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Polytope of Type {12,10,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,10,8}*1920
Also Known As : {{12,10|2},{10,8|2}}. if this polytope has another name.
Group : SmallGroup(1920,182101)
Rank : 4
Schlafli Type : {12,10,8}
Number of vertices, edges, etc : 12, 60, 40, 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 : {12,10,4}*960, {6,10,8}*960
   3-fold quotients : {4,10,8}*640
   4-fold quotients : {12,10,2}*480, {6,10,4}*480
   5-fold quotients : {12,2,8}*384
   6-fold quotients : {4,10,4}*320, {2,10,8}*320
   8-fold quotients : {6,10,2}*240
   10-fold quotients : {12,2,4}*192, {6,2,8}*192
   12-fold quotients : {2,10,4}*160, {4,10,2}*160
   15-fold quotients : {4,2,8}*128
   20-fold quotients : {3,2,8}*96, {12,2,2}*96, {6,2,4}*96
   24-fold quotients : {2,10,2}*80
   30-fold quotients : {4,2,4}*64, {2,2,8}*64
   40-fold quotients : {3,2,4}*48, {6,2,2}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {2,2,4}*32, {4,2,2}*32
   80-fold quotients : {3,2,2}*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)(  6,251)(  7,252)(  8,253)
(  9,254)( 10,255)( 11,246)( 12,247)( 13,248)( 14,249)( 15,250)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)( 24,269)
( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,281)( 37,282)( 38,283)( 39,284)( 40,285)
( 41,276)( 42,277)( 43,278)( 44,279)( 45,280)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)( 56,291)
( 57,292)( 58,293)( 59,294)( 60,295)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,311)( 67,312)( 68,313)( 69,314)( 70,315)( 71,306)( 72,307)
( 73,308)( 74,309)( 75,310)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,321)( 87,322)( 88,323)
( 89,324)( 90,325)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,341)
( 97,342)( 98,343)( 99,344)(100,345)(101,336)(102,337)(103,338)(104,339)
(105,340)(106,346)(107,347)(108,348)(109,349)(110,350)(111,356)(112,357)
(113,358)(114,359)(115,360)(116,351)(117,352)(118,353)(119,354)(120,355)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,371)(127,372)(128,373)
(129,374)(130,375)(131,366)(132,367)(133,368)(134,369)(135,370)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,386)(142,387)(143,388)(144,389)
(145,390)(146,381)(147,382)(148,383)(149,384)(150,385)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,401)(157,402)(158,403)(159,404)(160,405)
(161,396)(162,397)(163,398)(164,399)(165,400)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,416)(172,417)(173,418)(174,419)(175,420)(176,411)
(177,412)(178,413)(179,414)(180,415)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,431)(187,432)(188,433)(189,434)(190,435)(191,426)(192,427)
(193,428)(194,429)(195,430)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,446)(202,447)(203,448)(204,449)(205,450)(206,441)(207,442)(208,443)
(209,444)(210,445)(211,451)(212,452)(213,453)(214,454)(215,455)(216,461)
(217,462)(218,463)(219,464)(220,465)(221,456)(222,457)(223,458)(224,459)
(225,460)(226,466)(227,467)(228,468)(229,469)(230,470)(231,476)(232,477)
(233,478)(234,479)(235,480)(236,471)(237,472)(238,473)(239,474)(240,475)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,731)(487,732)(488,733)
(489,734)(490,735)(491,726)(492,727)(493,728)(494,729)(495,730)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,746)(502,747)(503,748)(504,749)
(505,750)(506,741)(507,742)(508,743)(509,744)(510,745)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,761)(517,762)(518,763)(519,764)(520,765)
(521,756)(522,757)(523,758)(524,759)(525,760)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,776)(532,777)(533,778)(534,779)(535,780)(536,771)
(537,772)(538,773)(539,774)(540,775)(541,781)(542,782)(543,783)(544,784)
(545,785)(546,791)(547,792)(548,793)(549,794)(550,795)(551,786)(552,787)
(553,788)(554,789)(555,790)(556,796)(557,797)(558,798)(559,799)(560,800)
(561,806)(562,807)(563,808)(564,809)(565,810)(566,801)(567,802)(568,803)
(569,804)(570,805)(571,811)(572,812)(573,813)(574,814)(575,815)(576,821)
(577,822)(578,823)(579,824)(580,825)(581,816)(582,817)(583,818)(584,819)
(585,820)(586,826)(587,827)(588,828)(589,829)(590,830)(591,836)(592,837)
(593,838)(594,839)(595,840)(596,831)(597,832)(598,833)(599,834)(600,835)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,851)(607,852)(608,853)
(609,854)(610,855)(611,846)(612,847)(613,848)(614,849)(615,850)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,866)(622,867)(623,868)(624,869)
(625,870)(626,861)(627,862)(628,863)(629,864)(630,865)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,881)(637,882)(638,883)(639,884)(640,885)
(641,876)(642,877)(643,878)(644,879)(645,880)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,896)(652,897)(653,898)(654,899)(655,900)(656,891)
(657,892)(658,893)(659,894)(660,895)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,911)(667,912)(668,913)(669,914)(670,915)(671,906)(672,907)
(673,908)(674,909)(675,910)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,926)(682,927)(683,928)(684,929)(685,930)(686,921)(687,922)(688,923)
(689,924)(690,925)(691,931)(692,932)(693,933)(694,934)(695,935)(696,941)
(697,942)(698,943)(699,944)(700,945)(701,936)(702,937)(703,938)(704,939)
(705,940)(706,946)(707,947)(708,948)(709,949)(710,950)(711,956)(712,957)
(713,958)(714,959)(715,960)(716,951)(717,952)(718,953)(719,954)(720,955);;
s1 := (  1,186)(  2,190)(  3,189)(  4,188)(  5,187)(  6,181)(  7,185)(  8,184)
(  9,183)( 10,182)( 11,191)( 12,195)( 13,194)( 14,193)( 15,192)( 16,201)
( 17,205)( 18,204)( 19,203)( 20,202)( 21,196)( 22,200)( 23,199)( 24,198)
( 25,197)( 26,206)( 27,210)( 28,209)( 29,208)( 30,207)( 31,216)( 32,220)
( 33,219)( 34,218)( 35,217)( 36,211)( 37,215)( 38,214)( 39,213)( 40,212)
( 41,221)( 42,225)( 43,224)( 44,223)( 45,222)( 46,231)( 47,235)( 48,234)
( 49,233)( 50,232)( 51,226)( 52,230)( 53,229)( 54,228)( 55,227)( 56,236)
( 57,240)( 58,239)( 59,238)( 60,237)( 61,141)( 62,145)( 63,144)( 64,143)
( 65,142)( 66,136)( 67,140)( 68,139)( 69,138)( 70,137)( 71,146)( 72,150)
( 73,149)( 74,148)( 75,147)( 76,126)( 77,130)( 78,129)( 79,128)( 80,127)
( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,131)( 87,135)( 88,134)
( 89,133)( 90,132)( 91,171)( 92,175)( 93,174)( 94,173)( 95,172)( 96,166)
( 97,170)( 98,169)( 99,168)(100,167)(101,176)(102,180)(103,179)(104,178)
(105,177)(106,156)(107,160)(108,159)(109,158)(110,157)(111,151)(112,155)
(113,154)(114,153)(115,152)(116,161)(117,165)(118,164)(119,163)(120,162)
(241,456)(242,460)(243,459)(244,458)(245,457)(246,451)(247,455)(248,454)
(249,453)(250,452)(251,461)(252,465)(253,464)(254,463)(255,462)(256,471)
(257,475)(258,474)(259,473)(260,472)(261,466)(262,470)(263,469)(264,468)
(265,467)(266,476)(267,480)(268,479)(269,478)(270,477)(271,426)(272,430)
(273,429)(274,428)(275,427)(276,421)(277,425)(278,424)(279,423)(280,422)
(281,431)(282,435)(283,434)(284,433)(285,432)(286,441)(287,445)(288,444)
(289,443)(290,442)(291,436)(292,440)(293,439)(294,438)(295,437)(296,446)
(297,450)(298,449)(299,448)(300,447)(301,411)(302,415)(303,414)(304,413)
(305,412)(306,406)(307,410)(308,409)(309,408)(310,407)(311,416)(312,420)
(313,419)(314,418)(315,417)(316,396)(317,400)(318,399)(319,398)(320,397)
(321,391)(322,395)(323,394)(324,393)(325,392)(326,401)(327,405)(328,404)
(329,403)(330,402)(331,381)(332,385)(333,384)(334,383)(335,382)(336,376)
(337,380)(338,379)(339,378)(340,377)(341,386)(342,390)(343,389)(344,388)
(345,387)(346,366)(347,370)(348,369)(349,368)(350,367)(351,361)(352,365)
(353,364)(354,363)(355,362)(356,371)(357,375)(358,374)(359,373)(360,372)
(481,606)(482,610)(483,609)(484,608)(485,607)(486,601)(487,605)(488,604)
(489,603)(490,602)(491,611)(492,615)(493,614)(494,613)(495,612)(496,621)
(497,625)(498,624)(499,623)(500,622)(501,616)(502,620)(503,619)(504,618)
(505,617)(506,626)(507,630)(508,629)(509,628)(510,627)(511,636)(512,640)
(513,639)(514,638)(515,637)(516,631)(517,635)(518,634)(519,633)(520,632)
(521,641)(522,645)(523,644)(524,643)(525,642)(526,651)(527,655)(528,654)
(529,653)(530,652)(531,646)(532,650)(533,649)(534,648)(535,647)(536,656)
(537,660)(538,659)(539,658)(540,657)(541,666)(542,670)(543,669)(544,668)
(545,667)(546,661)(547,665)(548,664)(549,663)(550,662)(551,671)(552,675)
(553,674)(554,673)(555,672)(556,681)(557,685)(558,684)(559,683)(560,682)
(561,676)(562,680)(563,679)(564,678)(565,677)(566,686)(567,690)(568,689)
(569,688)(570,687)(571,696)(572,700)(573,699)(574,698)(575,697)(576,691)
(577,695)(578,694)(579,693)(580,692)(581,701)(582,705)(583,704)(584,703)
(585,702)(586,711)(587,715)(588,714)(589,713)(590,712)(591,706)(592,710)
(593,709)(594,708)(595,707)(596,716)(597,720)(598,719)(599,718)(600,717)
(721,876)(722,880)(723,879)(724,878)(725,877)(726,871)(727,875)(728,874)
(729,873)(730,872)(731,881)(732,885)(733,884)(734,883)(735,882)(736,891)
(737,895)(738,894)(739,893)(740,892)(741,886)(742,890)(743,889)(744,888)
(745,887)(746,896)(747,900)(748,899)(749,898)(750,897)(751,846)(752,850)
(753,849)(754,848)(755,847)(756,841)(757,845)(758,844)(759,843)(760,842)
(761,851)(762,855)(763,854)(764,853)(765,852)(766,861)(767,865)(768,864)
(769,863)(770,862)(771,856)(772,860)(773,859)(774,858)(775,857)(776,866)
(777,870)(778,869)(779,868)(780,867)(781,936)(782,940)(783,939)(784,938)
(785,937)(786,931)(787,935)(788,934)(789,933)(790,932)(791,941)(792,945)
(793,944)(794,943)(795,942)(796,951)(797,955)(798,954)(799,953)(800,952)
(801,946)(802,950)(803,949)(804,948)(805,947)(806,956)(807,960)(808,959)
(809,958)(810,957)(811,906)(812,910)(813,909)(814,908)(815,907)(816,901)
(817,905)(818,904)(819,903)(820,902)(821,911)(822,915)(823,914)(824,913)
(825,912)(826,921)(827,925)(828,924)(829,923)(830,922)(831,916)(832,920)
(833,919)(834,918)(835,917)(836,926)(837,930)(838,929)(839,928)(840,927);;
s2 := (  1,122)(  2,121)(  3,125)(  4,124)(  5,123)(  6,127)(  7,126)(  8,130)
(  9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,137)
( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)( 24,144)
( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)( 32,151)
( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)( 40,158)
( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)( 48,170)
( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)( 56,177)
( 57,176)( 58,180)( 59,179)( 60,178)( 61,197)( 62,196)( 63,200)( 64,199)
( 65,198)( 66,202)( 67,201)( 68,205)( 69,204)( 70,203)( 71,207)( 72,206)
( 73,210)( 74,209)( 75,208)( 76,182)( 77,181)( 78,185)( 79,184)( 80,183)
( 81,187)( 82,186)( 83,190)( 84,189)( 85,188)( 86,192)( 87,191)( 88,195)
( 89,194)( 90,193)( 91,227)( 92,226)( 93,230)( 94,229)( 95,228)( 96,232)
( 97,231)( 98,235)( 99,234)(100,233)(101,237)(102,236)(103,240)(104,239)
(105,238)(106,212)(107,211)(108,215)(109,214)(110,213)(111,217)(112,216)
(113,220)(114,219)(115,218)(116,222)(117,221)(118,225)(119,224)(120,223)
(241,362)(242,361)(243,365)(244,364)(245,363)(246,367)(247,366)(248,370)
(249,369)(250,368)(251,372)(252,371)(253,375)(254,374)(255,373)(256,377)
(257,376)(258,380)(259,379)(260,378)(261,382)(262,381)(263,385)(264,384)
(265,383)(266,387)(267,386)(268,390)(269,389)(270,388)(271,392)(272,391)
(273,395)(274,394)(275,393)(276,397)(277,396)(278,400)(279,399)(280,398)
(281,402)(282,401)(283,405)(284,404)(285,403)(286,407)(287,406)(288,410)
(289,409)(290,408)(291,412)(292,411)(293,415)(294,414)(295,413)(296,417)
(297,416)(298,420)(299,419)(300,418)(301,437)(302,436)(303,440)(304,439)
(305,438)(306,442)(307,441)(308,445)(309,444)(310,443)(311,447)(312,446)
(313,450)(314,449)(315,448)(316,422)(317,421)(318,425)(319,424)(320,423)
(321,427)(322,426)(323,430)(324,429)(325,428)(326,432)(327,431)(328,435)
(329,434)(330,433)(331,467)(332,466)(333,470)(334,469)(335,468)(336,472)
(337,471)(338,475)(339,474)(340,473)(341,477)(342,476)(343,480)(344,479)
(345,478)(346,452)(347,451)(348,455)(349,454)(350,453)(351,457)(352,456)
(353,460)(354,459)(355,458)(356,462)(357,461)(358,465)(359,464)(360,463)
(481,602)(482,601)(483,605)(484,604)(485,603)(486,607)(487,606)(488,610)
(489,609)(490,608)(491,612)(492,611)(493,615)(494,614)(495,613)(496,617)
(497,616)(498,620)(499,619)(500,618)(501,622)(502,621)(503,625)(504,624)
(505,623)(506,627)(507,626)(508,630)(509,629)(510,628)(511,632)(512,631)
(513,635)(514,634)(515,633)(516,637)(517,636)(518,640)(519,639)(520,638)
(521,642)(522,641)(523,645)(524,644)(525,643)(526,647)(527,646)(528,650)
(529,649)(530,648)(531,652)(532,651)(533,655)(534,654)(535,653)(536,657)
(537,656)(538,660)(539,659)(540,658)(541,677)(542,676)(543,680)(544,679)
(545,678)(546,682)(547,681)(548,685)(549,684)(550,683)(551,687)(552,686)
(553,690)(554,689)(555,688)(556,662)(557,661)(558,665)(559,664)(560,663)
(561,667)(562,666)(563,670)(564,669)(565,668)(566,672)(567,671)(568,675)
(569,674)(570,673)(571,707)(572,706)(573,710)(574,709)(575,708)(576,712)
(577,711)(578,715)(579,714)(580,713)(581,717)(582,716)(583,720)(584,719)
(585,718)(586,692)(587,691)(588,695)(589,694)(590,693)(591,697)(592,696)
(593,700)(594,699)(595,698)(596,702)(597,701)(598,705)(599,704)(600,703)
(721,842)(722,841)(723,845)(724,844)(725,843)(726,847)(727,846)(728,850)
(729,849)(730,848)(731,852)(732,851)(733,855)(734,854)(735,853)(736,857)
(737,856)(738,860)(739,859)(740,858)(741,862)(742,861)(743,865)(744,864)
(745,863)(746,867)(747,866)(748,870)(749,869)(750,868)(751,872)(752,871)
(753,875)(754,874)(755,873)(756,877)(757,876)(758,880)(759,879)(760,878)
(761,882)(762,881)(763,885)(764,884)(765,883)(766,887)(767,886)(768,890)
(769,889)(770,888)(771,892)(772,891)(773,895)(774,894)(775,893)(776,897)
(777,896)(778,900)(779,899)(780,898)(781,917)(782,916)(783,920)(784,919)
(785,918)(786,922)(787,921)(788,925)(789,924)(790,923)(791,927)(792,926)
(793,930)(794,929)(795,928)(796,902)(797,901)(798,905)(799,904)(800,903)
(801,907)(802,906)(803,910)(804,909)(805,908)(806,912)(807,911)(808,915)
(809,914)(810,913)(811,947)(812,946)(813,950)(814,949)(815,948)(816,952)
(817,951)(818,955)(819,954)(820,953)(821,957)(822,956)(823,960)(824,959)
(825,958)(826,932)(827,931)(828,935)(829,934)(830,933)(831,937)(832,936)
(833,940)(834,939)(835,938)(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*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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(960)!(  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,251)(  7,252)
(  8,253)(  9,254)( 10,255)( 11,246)( 12,247)( 13,248)( 14,249)( 15,250)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)
( 24,269)( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,281)( 37,282)( 38,283)( 39,284)
( 40,285)( 41,276)( 42,277)( 43,278)( 44,279)( 45,280)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)
( 56,291)( 57,292)( 58,293)( 59,294)( 60,295)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,311)( 67,312)( 68,313)( 69,314)( 70,315)( 71,306)
( 72,307)( 73,308)( 74,309)( 75,310)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,321)( 87,322)
( 88,323)( 89,324)( 90,325)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,341)( 97,342)( 98,343)( 99,344)(100,345)(101,336)(102,337)(103,338)
(104,339)(105,340)(106,346)(107,347)(108,348)(109,349)(110,350)(111,356)
(112,357)(113,358)(114,359)(115,360)(116,351)(117,352)(118,353)(119,354)
(120,355)(121,361)(122,362)(123,363)(124,364)(125,365)(126,371)(127,372)
(128,373)(129,374)(130,375)(131,366)(132,367)(133,368)(134,369)(135,370)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,386)(142,387)(143,388)
(144,389)(145,390)(146,381)(147,382)(148,383)(149,384)(150,385)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,401)(157,402)(158,403)(159,404)
(160,405)(161,396)(162,397)(163,398)(164,399)(165,400)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,416)(172,417)(173,418)(174,419)(175,420)
(176,411)(177,412)(178,413)(179,414)(180,415)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,431)(187,432)(188,433)(189,434)(190,435)(191,426)
(192,427)(193,428)(194,429)(195,430)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,446)(202,447)(203,448)(204,449)(205,450)(206,441)(207,442)
(208,443)(209,444)(210,445)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,461)(217,462)(218,463)(219,464)(220,465)(221,456)(222,457)(223,458)
(224,459)(225,460)(226,466)(227,467)(228,468)(229,469)(230,470)(231,476)
(232,477)(233,478)(234,479)(235,480)(236,471)(237,472)(238,473)(239,474)
(240,475)(481,721)(482,722)(483,723)(484,724)(485,725)(486,731)(487,732)
(488,733)(489,734)(490,735)(491,726)(492,727)(493,728)(494,729)(495,730)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,746)(502,747)(503,748)
(504,749)(505,750)(506,741)(507,742)(508,743)(509,744)(510,745)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,761)(517,762)(518,763)(519,764)
(520,765)(521,756)(522,757)(523,758)(524,759)(525,760)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,776)(532,777)(533,778)(534,779)(535,780)
(536,771)(537,772)(538,773)(539,774)(540,775)(541,781)(542,782)(543,783)
(544,784)(545,785)(546,791)(547,792)(548,793)(549,794)(550,795)(551,786)
(552,787)(553,788)(554,789)(555,790)(556,796)(557,797)(558,798)(559,799)
(560,800)(561,806)(562,807)(563,808)(564,809)(565,810)(566,801)(567,802)
(568,803)(569,804)(570,805)(571,811)(572,812)(573,813)(574,814)(575,815)
(576,821)(577,822)(578,823)(579,824)(580,825)(581,816)(582,817)(583,818)
(584,819)(585,820)(586,826)(587,827)(588,828)(589,829)(590,830)(591,836)
(592,837)(593,838)(594,839)(595,840)(596,831)(597,832)(598,833)(599,834)
(600,835)(601,841)(602,842)(603,843)(604,844)(605,845)(606,851)(607,852)
(608,853)(609,854)(610,855)(611,846)(612,847)(613,848)(614,849)(615,850)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,866)(622,867)(623,868)
(624,869)(625,870)(626,861)(627,862)(628,863)(629,864)(630,865)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,881)(637,882)(638,883)(639,884)
(640,885)(641,876)(642,877)(643,878)(644,879)(645,880)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,896)(652,897)(653,898)(654,899)(655,900)
(656,891)(657,892)(658,893)(659,894)(660,895)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,911)(667,912)(668,913)(669,914)(670,915)(671,906)
(672,907)(673,908)(674,909)(675,910)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,926)(682,927)(683,928)(684,929)(685,930)(686,921)(687,922)
(688,923)(689,924)(690,925)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,941)(697,942)(698,943)(699,944)(700,945)(701,936)(702,937)(703,938)
(704,939)(705,940)(706,946)(707,947)(708,948)(709,949)(710,950)(711,956)
(712,957)(713,958)(714,959)(715,960)(716,951)(717,952)(718,953)(719,954)
(720,955);
s1 := Sym(960)!(  1,186)(  2,190)(  3,189)(  4,188)(  5,187)(  6,181)(  7,185)
(  8,184)(  9,183)( 10,182)( 11,191)( 12,195)( 13,194)( 14,193)( 15,192)
( 16,201)( 17,205)( 18,204)( 19,203)( 20,202)( 21,196)( 22,200)( 23,199)
( 24,198)( 25,197)( 26,206)( 27,210)( 28,209)( 29,208)( 30,207)( 31,216)
( 32,220)( 33,219)( 34,218)( 35,217)( 36,211)( 37,215)( 38,214)( 39,213)
( 40,212)( 41,221)( 42,225)( 43,224)( 44,223)( 45,222)( 46,231)( 47,235)
( 48,234)( 49,233)( 50,232)( 51,226)( 52,230)( 53,229)( 54,228)( 55,227)
( 56,236)( 57,240)( 58,239)( 59,238)( 60,237)( 61,141)( 62,145)( 63,144)
( 64,143)( 65,142)( 66,136)( 67,140)( 68,139)( 69,138)( 70,137)( 71,146)
( 72,150)( 73,149)( 74,148)( 75,147)( 76,126)( 77,130)( 78,129)( 79,128)
( 80,127)( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,131)( 87,135)
( 88,134)( 89,133)( 90,132)( 91,171)( 92,175)( 93,174)( 94,173)( 95,172)
( 96,166)( 97,170)( 98,169)( 99,168)(100,167)(101,176)(102,180)(103,179)
(104,178)(105,177)(106,156)(107,160)(108,159)(109,158)(110,157)(111,151)
(112,155)(113,154)(114,153)(115,152)(116,161)(117,165)(118,164)(119,163)
(120,162)(241,456)(242,460)(243,459)(244,458)(245,457)(246,451)(247,455)
(248,454)(249,453)(250,452)(251,461)(252,465)(253,464)(254,463)(255,462)
(256,471)(257,475)(258,474)(259,473)(260,472)(261,466)(262,470)(263,469)
(264,468)(265,467)(266,476)(267,480)(268,479)(269,478)(270,477)(271,426)
(272,430)(273,429)(274,428)(275,427)(276,421)(277,425)(278,424)(279,423)
(280,422)(281,431)(282,435)(283,434)(284,433)(285,432)(286,441)(287,445)
(288,444)(289,443)(290,442)(291,436)(292,440)(293,439)(294,438)(295,437)
(296,446)(297,450)(298,449)(299,448)(300,447)(301,411)(302,415)(303,414)
(304,413)(305,412)(306,406)(307,410)(308,409)(309,408)(310,407)(311,416)
(312,420)(313,419)(314,418)(315,417)(316,396)(317,400)(318,399)(319,398)
(320,397)(321,391)(322,395)(323,394)(324,393)(325,392)(326,401)(327,405)
(328,404)(329,403)(330,402)(331,381)(332,385)(333,384)(334,383)(335,382)
(336,376)(337,380)(338,379)(339,378)(340,377)(341,386)(342,390)(343,389)
(344,388)(345,387)(346,366)(347,370)(348,369)(349,368)(350,367)(351,361)
(352,365)(353,364)(354,363)(355,362)(356,371)(357,375)(358,374)(359,373)
(360,372)(481,606)(482,610)(483,609)(484,608)(485,607)(486,601)(487,605)
(488,604)(489,603)(490,602)(491,611)(492,615)(493,614)(494,613)(495,612)
(496,621)(497,625)(498,624)(499,623)(500,622)(501,616)(502,620)(503,619)
(504,618)(505,617)(506,626)(507,630)(508,629)(509,628)(510,627)(511,636)
(512,640)(513,639)(514,638)(515,637)(516,631)(517,635)(518,634)(519,633)
(520,632)(521,641)(522,645)(523,644)(524,643)(525,642)(526,651)(527,655)
(528,654)(529,653)(530,652)(531,646)(532,650)(533,649)(534,648)(535,647)
(536,656)(537,660)(538,659)(539,658)(540,657)(541,666)(542,670)(543,669)
(544,668)(545,667)(546,661)(547,665)(548,664)(549,663)(550,662)(551,671)
(552,675)(553,674)(554,673)(555,672)(556,681)(557,685)(558,684)(559,683)
(560,682)(561,676)(562,680)(563,679)(564,678)(565,677)(566,686)(567,690)
(568,689)(569,688)(570,687)(571,696)(572,700)(573,699)(574,698)(575,697)
(576,691)(577,695)(578,694)(579,693)(580,692)(581,701)(582,705)(583,704)
(584,703)(585,702)(586,711)(587,715)(588,714)(589,713)(590,712)(591,706)
(592,710)(593,709)(594,708)(595,707)(596,716)(597,720)(598,719)(599,718)
(600,717)(721,876)(722,880)(723,879)(724,878)(725,877)(726,871)(727,875)
(728,874)(729,873)(730,872)(731,881)(732,885)(733,884)(734,883)(735,882)
(736,891)(737,895)(738,894)(739,893)(740,892)(741,886)(742,890)(743,889)
(744,888)(745,887)(746,896)(747,900)(748,899)(749,898)(750,897)(751,846)
(752,850)(753,849)(754,848)(755,847)(756,841)(757,845)(758,844)(759,843)
(760,842)(761,851)(762,855)(763,854)(764,853)(765,852)(766,861)(767,865)
(768,864)(769,863)(770,862)(771,856)(772,860)(773,859)(774,858)(775,857)
(776,866)(777,870)(778,869)(779,868)(780,867)(781,936)(782,940)(783,939)
(784,938)(785,937)(786,931)(787,935)(788,934)(789,933)(790,932)(791,941)
(792,945)(793,944)(794,943)(795,942)(796,951)(797,955)(798,954)(799,953)
(800,952)(801,946)(802,950)(803,949)(804,948)(805,947)(806,956)(807,960)
(808,959)(809,958)(810,957)(811,906)(812,910)(813,909)(814,908)(815,907)
(816,901)(817,905)(818,904)(819,903)(820,902)(821,911)(822,915)(823,914)
(824,913)(825,912)(826,921)(827,925)(828,924)(829,923)(830,922)(831,916)
(832,920)(833,919)(834,918)(835,917)(836,926)(837,930)(838,929)(839,928)
(840,927);
s2 := Sym(960)!(  1,122)(  2,121)(  3,125)(  4,124)(  5,123)(  6,127)(  7,126)
(  8,130)(  9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)
( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)
( 24,144)( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)
( 32,151)( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)
( 40,158)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)
( 48,170)( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)
( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,197)( 62,196)( 63,200)
( 64,199)( 65,198)( 66,202)( 67,201)( 68,205)( 69,204)( 70,203)( 71,207)
( 72,206)( 73,210)( 74,209)( 75,208)( 76,182)( 77,181)( 78,185)( 79,184)
( 80,183)( 81,187)( 82,186)( 83,190)( 84,189)( 85,188)( 86,192)( 87,191)
( 88,195)( 89,194)( 90,193)( 91,227)( 92,226)( 93,230)( 94,229)( 95,228)
( 96,232)( 97,231)( 98,235)( 99,234)(100,233)(101,237)(102,236)(103,240)
(104,239)(105,238)(106,212)(107,211)(108,215)(109,214)(110,213)(111,217)
(112,216)(113,220)(114,219)(115,218)(116,222)(117,221)(118,225)(119,224)
(120,223)(241,362)(242,361)(243,365)(244,364)(245,363)(246,367)(247,366)
(248,370)(249,369)(250,368)(251,372)(252,371)(253,375)(254,374)(255,373)
(256,377)(257,376)(258,380)(259,379)(260,378)(261,382)(262,381)(263,385)
(264,384)(265,383)(266,387)(267,386)(268,390)(269,389)(270,388)(271,392)
(272,391)(273,395)(274,394)(275,393)(276,397)(277,396)(278,400)(279,399)
(280,398)(281,402)(282,401)(283,405)(284,404)(285,403)(286,407)(287,406)
(288,410)(289,409)(290,408)(291,412)(292,411)(293,415)(294,414)(295,413)
(296,417)(297,416)(298,420)(299,419)(300,418)(301,437)(302,436)(303,440)
(304,439)(305,438)(306,442)(307,441)(308,445)(309,444)(310,443)(311,447)
(312,446)(313,450)(314,449)(315,448)(316,422)(317,421)(318,425)(319,424)
(320,423)(321,427)(322,426)(323,430)(324,429)(325,428)(326,432)(327,431)
(328,435)(329,434)(330,433)(331,467)(332,466)(333,470)(334,469)(335,468)
(336,472)(337,471)(338,475)(339,474)(340,473)(341,477)(342,476)(343,480)
(344,479)(345,478)(346,452)(347,451)(348,455)(349,454)(350,453)(351,457)
(352,456)(353,460)(354,459)(355,458)(356,462)(357,461)(358,465)(359,464)
(360,463)(481,602)(482,601)(483,605)(484,604)(485,603)(486,607)(487,606)
(488,610)(489,609)(490,608)(491,612)(492,611)(493,615)(494,614)(495,613)
(496,617)(497,616)(498,620)(499,619)(500,618)(501,622)(502,621)(503,625)
(504,624)(505,623)(506,627)(507,626)(508,630)(509,629)(510,628)(511,632)
(512,631)(513,635)(514,634)(515,633)(516,637)(517,636)(518,640)(519,639)
(520,638)(521,642)(522,641)(523,645)(524,644)(525,643)(526,647)(527,646)
(528,650)(529,649)(530,648)(531,652)(532,651)(533,655)(534,654)(535,653)
(536,657)(537,656)(538,660)(539,659)(540,658)(541,677)(542,676)(543,680)
(544,679)(545,678)(546,682)(547,681)(548,685)(549,684)(550,683)(551,687)
(552,686)(553,690)(554,689)(555,688)(556,662)(557,661)(558,665)(559,664)
(560,663)(561,667)(562,666)(563,670)(564,669)(565,668)(566,672)(567,671)
(568,675)(569,674)(570,673)(571,707)(572,706)(573,710)(574,709)(575,708)
(576,712)(577,711)(578,715)(579,714)(580,713)(581,717)(582,716)(583,720)
(584,719)(585,718)(586,692)(587,691)(588,695)(589,694)(590,693)(591,697)
(592,696)(593,700)(594,699)(595,698)(596,702)(597,701)(598,705)(599,704)
(600,703)(721,842)(722,841)(723,845)(724,844)(725,843)(726,847)(727,846)
(728,850)(729,849)(730,848)(731,852)(732,851)(733,855)(734,854)(735,853)
(736,857)(737,856)(738,860)(739,859)(740,858)(741,862)(742,861)(743,865)
(744,864)(745,863)(746,867)(747,866)(748,870)(749,869)(750,868)(751,872)
(752,871)(753,875)(754,874)(755,873)(756,877)(757,876)(758,880)(759,879)
(760,878)(761,882)(762,881)(763,885)(764,884)(765,883)(766,887)(767,886)
(768,890)(769,889)(770,888)(771,892)(772,891)(773,895)(774,894)(775,893)
(776,897)(777,896)(778,900)(779,899)(780,898)(781,917)(782,916)(783,920)
(784,919)(785,918)(786,922)(787,921)(788,925)(789,924)(790,923)(791,927)
(792,926)(793,930)(794,929)(795,928)(796,902)(797,901)(798,905)(799,904)
(800,903)(801,907)(802,906)(803,910)(804,909)(805,908)(806,912)(807,911)
(808,915)(809,914)(810,913)(811,947)(812,946)(813,950)(814,949)(815,948)
(816,952)(817,951)(818,955)(819,954)(820,953)(821,957)(822,956)(823,960)
(824,959)(825,958)(826,932)(827,931)(828,935)(829,934)(830,933)(831,937)
(832,936)(833,940)(834,939)(835,938)(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*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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope