Polytope of Type {30,8} with group SmallGroup(1920,240269)

Overview

Group: SmallGroup(1920,240269)
Rank: 3
Schläfli Type: {30,8}
Vertices, edges, …: 120, 480, 32
Order of s₀s₁s₂: 30
Order of s₀s₁s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Self-Petrie

Quotients maximal quotients in bold

2-fold

3-fold

{10,8}*640a

4-fold

{15,4}*480

6-fold

12-fold

{5,4}*160

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References