Polytope of Type {8,120} with group SmallGroup(1920,14512)

Overview

Group: SmallGroup(1920,14512)
Rank: 3
Schläfli Type: {8,120}
Vertices, edges, …: 8, 480, 120
Order of s₀s₁s₂: 120
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat

Quotients maximal quotients in bold

2-fold

3-fold

{8,40}*640d

4-fold

5-fold

{8,24}*384d

6-fold

8-fold

10-fold

12-fold

15-fold

{8,8}*128c

16-fold

{2,30}*120

20-fold

24-fold

30-fold

32-fold

{2,15}*60

40-fold

48-fold

{2,10}*40

60-fold

80-fold

{2,6}*24

96-fold

{2,5}*20

120-fold

160-fold

{2,3}*12

240-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

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, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 81)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(101,111)(102,115)(103,114)(104,113)(105,112)(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)(181,226)(182,230)(183,229)(184,228)(185,227)(186,236)(187,240)(188,239)(189,238)(190,237)(191,231)(192,235)(193,234)(194,233)(195,232)(196,211)(197,215)(198,214)(199,213)(200,212)(201,221)(202,225)(203,224)(204,223)(205,222)(206,216)(207,220)(208,219)(209,218)(210,217)(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)(541,676)(542,680)(543,679)(544,678)(545,677)(546,686)(547,690)(548,689)(549,688)(550,687)(551,681)(552,685)(553,684)(554,683)(555,682)(556,661)(557,665)(558,664)(559,663)(560,662)(561,671)(562,675)(563,674)(564,673)(565,672)(566,666)(567,670)(568,669)(569,668)(570,667)(571,706)(572,710)(573,709)(574,708)(575,707)(576,716)(577,720)(578,719)(579,718)(580,717)(581,711)(582,715)(583,714)(584,713)(585,712)(586,691)(587,695)(588,694)(589,693)(590,692)(591,701)(592,705)(593,704)(594,703)(595,702)(596,696)(597,700)(598,699)(599,698)(600,697)(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)( 61,322)( 62,321)( 63,325)( 64,324)( 65,323)( 66,317)( 67,316)( 68,320)( 69,319)( 70,318)( 71,327)( 72,326)( 73,330)( 74,329)( 75,328)( 76,307)( 77,306)( 78,310)( 79,309)( 80,308)( 81,302)( 82,301)( 83,305)( 84,304)( 85,303)( 86,312)( 87,311)( 88,315)( 89,314)( 90,313)( 91,352)( 92,351)( 93,355)( 94,354)( 95,353)( 96,347)( 97,346)( 98,350)( 99,349)(100,348)(101,357)(102,356)(103,360)(104,359)(105,358)(106,337)(107,336)(108,340)(109,339)(110,338)(111,332)(112,331)(113,335)(114,334)(115,333)(116,342)(117,341)(118,345)(119,344)(120,343)(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)(181,427)(182,426)(183,430)(184,429)(185,428)(186,422)(187,421)(188,425)(189,424)(190,423)(191,432)(192,431)(193,435)(194,434)(195,433)(196,442)(197,441)(198,445)(199,444)(200,443)(201,437)(202,436)(203,440)(204,439)(205,438)(206,447)(207,446)(208,450)(209,449)(210,448)(211,457)(212,456)(213,460)(214,459)(215,458)(216,452)(217,451)(218,455)(219,454)(220,453)(221,462)(222,461)(223,465)(224,464)(225,463)(226,472)(227,471)(228,475)(229,474)(230,473)(231,467)(232,466)(233,470)(234,469)(235,468)(236,477)(237,476)(238,480)(239,479)(240,478)(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)(541,802)(542,801)(543,805)(544,804)(545,803)(546,797)(547,796)(548,800)(549,799)(550,798)(551,807)(552,806)(553,810)(554,809)(555,808)(556,787)(557,786)(558,790)(559,789)(560,788)(561,782)(562,781)(563,785)(564,784)(565,783)(566,792)(567,791)(568,795)(569,794)(570,793)(571,832)(572,831)(573,835)(574,834)(575,833)(576,827)(577,826)(578,830)(579,829)(580,828)(581,837)(582,836)(583,840)(584,839)(585,838)(586,817)(587,816)(588,820)(589,819)(590,818)(591,812)(592,811)(593,815)(594,814)(595,813)(596,822)(597,821)(598,825)(599,824)(600,823)(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)(661,907)(662,906)(663,910)(664,909)(665,908)(666,902)(667,901)(668,905)(669,904)(670,903)(671,912)(672,911)(673,915)(674,914)(675,913)(676,922)(677,921)(678,925)(679,924)(680,923)(681,917)(682,916)(683,920)(684,919)(685,918)(686,927)(687,926)(688,930)(689,929)(690,928)(691,937)(692,936)(693,940)(694,939)(695,938)(696,932)(697,931)(698,935)(699,934)(700,933)(701,942)(702,941)(703,945)(704,944)(705,943)(706,952)(707,951)(708,955)(709,954)(710,953)(711,947)(712,946)(713,950)(714,949)
(715,948)(716,957)(717,956)(718,960)(719,959)(720,958);;
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*s2*s1*s2*s0*s1*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1 ];;
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, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 86)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 81)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)( 96,116)( 97,120)( 98,119)( 99,118)(100,117)(101,111)(102,115)(103,114)(104,113)(105,112)(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)(181,226)(182,230)(183,229)(184,228)(185,227)(186,236)(187,240)(188,239)(189,238)(190,237)(191,231)(192,235)(193,234)(194,233)(195,232)(196,211)(197,215)(198,214)(199,213)(200,212)(201,221)(202,225)(203,224)(204,223)(205,222)(206,216)(207,220)(208,219)(209,218)(210,217)(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)(541,676)(542,680)(543,679)(544,678)(545,677)(546,686)(547,690)(548,689)(549,688)(550,687)(551,681)(552,685)(553,684)(554,683)(555,682)(556,661)(557,665)(558,664)(559,663)(560,662)(561,671)(562,675)(563,674)(564,673)(565,672)(566,666)(567,670)(568,669)(569,668)(570,667)(571,706)(572,710)(573,709)(574,708)(575,707)(576,716)(577,720)(578,719)(579,718)(580,717)(581,711)(582,715)(583,714)(584,713)(585,712)(586,691)(587,695)(588,694)(589,693)(590,692)(591,701)(592,705)(593,704)(594,703)(595,702)(596,696)(597,700)(598,699)(599,698)(600,697)(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)( 61,322)( 62,321)( 63,325)( 64,324)( 65,323)( 66,317)( 67,316)( 68,320)( 69,319)( 70,318)( 71,327)( 72,326)( 73,330)( 74,329)( 75,328)( 76,307)( 77,306)( 78,310)( 79,309)( 80,308)( 81,302)( 82,301)( 83,305)( 84,304)( 85,303)( 86,312)( 87,311)( 88,315)( 89,314)( 90,313)( 91,352)( 92,351)( 93,355)( 94,354)( 95,353)( 96,347)( 97,346)( 98,350)( 99,349)(100,348)(101,357)(102,356)(103,360)(104,359)(105,358)(106,337)(107,336)(108,340)(109,339)(110,338)(111,332)(112,331)(113,335)(114,334)(115,333)(116,342)(117,341)(118,345)(119,344)(120,343)(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)(181,427)(182,426)(183,430)(184,429)(185,428)(186,422)(187,421)(188,425)(189,424)(190,423)(191,432)(192,431)(193,435)(194,434)(195,433)(196,442)(197,441)(198,445)(199,444)(200,443)(201,437)(202,436)(203,440)(204,439)(205,438)(206,447)(207,446)(208,450)(209,449)(210,448)(211,457)(212,456)(213,460)(214,459)(215,458)(216,452)(217,451)(218,455)(219,454)(220,453)(221,462)(222,461)(223,465)(224,464)(225,463)(226,472)(227,471)(228,475)(229,474)(230,473)(231,467)(232,466)(233,470)(234,469)(235,468)(236,477)(237,476)(238,480)(239,479)(240,478)(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)(541,802)(542,801)(543,805)(544,804)(545,803)(546,797)(547,796)(548,800)(549,799)(550,798)(551,807)(552,806)(553,810)(554,809)(555,808)(556,787)(557,786)(558,790)(559,789)(560,788)(561,782)(562,781)(563,785)(564,784)(565,783)(566,792)(567,791)(568,795)(569,794)(570,793)(571,832)(572,831)(573,835)(574,834)(575,833)(576,827)(577,826)(578,830)(579,829)(580,828)(581,837)(582,836)(583,840)(584,839)(585,838)(586,817)(587,816)(588,820)(589,819)(590,818)(591,812)(592,811)(593,815)(594,814)(595,813)(596,822)(597,821)(598,825)(599,824)(600,823)(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)(661,907)(662,906)(663,910)(664,909)(665,908)(666,902)(667,901)(668,905)(669,904)(670,903)(671,912)(672,911)(673,915)(674,914)(675,913)(676,922)(677,921)(678,925)(679,924)(680,923)(681,917)(682,916)(683,920)(684,919)(685,918)(686,927)(687,926)(688,930)(689,929)(690,928)(691,937)(692,936)(693,940)(694,939)(695,938)(696,932)(697,931)(698,935)(699,934)(700,933)(701,942)(702,941)(703,945)(704,944)(705,943)(706,952)(707,951)(708,955)(709,954)(710,953)(711,947)(712,946)(713,950)
(714,949)(715,948)(716,957)(717,956)(718,960)(719,959)(720,958);
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*s2*s1*s2*s0*s1*s0*s1*s2*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*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1 >;

References