)(217,240)(218,239)(219,238)
(220,237)(221,231)(222,235)(223,234)(224,233)(225,232)(241,301)(242,305)
(243,304)(244,303)(245,302)(246,311)(247,315)(248,314)(249,313)(250,312)
(251,306)(252,310)(253,309)(254,308)(255,307)(256,316)(257,320)(258,319)
(259,318)(260,317)(261,326)(262,330)(263,329)(264,328)(265,327)(266,321)
(267,325)(268,324)(269,323)(270,322)(271,331)(272,335)(273,334)(274,333)
(275,332)(276,341)(277,345)(278,344)(279,343)(280,342)(281,336)(282,340)
(283,339)(284,338)(285,337)(286,346)(287,350)(288,349)(289,348)(290,347)
(291,356)(292,360)(293,359)(294,358)(295,357)(296,351)(297,355)(298,354)
(299,353)(300,352)(361,451)(362,455)(363,454)(364,453)(365,452)(366,461)
(367,465)(368,464)(369,463)(370,462)(371,456)(372,460)(373,459)(374,458)
(375,457)(376,466)(377,470)(378,469)(379,468)(380,467)(381,476)(382,480)
(383,479)(384,478)(385,477)(386,471)(387,475)(388,474)(389,473)(390,472)
(391,421)(392,425)(393,424)(394,423)(395,422)(396,431)(397,435)(398,434)
(399,433)(400,432)(401,426)(402,430)(403,429)(404,428)(405,427)(406,436)
(407,440)(408,439)(409,438)(410,437)(411,446)(412,450)(413,449)(414,448)
(415,447)(416,441)(417,445)(418,444)(419,443)(420,442)(481,601)(482,605)
(483,604)(484,603)(485,602)(486,611)(487,615)(488,614)(489,613)(490,612)
(491,606)(492,610)(493,609)(494,608)(495,607)(496,616)(497,620)(498,619)
(499,618)(500,617)(501,626)(502,630)(503,629)(504,628)(505,627)(506,621)
(507,625)(508,624)(509,623)(510,622)(511,631)(512,635)(513,634)(514,633)
(515,632)(516,641)(517,645)(518,644)(519,643)(520,642)(521,636)(522,640)
(523,639)(524,638)(525,637)(526,646)(527,650)(528,649)(529,648)(530,647)
(531,656)(532,660)(533,659)(534,658)(535,657)(536,651)(537,655)(538,654)
(539,653)(540,652)(541,706)(542,710)(543,709)(544,708)(545,707)(546,716)
(547,720)(548,719)(549,718)(550,717)(551,711)(552,715)(553,714)(554,713)
(555,712)(556,691)(557,695)(558,694)(559,693)(560,692)(561,701)(562,705)
(563,704)(564,703)(565,702)(566,696)(567,700)(568,699)(569,698)(570,697)
(571,676)(572,680)(573,679)(574,678)(575,677)(576,686)(577,690)(578,689)
(579,688)(580,687)(581,681)(582,685)(583,684)(584,683)(585,682)(586,661)
(587,665)(588,664)(589,663)(590,662)(591,671)(592,675)(593,674)(594,673)
(595,672)(596,666)(597,670)(598,669)(599,668)(600,667)(721,916)(722,920)
(723,919)(724,918)(725,917)(726,926)(727,930)(728,929)(729,928)(730,927)
(731,921)(732,925)(733,924)(734,923)(735,922)(736,901)(737,905)(738,904)
(739,903)(740,902)(741,911)(742,915)(743,914)(744,913)(745,912)(746,906)
(747,910)(748,909)(749,908)(750,907)(751,946)(752,950)(753,949)(754,948)
(755,947)(756,956)(757,960)(758,959)(759,958)(760,957)(761,951)(762,955)
(763,954)(764,953)(765,952)(766,931)(767,935)(768,934)(769,933)(770,932)
(771,941)(772,945)(773,944)(774,943)(775,942)(776,936)(777,940)(778,939)
(779,938)(780,937)(781,856)(782,860)(783,859)(784,858)(785,857)(786,866)
(787,870)(788,869)(789,868)(790,867)(791,861)(792,865)(793,864)(794,863)
(795,862)(796,841)(797,845)(798,844)(799,843)(800,842)(801,851)(802,855)
(803,854)(804,853)(805,852)(806,846)(807,850)(808,849)(809,848)(810,847)
(811,886)(812,890)(813,889)(814,888)(815,887)(816,896)(817,900)(818,899)
(819,898)(820,897)(821,891)(822,895)(823,894)(824,893)(825,892)(826,871)
(827,875)(828,874)(829,873)(830,872)(831,881)(832,885)(833,884)(834,883)
(835,882)(836,876)(837,880)(838,879)(839,878)(840,877);;
s2 := (  1,247)(  2,246)(  3,250)(  4,249)(  5,248)(  6,242)(  7,241)(  8,245)
(  9,244)( 10,243)( 11,252)( 12,251)( 13,255)( 14,254)( 15,253)( 16,262)
( 17,261)( 18,265)( 19,264)( 20,263)( 21,257)( 22,256)( 23,260)( 24,259)
( 25,258)( 26,267)( 27,266)( 28,270)( 29,269)( 30,268)( 31,277)( 32,276)
( 33,280)( 34,279)( 35,278)( 36,272)( 37,271)( 38,275)( 39,274)( 40,273)
( 41,282)( 42,281)( 43,285)( 44,284)( 45,283)( 46,292)( 47,291)( 48,295)
( 49,294)( 50,293)( 51,287)( 52,286)( 53,290)( 54,289)( 55,288)( 56,297)
( 57,296)( 58,300)( 59,299)( 60,298)( 61,352)( 62,351)( 63,355)( 64,354)
( 65,353)( 66,347)( 67,346)( 68,350)( 69,349)( 70,348)( 71,357)( 72,356)
( 73,360)( 74,359)( 75,358)( 76,337)( 77,336)( 78,340)( 79,339)( 80,338)
( 81,332)( 82,331)( 83,335)( 84,334)( 85,333)( 86,342)( 87,341)( 88,345)
( 89,344)( 90,343)( 91,322)( 92,321)( 93,325)( 94,324)( 95,323)( 96,317)
( 97,316)( 98,320)( 99,319)(100,318)(101,327)(102,326)(103,330)(104,329)
(105,328)(106,307)(107,306)(108,310)(109,309)(110,308)(111,302)(112,301)
(113,305)(114,304)(115,303)(116,312)(117,311)(118,315)(119,314)(120,313)
(121,382)(122,381)(123,385)(124,384)(125,383)(126,377)(127,376)(128,380)
(129,379)(130,378)(131,387)(132,386)(133,390)(134,389)(135,388)(136,367)
(137,366)(138,370)(139,369)(140,368)(141,362)(142,361)(143,365)(144,364)
(145,363)(146,372)(147,371)(148,375)(149,374)(150,373)(151,412)(152,411)
(153,415)(154,414)(155,413)(156,407)(157,406)(158,410)(159,409)(160,408)
(161,417)(162,416)(163,420)(164,419)(165,418)(166,397)(167,396)(168,400)
(169,399)(170,398)(171,392)(172,391)(173,395)(174,394)(175,393)(176,402)
(177,401)(178,405)(179,404)(180,403)(181,457)(182,456)(183,460)(184,459)
(185,458)(186,452)(187,451)(188,455)(189,454)(190,453)(191,462)(192,461)
(193,465)(194,464)(195,463)(196,472)(197,471)(198,475)(199,474)(200,473)
(201,467)(202,466)(203,470)(204,469)(205,468)(206,477)(207,476)(208,480)
(209,479)(210,478)(211,427)(212,426)(213,430)(214,429)(215,428)(216,422)
(217,421)(218,425)(219,424)(220,423)(221,432)(222,431)(223,435)(224,434)
(225,433)(226,442)(227,441)(228,445)(229,444)(230,443)(231,437)(232,436)
(233,440)(234,439)(235,438)(236,447)(237,446)(238,450)(239,449)(240,448)
(481,727)(482,726)(483,730)(484,729)(485,728)(486,722)(487,721)(488,725)
(489,724)(490,723)(491,732)(492,731)(493,735)(494,734)(495,733)(496,742)
(497,741)(498,745)(499,744)(500,743)(501,737)(502,736)(503,740)(504,739)
(505,738)(506,747)(507,746)(508,750)(509,749)(510,748)(511,757)(512,756)
(513,760)(514,759)(515,758)(516,752)(517,751)(518,755)(519,754)(520,753)
(521,762)(522,761)(523,765)(524,764)(525,763)(526,772)(527,771)(528,775)
(529,774)(530,773)(531,767)(532,766)(533,770)(534,769)(535,768)(536,777)
(537,776)(538,780)(539,779)(540,778)(541,832)(542,831)(543,835)(544,834)
(545,833)(546,827)(547,826)(548,830)(549,829)(550,828)(551,837)(552,836)
(553,840)(554,839)(555,838)(556,817)(557,816)(558,820)(559,819)(560,818)
(561,812)(562,811)(563,815)(564,814)(565,813)(566,822)(567,821)(568,825)
(569,824)(570,823)(571,802)(572,801)(573,805)(574,804)(575,803)(576,797)
(577,796)(578,800)(579,799)(580,798)(581,807)(582,806)(583,810)(584,809)
(585,808)(586,787)(587,786)(588,790)(589,789)(590,788)(591,782)(592,781)
(593,785)(594,784)(595,783)(596,792)(597,791)(598,795)(599,794)(600,793)
(601,862)(602,861)(603,865)(604,864)(605,863)(606,857)(607,856)(608,860)
(609,859)(610,858)(611,867)(612,866)(613,870)(614,869)(615,868)(616,847)
(617,846)(618,850)(619,849)(620,848)(621,842)(622,841)(623,845)(624,844)
(625,843)(626,852)(627,851)(628,855)(629,854)(630,853)(631,892)(632,891)
(633,895)(634,894)(635,893)(636,887)(637,886)(638,890)(639,889)(640,888)
(641,897)(642,896)(643,900)(644,899)(645,898)(646,877)(647,876)(648,880)
(649,879)(650,878)(651,872)(652,871)(653,875)(654,874)(655,873)(656,882)
(657,881)(658,885)(659,884)(660,883)(661,937)(662,936)(663,940)(664,939)
(665,938)(666,932)(667,931)(668,935)(669,934)(670,933)(671,942)(672,941)
(673,945)(674,944)(675,943)(676,952)(677,951)(678,955)(679,954)(680,953)
(681,947)(682,946)(683,950)(684,949)(685,948)(686,957)(687,956)(688,960)
(689,959)(690,958)(691,907)(692,906)(693,910)(694,909)(695,908)(696,902)
(697,901)(698,905)(699,904)(700,903)(701,912)(702,911)(703,915)(704,914)
(705,913)(706,922)(707,921)(708,925)(709,924)(710,923)(711,917)(712,916)
(713,920)(714,919)(715,918)(716,927)(717,926)(718,930)(719,929)(720,928);;
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, s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
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*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope