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# Polytope of Type {24,40}

Atlas Canonical Name : {24,40}*1920b
if this polytope has a name.
Group : SmallGroup(1920,14535)
Rank : 3
Schlafli Type : {24,40}
Number of vertices, edges, etc : 24, 480, 40
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 : {24,20}*960a, {12,40}*960b
3-fold quotients : {8,40}*640d
4-fold quotients : {24,10}*480, {12,20}*480
5-fold quotients : {24,8}*384a
6-fold quotients : {4,40}*320b, {8,20}*320a
8-fold quotients : {12,10}*240, {6,20}*240a
10-fold quotients : {24,4}*192a, {12,8}*192b
12-fold quotients : {4,20}*160, {8,10}*160
15-fold quotients : {8,8}*128c
16-fold quotients : {6,10}*120
20-fold quotients : {12,4}*96a, {24,2}*96
24-fold quotients : {2,20}*80, {4,10}*80
30-fold quotients : {8,4}*64a, {4,8}*64b
40-fold quotients : {12,2}*48, {6,4}*48a
48-fold quotients : {2,10}*40
60-fold quotients : {4,4}*32, {8,2}*32
80-fold quotients : {6,2}*24
96-fold quotients : {2,5}*20
120-fold quotients : {2,4}*16, {4,2}*16
160-fold quotients : {3,2}*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)(  6,491)(  7,492)(  8,493)
(  9,494)( 10,495)( 11,486)( 12,487)( 13,488)( 14,489)( 15,490)( 16,496)
( 17,497)( 18,498)( 19,499)( 20,500)( 21,506)( 22,507)( 23,508)( 24,509)
( 25,510)( 26,501)( 27,502)( 28,503)( 29,504)( 30,505)( 31,511)( 32,512)
( 33,513)( 34,514)( 35,515)( 36,521)( 37,522)( 38,523)( 39,524)( 40,525)
( 41,516)( 42,517)( 43,518)( 44,519)( 45,520)( 46,526)( 47,527)( 48,528)
( 49,529)( 50,530)( 51,536)( 52,537)( 53,538)( 54,539)( 55,540)( 56,531)
( 57,532)( 58,533)( 59,534)( 60,535)( 61,556)( 62,557)( 63,558)( 64,559)
( 65,560)( 66,566)( 67,567)( 68,568)( 69,569)( 70,570)( 71,561)( 72,562)
( 73,563)( 74,564)( 75,565)( 76,541)( 77,542)( 78,543)( 79,544)( 80,545)
( 81,551)( 82,552)( 83,553)( 84,554)( 85,555)( 86,546)( 87,547)( 88,548)
( 89,549)( 90,550)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,596)
( 97,597)( 98,598)( 99,599)(100,600)(101,591)(102,592)(103,593)(104,594)
(105,595)(106,571)(107,572)(108,573)(109,574)(110,575)(111,581)(112,582)
(113,583)(114,584)(115,585)(116,576)(117,577)(118,578)(119,579)(120,580)
(121,631)(122,632)(123,633)(124,634)(125,635)(126,641)(127,642)(128,643)
(129,644)(130,645)(131,636)(132,637)(133,638)(134,639)(135,640)(136,646)
(137,647)(138,648)(139,649)(140,650)(141,656)(142,657)(143,658)(144,659)
(145,660)(146,651)(147,652)(148,653)(149,654)(150,655)(151,601)(152,602)
(153,603)(154,604)(155,605)(156,611)(157,612)(158,613)(159,614)(160,615)
(161,606)(162,607)(163,608)(164,609)(165,610)(166,616)(167,617)(168,618)
(169,619)(170,620)(171,626)(172,627)(173,628)(174,629)(175,630)(176,621)
(177,622)(178,623)(179,624)(180,625)(181,706)(182,707)(183,708)(184,709)
(185,710)(186,716)(187,717)(188,718)(189,719)(190,720)(191,711)(192,712)
(193,713)(194,714)(195,715)(196,691)(197,692)(198,693)(199,694)(200,695)
(201,701)(202,702)(203,703)(204,704)(205,705)(206,696)(207,697)(208,698)
(209,699)(210,700)(211,676)(212,677)(213,678)(214,679)(215,680)(216,686)
(217,687)(218,688)(219,689)(220,690)(221,681)(222,682)(223,683)(224,684)
(225,685)(226,661)(227,662)(228,663)(229,664)(230,665)(231,671)(232,672)
(233,673)(234,674)(235,675)(236,666)(237,667)(238,668)(239,669)(240,670)
(241,721)(242,722)(243,723)(244,724)(245,725)(246,731)(247,732)(248,733)
(249,734)(250,735)(251,726)(252,727)(253,728)(254,729)(255,730)(256,736)
(257,737)(258,738)(259,739)(260,740)(261,746)(262,747)(263,748)(264,749)
(265,750)(266,741)(267,742)(268,743)(269,744)(270,745)(271,751)(272,752)
(273,753)(274,754)(275,755)(276,761)(277,762)(278,763)(279,764)(280,765)
(281,756)(282,757)(283,758)(284,759)(285,760)(286,766)(287,767)(288,768)
(289,769)(290,770)(291,776)(292,777)(293,778)(294,779)(295,780)(296,771)
(297,772)(298,773)(299,774)(300,775)(301,796)(302,797)(303,798)(304,799)
(305,800)(306,806)(307,807)(308,808)(309,809)(310,810)(311,801)(312,802)
(313,803)(314,804)(315,805)(316,781)(317,782)(318,783)(319,784)(320,785)
(321,791)(322,792)(323,793)(324,794)(325,795)(326,786)(327,787)(328,788)
(329,789)(330,790)(331,826)(332,827)(333,828)(334,829)(335,830)(336,836)
(337,837)(338,838)(339,839)(340,840)(341,831)(342,832)(343,833)(344,834)
(345,835)(346,811)(347,812)(348,813)(349,814)(350,815)(351,821)(352,822)
(353,823)(354,824)(355,825)(356,816)(357,817)(358,818)(359,819)(360,820)
(361,871)(362,872)(363,873)(364,874)(365,875)(366,881)(367,882)(368,883)
(369,884)(370,885)(371,876)(372,877)(373,878)(374,879)(375,880)(376,886)
(377,887)(378,888)(379,889)(380,890)(381,896)(382,897)(383,898)(384,899)
(385,900)(386,891)(387,892)(388,893)(389,894)(390,895)(391,841)(392,842)
(393,843)(394,844)(395,845)(396,851)(397,852)(398,853)(399,854)(400,855)
(401,846)(402,847)(403,848)(404,849)(405,850)(406,856)(407,857)(408,858)
(409,859)(410,860)(411,866)(412,867)(413,868)(414,869)(415,870)(416,861)
(417,862)(418,863)(419,864)(420,865)(421,946)(422,947)(423,948)(424,949)
(425,950)(426,956)(427,957)(428,958)(429,959)(430,960)(431,951)(432,952)
(433,953)(434,954)(435,955)(436,931)(437,932)(438,933)(439,934)(440,935)
(441,941)(442,942)(443,943)(444,944)(445,945)(446,936)(447,937)(448,938)
(449,939)(450,940)(451,916)(452,917)(453,918)(454,919)(455,920)(456,926)
(457,927)(458,928)(459,929)(460,930)(461,921)(462,922)(463,923)(464,924)
(465,925)(466,901)(467,902)(468,903)(469,904)(470,905)(471,911)(472,912)
(473,913)(474,914)(475,915)(476,906)(477,907)(478,908)(479,909)(480,910);;
s1 := (  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 12, 15)( 13, 14)( 16, 21)
( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 36)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 42, 45)( 43, 44)( 46, 51)( 47, 55)( 48, 54)
( 49, 53)( 50, 52)( 57, 60)( 58, 59)( 61, 81)( 62, 85)( 63, 84)( 64, 83)
( 65, 82)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 71, 86)( 72, 90)
( 73, 89)( 74, 88)( 75, 87)( 91,111)( 92,115)( 93,114)( 94,113)( 95,112)
( 96,106)( 97,110)( 98,109)( 99,108)(100,107)(101,116)(102,120)(103,119)
(104,118)(105,117)(121,156)(122,160)(123,159)(124,158)(125,157)(126,151)
(127,155)(128,154)(129,153)(130,152)(131,161)(132,165)(133,164)(134,163)
(135,162)(136,171)(137,175)(138,174)(139,173)(140,172)(141,166)(142,170)
(143,169)(144,168)(145,167)(146,176)(147,180)(148,179)(149,178)(150,177)
(181,231)(182,235)(183,234)(184,233)(185,232)(186,226)(187,230)(188,229)
(189,228)(190,227)(191,236)(192,240)(193,239)(194,238)(195,237)(196,216)
(197,220)(198,219)(199,218)(200,217)(201,211)(202,215)(203,214)(204,213)
(205,212)(206,221)(207,225)(208,224)(209,223)(210,222)(241,306)(242,310)
(243,309)(244,308)(245,307)(246,301)(247,305)(248,304)(249,303)(250,302)
(251,311)(252,315)(253,314)(254,313)(255,312)(256,321)(257,325)(258,324)
(259,323)(260,322)(261,316)(262,320)(263,319)(264,318)(265,317)(266,326)
(267,330)(268,329)(269,328)(270,327)(271,336)(272,340)(273,339)(274,338)
(275,337)(276,331)(277,335)(278,334)(279,333)(280,332)(281,341)(282,345)
(283,344)(284,343)(285,342)(286,351)(287,355)(288,354)(289,353)(290,352)
(291,346)(292,350)(293,349)(294,348)(295,347)(296,356)(297,360)(298,359)
(299,358)(300,357)(361,456)(362,460)(363,459)(364,458)(365,457)(366,451)
(367,455)(368,454)(369,453)(370,452)(371,461)(372,465)(373,464)(374,463)
(375,462)(376,471)(377,475)(378,474)(379,473)(380,472)(381,466)(382,470)
(383,469)(384,468)(385,467)(386,476)(387,480)(388,479)(389,478)(390,477)
(391,426)(392,430)(393,429)(394,428)(395,427)(396,421)(397,425)(398,424)
(399,423)(400,422)(401,431)(402,435)(403,434)(404,433)(405,432)(406,441)
(407,445)(408,444)(409,443)(410,442)(411,436)(412,440)(413,439)(414,438)
(415,437)(416,446)(417,450)(418,449)(419,448)(420,447)(481,606)(482,610)
(483,609)(484,608)(485,607)(486,601)(487,605)(488,604)(489,603)(490,602)
(491,611)(492,615)(493,614)(494,613)(495,612)(496,621)(497,625)(498,624)
(499,623)(500,622)(501,616)(502,620)(503,619)(504,618)(505,617)(506,626)
(507,630)(508,629)(509,628)(510,627)(511,636)(512,640)(513,639)(514,638)
(515,637)(516,631)(517,635)(518,634)(519,633)(520,632)(521,641)(522,645)
(523,644)(524,643)(525,642)(526,651)(527,655)(528,654)(529,653)(530,652)
(531,646)(532,650)(533,649)(534,648)(535,647)(536,656)(537,660)(538,659)
(539,658)(540,657)(541,681)(542,685)(543,684)(544,683)(545,682)(546,676)
(547,680)(548,679)(549,678)(550,677)(551,686)(552,690)(553,689)(554,688)
(555,687)(556,666)(557,670)(558,669)(559,668)(560,667)(561,661)(562,665)
(563,664)(564,663)(565,662)(566,671)(567,675)(568,674)(569,673)(570,672)
(571,711)(572,715)(573,714)(574,713)(575,712)(576,706)(577,710)(578,709)
(579,708)(580,707)(581,716)(582,720)(583,719)(584,718)(585,717)(586,696)
(587,700)(588,699)(589,698)(590,697)(591,691)(592,695)(593,694)(594,693)
(595,692)(596,701)(597,705)(598,704)(599,703)(600,702)(721,921)(722,925)
(723,924)(724,923)(725,922)(726,916)(727,920)(728,919)(729,918)(730,917)
(731,926)(732,930)(733,929)(734,928)(735,927)(736,906)(737,910)(738,909)
(739,908)(740,907)(741,901)(742,905)(743,904)(744,903)(745,902)(746,911)
(747,915)(748,914)(749,913)(750,912)(751,951)(752,955)(753,954)(754,953)
(755,952)(756,946)(757,950)(758,949)(759,948)(760,947)(761,956)(762,960)
(763,959)(764,958)(765,957)(766,936)(767,940)(768,939)(769,938)(770,937)
(771,931)(772,935)(773,934)(774,933)(775,932)(776,941)(777,945)(778,944)
(779,943)(780,942)(781,861)(782,865)(783,864)(784,863)(785,862)(786,856)
(787,860)(788,859)(789,858)(790,857)(791,866)(792,870)(793,869)(794,868)
(795,867)(796,846)(797,850)(798,849)(799,848)(800,847)(801,841)(802,845)
(803,844)(804,843)(805,842)(806,851)(807,855)(808,854)(809,853)(810,852)
(811,891)(812,895)(813,894)(814,893)(815,892)(816,886)(817,890)(818,889)
(819,888)(820,887)(821,896)(822,900)(823,899)(824,898)(825,897)(826,876)
(827,880)(828,879)(829,878)(830,877)(831,871)(832,875)(833,874)(834,873)
(835,872)(836,881)(837,885)(838,884)(839,883)(840,882);;
s2 := (  1,722)(  2,721)(  3,725)(  4,724)(  5,723)(  6,727)(  7,726)(  8,730)
(  9,729)( 10,728)( 11,732)( 12,731)( 13,735)( 14,734)( 15,733)( 16,737)
( 17,736)( 18,740)( 19,739)( 20,738)( 21,742)( 22,741)( 23,745)( 24,744)
( 25,743)( 26,747)( 27,746)( 28,750)( 29,749)( 30,748)( 31,752)( 32,751)
( 33,755)( 34,754)( 35,753)( 36,757)( 37,756)( 38,760)( 39,759)( 40,758)
( 41,762)( 42,761)( 43,765)( 44,764)( 45,763)( 46,767)( 47,766)( 48,770)
( 49,769)( 50,768)( 51,772)( 52,771)( 53,775)( 54,774)( 55,773)( 56,777)
( 57,776)( 58,780)( 59,779)( 60,778)( 61,782)( 62,781)( 63,785)( 64,784)
( 65,783)( 66,787)( 67,786)( 68,790)( 69,789)( 70,788)( 71,792)( 72,791)
( 73,795)( 74,794)( 75,793)( 76,797)( 77,796)( 78,800)( 79,799)( 80,798)
( 81,802)( 82,801)( 83,805)( 84,804)( 85,803)( 86,807)( 87,806)( 88,810)
( 89,809)( 90,808)( 91,812)( 92,811)( 93,815)( 94,814)( 95,813)( 96,817)
( 97,816)( 98,820)( 99,819)(100,818)(101,822)(102,821)(103,825)(104,824)
(105,823)(106,827)(107,826)(108,830)(109,829)(110,828)(111,832)(112,831)
(113,835)(114,834)(115,833)(116,837)(117,836)(118,840)(119,839)(120,838)
(121,887)(122,886)(123,890)(124,889)(125,888)(126,892)(127,891)(128,895)
(129,894)(130,893)(131,897)(132,896)(133,900)(134,899)(135,898)(136,872)
(137,871)(138,875)(139,874)(140,873)(141,877)(142,876)(143,880)(144,879)
(145,878)(146,882)(147,881)(148,885)(149,884)(150,883)(151,857)(152,856)
(153,860)(154,859)(155,858)(156,862)(157,861)(158,865)(159,864)(160,863)
(161,867)(162,866)(163,870)(164,869)(165,868)(166,842)(167,841)(168,845)
(169,844)(170,843)(171,847)(172,846)(173,850)(174,849)(175,848)(176,852)
(177,851)(178,855)(179,854)(180,853)(181,947)(182,946)(183,950)(184,949)
(185,948)(186,952)(187,951)(188,955)(189,954)(190,953)(191,957)(192,956)
(193,960)(194,959)(195,958)(196,932)(197,931)(198,935)(199,934)(200,933)
(201,937)(202,936)(203,940)(204,939)(205,938)(206,942)(207,941)(208,945)
(209,944)(210,943)(211,917)(212,916)(213,920)(214,919)(215,918)(216,922)
(217,921)(218,925)(219,924)(220,923)(221,927)(222,926)(223,930)(224,929)
(225,928)(226,902)(227,901)(228,905)(229,904)(230,903)(231,907)(232,906)
(233,910)(234,909)(235,908)(236,912)(237,911)(238,915)(239,914)(240,913)
(241,482)(242,481)(243,485)(244,484)(245,483)(246,487)(247,486)(248,490)
(249,489)(250,488)(251,492)(252,491)(253,495)(254,494)(255,493)(256,497)
(257,496)(258,500)(259,499)(260,498)(261,502)(262,501)(263,505)(264,504)
(265,503)(266,507)(267,506)(268,510)(269,509)(270,508)(271,512)(272,511)
(273,515)(274,514)(275,513)(276,517)(277,516)(278,520)(279,519)(280,518)
(281,522)(282,521)(283,525)(284,524)(285,523)(286,527)(287,526)(288,530)
(289,529)(290,528)(291,532)(292,531)(293,535)(294,534)(295,533)(296,537)
(297,536)(298,540)(299,539)(300,538)(301,542)(302,541)(303,545)(304,544)
(305,543)(306,547)(307,546)(308,550)(309,549)(310,548)(311,552)(312,551)
(313,555)(314,554)(315,553)(316,557)(317,556)(318,560)(319,559)(320,558)
(321,562)(322,561)(323,565)(324,564)(325,563)(326,567)(327,566)(328,570)
(329,569)(330,568)(331,572)(332,571)(333,575)(334,574)(335,573)(336,577)
(337,576)(338,580)(339,579)(340,578)(341,582)(342,581)(343,585)(344,584)
(345,583)(346,587)(347,586)(348,590)(349,589)(350,588)(351,592)(352,591)
(353,595)(354,594)(355,593)(356,597)(357,596)(358,600)(359,599)(360,598)
(361,647)(362,646)(363,650)(364,649)(365,648)(366,652)(367,651)(368,655)
(369,654)(370,653)(371,657)(372,656)(373,660)(374,659)(375,658)(376,632)
(377,631)(378,635)(379,634)(380,633)(381,637)(382,636)(383,640)(384,639)
(385,638)(386,642)(387,641)(388,645)(389,644)(390,643)(391,617)(392,616)
(393,620)(394,619)(395,618)(396,622)(397,621)(398,625)(399,624)(400,623)
(401,627)(402,626)(403,630)(404,629)(405,628)(406,602)(407,601)(408,605)
(409,604)(410,603)(411,607)(412,606)(413,610)(414,609)(415,608)(416,612)
(417,611)(418,615)(419,614)(420,613)(421,707)(422,706)(423,710)(424,709)
(425,708)(426,712)(427,711)(428,715)(429,714)(430,713)(431,717)(432,716)
(433,720)(434,719)(435,718)(436,692)(437,691)(438,695)(439,694)(440,693)
(441,697)(442,696)(443,700)(444,699)(445,698)(446,702)(447,701)(448,705)
(449,704)(450,703)(451,677)(452,676)(453,680)(454,679)(455,678)(456,682)
(457,681)(458,685)(459,684)(460,683)(461,687)(462,686)(463,690)(464,689)
(465,688)(466,662)(467,661)(468,665)(469,664)(470,663)(471,667)(472,666)
(473,670)(474,669)(475,668)(476,672)(477,671)(478,675)(479,674)(480,673);;
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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*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*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 ];;
poly := F / rels;;

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

```
References : None.
to this polytope