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Polytope of Type {4,30,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30,8}*1920a
Also Known As : {{4,30|2},{30,8|2}}. if this polytope has another name.
Group : SmallGroup(1920,182073)
Rank : 4
Schlafli Type : {4,30,8}
Number of vertices, edges, etc : 4, 60, 120, 8
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   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 : {4,30,4}*960a, {2,30,8}*960
   3-fold quotients : {4,10,8}*640
   4-fold quotients : {2,30,4}*480a, {4,30,2}*480a
   5-fold quotients : {4,6,8}*384a
   6-fold quotients : {4,10,4}*320, {2,10,8}*320
   8-fold quotients : {2,30,2}*240
   10-fold quotients : {4,6,4}*192a, {2,6,8}*192
   12-fold quotients : {2,10,4}*160, {4,10,2}*160
   15-fold quotients : {4,2,8}*128
   16-fold quotients : {2,15,2}*120
   20-fold quotients : {2,6,4}*96a, {4,6,2}*96a
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {4,2,4}*64, {2,2,8}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,4}*32, {4,2,2}*32
   80-fold quotients : {2,3,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)(  8,248)
(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)
(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)
(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)
(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)
(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)
(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)(240,480)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)(488,728)
(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)(504,744)
(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)(520,760)
(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)(536,776)
(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)(544,784)
(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)(552,792)
(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)(560,800)
(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)(568,808)
(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)(576,816)
(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)(584,824)
(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)(592,832)
(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)(600,840)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)(608,848)
(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)(624,864)
(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)(640,880)
(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)(656,896)
(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)(672,912)
(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)(688,928)
(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)(696,936)
(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)(704,944)
(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)(712,952)
(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)(720,960);;
s1 := (  1,181)(  2,185)(  3,184)(  4,183)(  5,182)(  6,191)(  7,195)(  8,194)
(  9,193)( 10,192)( 11,186)( 12,190)( 13,189)( 14,188)( 15,187)( 16,196)
( 17,200)( 18,199)( 19,198)( 20,197)( 21,206)( 22,210)( 23,209)( 24,208)
( 25,207)( 26,201)( 27,205)( 28,204)( 29,203)( 30,202)( 31,211)( 32,215)
( 33,214)( 34,213)( 35,212)( 36,221)( 37,225)( 38,224)( 39,223)( 40,222)
( 41,216)( 42,220)( 43,219)( 44,218)( 45,217)( 46,226)( 47,230)( 48,229)
( 49,228)( 50,227)( 51,236)( 52,240)( 53,239)( 54,238)( 55,237)( 56,231)
( 57,235)( 58,234)( 59,233)( 60,232)( 61,136)( 62,140)( 63,139)( 64,138)
( 65,137)( 66,146)( 67,150)( 68,149)( 69,148)( 70,147)( 71,141)( 72,145)
( 73,144)( 74,143)( 75,142)( 76,121)( 77,125)( 78,124)( 79,123)( 80,122)
( 81,131)( 82,135)( 83,134)( 84,133)( 85,132)( 86,126)( 87,130)( 88,129)
( 89,128)( 90,127)( 91,166)( 92,170)( 93,169)( 94,168)( 95,167)( 96,176)
( 97,180)( 98,179)( 99,178)(100,177)(101,171)(102,175)(103,174)(104,173)
(105,172)(106,151)(107,155)(108,154)(109,153)(110,152)(111,161)(112,165)
(113,164)(114,163)(115,162)(116,156)(117,160)(118,159)(119,158)(120,157)
(241,451)(242,455)(243,454)(244,453)(245,452)(246,461)(247,465)(248,464)
(249,463)(250,462)(251,456)(252,460)(253,459)(254,458)(255,457)(256,466)
(257,470)(258,469)(259,468)(260,467)(261,476)(262,480)(263,479)(264,478)
(265,477)(266,471)(267,475)(268,474)(269,473)(270,472)(271,421)(272,425)
(273,424)(274,423)(275,422)(276,431)(277,435)(278,434)(279,433)(280,432)
(281,426)(282,430)(283,429)(284,428)(285,427)(286,436)(287,440)(288,439)
(289,438)(290,437)(291,446)(292,450)(293,449)(294,448)(295,447)(296,441)
(297,445)(298,444)(299,443)(300,442)(301,406)(302,410)(303,409)(304,408)
(305,407)(306,416)(307,420)(308,419)(309,418)(310,417)(311,411)(312,415)
(313,414)(314,413)(315,412)(316,391)(317,395)(318,394)(319,393)(320,392)
(321,401)(322,405)(323,404)(324,403)(325,402)(326,396)(327,400)(328,399)
(329,398)(330,397)(331,376)(332,380)(333,379)(334,378)(335,377)(336,386)
(337,390)(338,389)(339,388)(340,387)(341,381)(342,385)(343,384)(344,383)
(345,382)(346,361)(347,365)(348,364)(349,363)(350,362)(351,371)(352,375)
(353,374)(354,373)(355,372)(356,366)(357,370)(358,369)(359,368)(360,367)
(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)(541,661)(542,665)(543,664)(544,663)
(545,662)(546,671)(547,675)(548,674)(549,673)(550,672)(551,666)(552,670)
(553,669)(554,668)(555,667)(556,676)(557,680)(558,679)(559,678)(560,677)
(561,686)(562,690)(563,689)(564,688)(565,687)(566,681)(567,685)(568,684)
(569,683)(570,682)(571,691)(572,695)(573,694)(574,693)(575,692)(576,701)
(577,705)(578,704)(579,703)(580,702)(581,696)(582,700)(583,699)(584,698)
(585,697)(586,706)(587,710)(588,709)(589,708)(590,707)(591,716)(592,720)
(593,719)(594,718)(595,717)(596,711)(597,715)(598,714)(599,713)(600,712)
(721,871)(722,875)(723,874)(724,873)(725,872)(726,881)(727,885)(728,884)
(729,883)(730,882)(731,876)(732,880)(733,879)(734,878)(735,877)(736,886)
(737,890)(738,889)(739,888)(740,887)(741,896)(742,900)(743,899)(744,898)
(745,897)(746,891)(747,895)(748,894)(749,893)(750,892)(751,841)(752,845)
(753,844)(754,843)(755,842)(756,851)(757,855)(758,854)(759,853)(760,852)
(761,846)(762,850)(763,849)(764,848)(765,847)(766,856)(767,860)(768,859)
(769,858)(770,857)(771,866)(772,870)(773,869)(774,868)(775,867)(776,861)
(777,865)(778,864)(779,863)(780,862)(781,931)(782,935)(783,934)(784,933)
(785,932)(786,941)(787,945)(788,944)(789,943)(790,942)(791,936)(792,940)
(793,939)(794,938)(795,937)(796,946)(797,950)(798,949)(799,948)(800,947)
(801,956)(802,960)(803,959)(804,958)(805,957)(806,951)(807,955)(808,954)
(809,953)(810,952)(811,901)(812,905)(813,904)(814,903)(815,902)(816,911)
(817,915)(818,914)(819,913)(820,912)(821,906)(822,910)(823,909)(824,908)
(825,907)(826,916)(827,920)(828,919)(829,918)(830,917)(831,926)(832,930)
(833,929)(834,928)(835,927)(836,921)(837,925)(838,924)(839,923)(840,922);;
s2 := (  1,127)(  2,126)(  3,130)(  4,129)(  5,128)(  6,122)(  7,121)(  8,125)
(  9,124)( 10,123)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,142)
( 17,141)( 18,145)( 19,144)( 20,143)( 21,137)( 22,136)( 23,140)( 24,139)
( 25,138)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,157)( 32,156)
( 33,160)( 34,159)( 35,158)( 36,152)( 37,151)( 38,155)( 39,154)( 40,153)
( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,172)( 47,171)( 48,175)
( 49,174)( 50,173)( 51,167)( 52,166)( 53,170)( 54,169)( 55,168)( 56,177)
( 57,176)( 58,180)( 59,179)( 60,178)( 61,202)( 62,201)( 63,205)( 64,204)
( 65,203)( 66,197)( 67,196)( 68,200)( 69,199)( 70,198)( 71,207)( 72,206)
( 73,210)( 74,209)( 75,208)( 76,187)( 77,186)( 78,190)( 79,189)( 80,188)
( 81,182)( 82,181)( 83,185)( 84,184)( 85,183)( 86,192)( 87,191)( 88,195)
( 89,194)( 90,193)( 91,232)( 92,231)( 93,235)( 94,234)( 95,233)( 96,227)
( 97,226)( 98,230)( 99,229)(100,228)(101,237)(102,236)(103,240)(104,239)
(105,238)(106,217)(107,216)(108,220)(109,219)(110,218)(111,212)(112,211)
(113,215)(114,214)(115,213)(116,222)(117,221)(118,225)(119,224)(120,223)
(241,367)(242,366)(243,370)(244,369)(245,368)(246,362)(247,361)(248,365)
(249,364)(250,363)(251,372)(252,371)(253,375)(254,374)(255,373)(256,382)
(257,381)(258,385)(259,384)(260,383)(261,377)(262,376)(263,380)(264,379)
(265,378)(266,387)(267,386)(268,390)(269,389)(270,388)(271,397)(272,396)
(273,400)(274,399)(275,398)(276,392)(277,391)(278,395)(279,394)(280,393)
(281,402)(282,401)(283,405)(284,404)(285,403)(286,412)(287,411)(288,415)
(289,414)(290,413)(291,407)(292,406)(293,410)(294,409)(295,408)(296,417)
(297,416)(298,420)(299,419)(300,418)(301,442)(302,441)(303,445)(304,444)
(305,443)(306,437)(307,436)(308,440)(309,439)(310,438)(311,447)(312,446)
(313,450)(314,449)(315,448)(316,427)(317,426)(318,430)(319,429)(320,428)
(321,422)(322,421)(323,425)(324,424)(325,423)(326,432)(327,431)(328,435)
(329,434)(330,433)(331,472)(332,471)(333,475)(334,474)(335,473)(336,467)
(337,466)(338,470)(339,469)(340,468)(341,477)(342,476)(343,480)(344,479)
(345,478)(346,457)(347,456)(348,460)(349,459)(350,458)(351,452)(352,451)
(353,455)(354,454)(355,453)(356,462)(357,461)(358,465)(359,464)(360,463)
(481,607)(482,606)(483,610)(484,609)(485,608)(486,602)(487,601)(488,605)
(489,604)(490,603)(491,612)(492,611)(493,615)(494,614)(495,613)(496,622)
(497,621)(498,625)(499,624)(500,623)(501,617)(502,616)(503,620)(504,619)
(505,618)(506,627)(507,626)(508,630)(509,629)(510,628)(511,637)(512,636)
(513,640)(514,639)(515,638)(516,632)(517,631)(518,635)(519,634)(520,633)
(521,642)(522,641)(523,645)(524,644)(525,643)(526,652)(527,651)(528,655)
(529,654)(530,653)(531,647)(532,646)(533,650)(534,649)(535,648)(536,657)
(537,656)(538,660)(539,659)(540,658)(541,682)(542,681)(543,685)(544,684)
(545,683)(546,677)(547,676)(548,680)(549,679)(550,678)(551,687)(552,686)
(553,690)(554,689)(555,688)(556,667)(557,666)(558,670)(559,669)(560,668)
(561,662)(562,661)(563,665)(564,664)(565,663)(566,672)(567,671)(568,675)
(569,674)(570,673)(571,712)(572,711)(573,715)(574,714)(575,713)(576,707)
(577,706)(578,710)(579,709)(580,708)(581,717)(582,716)(583,720)(584,719)
(585,718)(586,697)(587,696)(588,700)(589,699)(590,698)(591,692)(592,691)
(593,695)(594,694)(595,693)(596,702)(597,701)(598,705)(599,704)(600,703)
(721,847)(722,846)(723,850)(724,849)(725,848)(726,842)(727,841)(728,845)
(729,844)(730,843)(731,852)(732,851)(733,855)(734,854)(735,853)(736,862)
(737,861)(738,865)(739,864)(740,863)(741,857)(742,856)(743,860)(744,859)
(745,858)(746,867)(747,866)(748,870)(749,869)(750,868)(751,877)(752,876)
(753,880)(754,879)(755,878)(756,872)(757,871)(758,875)(759,874)(760,873)
(761,882)(762,881)(763,885)(764,884)(765,883)(766,892)(767,891)(768,895)
(769,894)(770,893)(771,887)(772,886)(773,890)(774,889)(775,888)(776,897)
(777,896)(778,900)(779,899)(780,898)(781,922)(782,921)(783,925)(784,924)
(785,923)(786,917)(787,916)(788,920)(789,919)(790,918)(791,927)(792,926)
(793,930)(794,929)(795,928)(796,907)(797,906)(798,910)(799,909)(800,908)
(801,902)(802,901)(803,905)(804,904)(805,903)(806,912)(807,911)(808,915)
(809,914)(810,913)(811,952)(812,951)(813,955)(814,954)(815,953)(816,947)
(817,946)(818,950)(819,949)(820,948)(821,957)(822,956)(823,960)(824,959)
(825,958)(826,937)(827,936)(828,940)(829,939)(830,938)(831,932)(832,931)
(833,935)(834,934)(835,933)(836,942)(837,941)(838,945)(839,944)(840,943);;
s3 := (  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)
(121,661)(122,662)(123,663)(124,664)(125,665)(126,666)(127,667)(128,668)
(129,669)(130,670)(131,671)(132,672)(133,673)(134,674)(135,675)(136,676)
(137,677)(138,678)(139,679)(140,680)(141,681)(142,682)(143,683)(144,684)
(145,685)(146,686)(147,687)(148,688)(149,689)(150,690)(151,691)(152,692)
(153,693)(154,694)(155,695)(156,696)(157,697)(158,698)(159,699)(160,700)
(161,701)(162,702)(163,703)(164,704)(165,705)(166,706)(167,707)(168,708)
(169,709)(170,710)(171,711)(172,712)(173,713)(174,714)(175,715)(176,716)
(177,717)(178,718)(179,719)(180,720)(181,601)(182,602)(183,603)(184,604)
(185,605)(186,606)(187,607)(188,608)(189,609)(190,610)(191,611)(192,612)
(193,613)(194,614)(195,615)(196,616)(197,617)(198,618)(199,619)(200,620)
(201,621)(202,622)(203,623)(204,624)(205,625)(206,626)(207,627)(208,628)
(209,629)(210,630)(211,631)(212,632)(213,633)(214,634)(215,635)(216,636)
(217,637)(218,638)(219,639)(220,640)(221,641)(222,642)(223,643)(224,644)
(225,645)(226,646)(227,647)(228,648)(229,649)(230,650)(231,651)(232,652)
(233,653)(234,654)(235,655)(236,656)(237,657)(238,658)(239,659)(240,660)
(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)
(361,901)(362,902)(363,903)(364,904)(365,905)(366,906)(367,907)(368,908)
(369,909)(370,910)(371,911)(372,912)(373,913)(374,914)(375,915)(376,916)
(377,917)(378,918)(379,919)(380,920)(381,921)(382,922)(383,923)(384,924)
(385,925)(386,926)(387,927)(388,928)(389,929)(390,930)(391,931)(392,932)
(393,933)(394,934)(395,935)(396,936)(397,937)(398,938)(399,939)(400,940)
(401,941)(402,942)(403,943)(404,944)(405,945)(406,946)(407,947)(408,948)
(409,949)(410,950)(411,951)(412,952)(413,953)(414,954)(415,955)(416,956)
(417,957)(418,958)(419,959)(420,960)(421,841)(422,842)(423,843)(424,844)
(425,845)(426,846)(427,847)(428,848)(429,849)(430,850)(431,851)(432,852)
(433,853)(434,854)(435,855)(436,856)(437,857)(438,858)(439,859)(440,860)
(441,861)(442,862)(443,863)(444,864)(445,865)(446,866)(447,867)(448,868)
(449,869)(450,870)(451,871)(452,872)(453,873)(454,874)(455,875)(456,876)
(457,877)(458,878)(459,879)(460,880)(461,881)(462,882)(463,883)(464,884)
(465,885)(466,886)(467,887)(468,888)(469,889)(470,890)(471,891)(472,892)
(473,893)(474,894)(475,895)(476,896)(477,897)(478,898)(479,899)(480,900);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(960)!(  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)
(  8,248)(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)
(176,416)(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)
(192,432)(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)
(224,464)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)
(232,472)(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)
(240,480)(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)
(488,728)(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)
(504,744)(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)
(520,760)(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)
(536,776)(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)
(544,784)(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)
(552,792)(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)
(560,800)(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)
(568,808)(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)
(576,816)(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)
(584,824)(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)
(592,832)(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)
(600,840)(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)
(608,848)(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)
(624,864)(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)
(640,880)(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)
(656,896)(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)
(672,912)(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)
(688,928)(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,936)(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)
(704,944)(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)
(712,952)(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)
(720,960);
s1 := Sym(960)!(  1,181)(  2,185)(  3,184)(  4,183)(  5,182)(  6,191)(  7,195)
(  8,194)(  9,193)( 10,192)( 11,186)( 12,190)( 13,189)( 14,188)( 15,187)
( 16,196)( 17,200)( 18,199)( 19,198)( 20,197)( 21,206)( 22,210)( 23,209)
( 24,208)( 25,207)( 26,201)( 27,205)( 28,204)( 29,203)( 30,202)( 31,211)
( 32,215)( 33,214)( 34,213)( 35,212)( 36,221)( 37,225)( 38,224)( 39,223)
( 40,222)( 41,216)( 42,220)( 43,219)( 44,218)( 45,217)( 46,226)( 47,230)
( 48,229)( 49,228)( 50,227)( 51,236)( 52,240)( 53,239)( 54,238)( 55,237)
( 56,231)( 57,235)( 58,234)( 59,233)( 60,232)( 61,136)( 62,140)( 63,139)
( 64,138)( 65,137)( 66,146)( 67,150)( 68,149)( 69,148)( 70,147)( 71,141)
( 72,145)( 73,144)( 74,143)( 75,142)( 76,121)( 77,125)( 78,124)( 79,123)
( 80,122)( 81,131)( 82,135)( 83,134)( 84,133)( 85,132)( 86,126)( 87,130)
( 88,129)( 89,128)( 90,127)( 91,166)( 92,170)( 93,169)( 94,168)( 95,167)
( 96,176)( 97,180)( 98,179)( 99,178)(100,177)(101,171)(102,175)(103,174)
(104,173)(105,172)(106,151)(107,155)(108,154)(109,153)(110,152)(111,161)
(112,165)(113,164)(114,163)(115,162)(116,156)(117,160)(118,159)(119,158)
(120,157)(241,451)(242,455)(243,454)(244,453)(245,452)(246,461)(247,465)
(248,464)(249,463)(250,462)(251,456)(252,460)(253,459)(254,458)(255,457)
(256,466)(257,470)(258,469)(259,468)(260,467)(261,476)(262,480)(263,479)
(264,478)(265,477)(266,471)(267,475)(268,474)(269,473)(270,472)(271,421)
(272,425)(273,424)(274,423)(275,422)(276,431)(277,435)(278,434)(279,433)
(280,432)(281,426)(282,430)(283,429)(284,428)(285,427)(286,436)(287,440)
(288,439)(289,438)(290,437)(291,446)(292,450)(293,449)(294,448)(295,447)
(296,441)(297,445)(298,444)(299,443)(300,442)(301,406)(302,410)(303,409)
(304,408)(305,407)(306,416)(307,420)(308,419)(309,418)(310,417)(311,411)
(312,415)(313,414)(314,413)(315,412)(316,391)(317,395)(318,394)(319,393)
(320,392)(321,401)(322,405)(323,404)(324,403)(325,402)(326,396)(327,400)
(328,399)(329,398)(330,397)(331,376)(332,380)(333,379)(334,378)(335,377)
(336,386)(337,390)(338,389)(339,388)(340,387)(341,381)(342,385)(343,384)
(344,383)(345,382)(346,361)(347,365)(348,364)(349,363)(350,362)(351,371)
(352,375)(353,374)(354,373)(355,372)(356,366)(357,370)(358,369)(359,368)
(360,367)(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)(541,661)(542,665)(543,664)
(544,663)(545,662)(546,671)(547,675)(548,674)(549,673)(550,672)(551,666)
(552,670)(553,669)(554,668)(555,667)(556,676)(557,680)(558,679)(559,678)
(560,677)(561,686)(562,690)(563,689)(564,688)(565,687)(566,681)(567,685)
(568,684)(569,683)(570,682)(571,691)(572,695)(573,694)(574,693)(575,692)
(576,701)(577,705)(578,704)(579,703)(580,702)(581,696)(582,700)(583,699)
(584,698)(585,697)(586,706)(587,710)(588,709)(589,708)(590,707)(591,716)
(592,720)(593,719)(594,718)(595,717)(596,711)(597,715)(598,714)(599,713)
(600,712)(721,871)(722,875)(723,874)(724,873)(725,872)(726,881)(727,885)
(728,884)(729,883)(730,882)(731,876)(732,880)(733,879)(734,878)(735,877)
(736,886)(737,890)(738,889)(739,888)(740,887)(741,896)(742,900)(743,899)
(744,898)(745,897)(746,891)(747,895)(748,894)(749,893)(750,892)(751,841)
(752,845)(753,844)(754,843)(755,842)(756,851)(757,855)(758,854)(759,853)
(760,852)(761,846)(762,850)(763,849)(764,848)(765,847)(766,856)(767,860)
(768,859)(769,858)(770,857)(771,866)(772,870)(773,869)(774,868)(775,867)
(776,861)(777,865)(778,864)(779,863)(780,862)(781,931)(782,935)(783,934)
(784,933)(785,932)(786,941)(787,945)(788,944)(789,943)(790,942)(791,936)
(792,940)(793,939)(794,938)(795,937)(796,946)(797,950)(798,949)(799,948)
(800,947)(801,956)(802,960)(803,959)(804,958)(805,957)(806,951)(807,955)
(808,954)(809,953)(810,952)(811,901)(812,905)(813,904)(814,903)(815,902)
(816,911)(817,915)(818,914)(819,913)(820,912)(821,906)(822,910)(823,909)
(824,908)(825,907)(826,916)(827,920)(828,919)(829,918)(830,917)(831,926)
(832,930)(833,929)(834,928)(835,927)(836,921)(837,925)(838,924)(839,923)
(840,922);
s2 := Sym(960)!(  1,127)(  2,126)(  3,130)(  4,129)(  5,128)(  6,122)(  7,121)
(  8,125)(  9,124)( 10,123)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)
( 16,142)( 17,141)( 18,145)( 19,144)( 20,143)( 21,137)( 22,136)( 23,140)
( 24,139)( 25,138)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,157)
( 32,156)( 33,160)( 34,159)( 35,158)( 36,152)( 37,151)( 38,155)( 39,154)
( 40,153)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,172)( 47,171)
( 48,175)( 49,174)( 50,173)( 51,167)( 52,166)( 53,170)( 54,169)( 55,168)
( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,202)( 62,201)( 63,205)
( 64,204)( 65,203)( 66,197)( 67,196)( 68,200)( 69,199)( 70,198)( 71,207)
( 72,206)( 73,210)( 74,209)( 75,208)( 76,187)( 77,186)( 78,190)( 79,189)
( 80,188)( 81,182)( 82,181)( 83,185)( 84,184)( 85,183)( 86,192)( 87,191)
( 88,195)( 89,194)( 90,193)( 91,232)( 92,231)( 93,235)( 94,234)( 95,233)
( 96,227)( 97,226)( 98,230)( 99,229)(100,228)(101,237)(102,236)(103,240)
(104,239)(105,238)(106,217)(107,216)(108,220)(109,219)(110,218)(111,212)
(112,211)(113,215)(114,214)(115,213)(116,222)(117,221)(118,225)(119,224)
(120,223)(241,367)(242,366)(243,370)(244,369)(245,368)(246,362)(247,361)
(248,365)(249,364)(250,363)(251,372)(252,371)(253,375)(254,374)(255,373)
(256,382)(257,381)(258,385)(259,384)(260,383)(261,377)(262,376)(263,380)
(264,379)(265,378)(266,387)(267,386)(268,390)(269,389)(270,388)(271,397)
(272,396)(273,400)(274,399)(275,398)(276,392)(277,391)(278,395)(279,394)
(280,393)(281,402)(282,401)(283,405)(284,404)(285,403)(286,412)(287,411)
(288,415)(289,414)(290,413)(291,407)(292,406)(293,410)(294,409)(295,408)
(296,417)(297,416)(298,420)(299,419)(300,418)(301,442)(302,441)(303,445)
(304,444)(305,443)(306,437)(307,436)(308,440)(309,439)(310,438)(311,447)
(312,446)(313,450)(314,449)(315,448)(316,427)(317,426)(318,430)(319,429)
(320,428)(321,422)(322,421)(323,425)(324,424)(325,423)(326,432)(327,431)
(328,435)(329,434)(330,433)(331,472)(332,471)(333,475)(334,474)(335,473)
(336,467)(337,466)(338,470)(339,469)(340,468)(341,477)(342,476)(343,480)
(344,479)(345,478)(346,457)(347,456)(348,460)(349,459)(350,458)(351,452)
(352,451)(353,455)(354,454)(355,453)(356,462)(357,461)(358,465)(359,464)
(360,463)(481,607)(482,606)(483,610)(484,609)(485,608)(486,602)(487,601)
(488,605)(489,604)(490,603)(491,612)(492,611)(493,615)(494,614)(495,613)
(496,622)(497,621)(498,625)(499,624)(500,623)(501,617)(502,616)(503,620)
(504,619)(505,618)(506,627)(507,626)(508,630)(509,629)(510,628)(511,637)
(512,636)(513,640)(514,639)(515,638)(516,632)(517,631)(518,635)(519,634)
(520,633)(521,642)(522,641)(523,645)(524,644)(525,643)(526,652)(527,651)
(528,655)(529,654)(530,653)(531,647)(532,646)(533,650)(534,649)(535,648)
(536,657)(537,656)(538,660)(539,659)(540,658)(541,682)(542,681)(543,685)
(544,684)(545,683)(546,677)(547,676)(548,680)(549,679)(550,678)(551,687)
(552,686)(553,690)(554,689)(555,688)(556,667)(557,666)(558,670)(559,669)
(560,668)(561,662)(562,661)(563,665)(564,664)(565,663)(566,672)(567,671)
(568,675)(569,674)(570,673)(571,712)(572,711)(573,715)(574,714)(575,713)
(576,707)(577,706)(578,710)(579,709)(580,708)(581,717)(582,716)(583,720)
(584,719)(585,718)(586,697)(587,696)(588,700)(589,699)(590,698)(591,692)
(592,691)(593,695)(594,694)(595,693)(596,702)(597,701)(598,705)(599,704)
(600,703)(721,847)(722,846)(723,850)(724,849)(725,848)(726,842)(727,841)
(728,845)(729,844)(730,843)(731,852)(732,851)(733,855)(734,854)(735,853)
(736,862)(737,861)(738,865)(739,864)(740,863)(741,857)(742,856)(743,860)
(744,859)(745,858)(746,867)(747,866)(748,870)(749,869)(750,868)(751,877)
(752,876)(753,880)(754,879)(755,878)(756,872)(757,871)(758,875)(759,874)
(760,873)(761,882)(762,881)(763,885)(764,884)(765,883)(766,892)(767,891)
(768,895)(769,894)(770,893)(771,887)(772,886)(773,890)(774,889)(775,888)
(776,897)(777,896)(778,900)(779,899)(780,898)(781,922)(782,921)(783,925)
(784,924)(785,923)(786,917)(787,916)(788,920)(789,919)(790,918)(791,927)
(792,926)(793,930)(794,929)(795,928)(796,907)(797,906)(798,910)(799,909)
(800,908)(801,902)(802,901)(803,905)(804,904)(805,903)(806,912)(807,911)
(808,915)(809,914)(810,913)(811,952)(812,951)(813,955)(814,954)(815,953)
(816,947)(817,946)(818,950)(819,949)(820,948)(821,957)(822,956)(823,960)
(824,959)(825,958)(826,937)(827,936)(828,940)(829,939)(830,938)(831,932)
(832,931)(833,935)(834,934)(835,933)(836,942)(837,941)(838,945)(839,944)
(840,943);
s3 := 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)(121,661)(122,662)(123,663)(124,664)(125,665)(126,666)(127,667)
(128,668)(129,669)(130,670)(131,671)(132,672)(133,673)(134,674)(135,675)
(136,676)(137,677)(138,678)(139,679)(140,680)(141,681)(142,682)(143,683)
(144,684)(145,685)(146,686)(147,687)(148,688)(149,689)(150,690)(151,691)
(152,692)(153,693)(154,694)(155,695)(156,696)(157,697)(158,698)(159,699)
(160,700)(161,701)(162,702)(163,703)(164,704)(165,705)(166,706)(167,707)
(168,708)(169,709)(170,710)(171,711)(172,712)(173,713)(174,714)(175,715)
(176,716)(177,717)(178,718)(179,719)(180,720)(181,601)(182,602)(183,603)
(184,604)(185,605)(186,606)(187,607)(188,608)(189,609)(190,610)(191,611)
(192,612)(193,613)(194,614)(195,615)(196,616)(197,617)(198,618)(199,619)
(200,620)(201,621)(202,622)(203,623)(204,624)(205,625)(206,626)(207,627)
(208,628)(209,629)(210,630)(211,631)(212,632)(213,633)(214,634)(215,635)
(216,636)(217,637)(218,638)(219,639)(220,640)(221,641)(222,642)(223,643)
(224,644)(225,645)(226,646)(227,647)(228,648)(229,649)(230,650)(231,651)
(232,652)(233,653)(234,654)(235,655)(236,656)(237,657)(238,658)(239,659)
(240,660)(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)(361,901)(362,902)(363,903)(364,904)(365,905)(366,906)(367,907)
(368,908)(369,909)(370,910)(371,911)(372,912)(373,913)(374,914)(375,915)
(376,916)(377,917)(378,918)(379,919)(380,920)(381,921)(382,922)(383,923)
(384,924)(385,925)(386,926)(387,927)(388,928)(389,929)(390,930)(391,931)
(392,932)(393,933)(394,934)(395,935)(396,936)(397,937)(398,938)(399,939)
(400,940)(401,941)(402,942)(403,943)(404,944)(405,945)(406,946)(407,947)
(408,948)(409,949)(410,950)(411,951)(412,952)(413,953)(414,954)(415,955)
(416,956)(417,957)(418,958)(419,959)(420,960)(421,841)(422,842)(423,843)
(424,844)(425,845)(426,846)(427,847)(428,848)(429,849)(430,850)(431,851)
(432,852)(433,853)(434,854)(435,855)(436,856)(437,857)(438,858)(439,859)
(440,860)(441,861)(442,862)(443,863)(444,864)(445,865)(446,866)(447,867)
(448,868)(449,869)(450,870)(451,871)(452,872)(453,873)(454,874)(455,875)
(456,876)(457,877)(458,878)(459,879)(460,880)(461,881)(462,882)(463,883)
(464,884)(465,885)(466,886)(467,887)(468,888)(469,889)(470,890)(471,891)
(472,892)(473,893)(474,894)(475,895)(476,896)(477,897)(478,898)(479,899)
(480,900);
poly := sub<Sym(960)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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 >; 
 
References : None.
to this polytope