Polytope of Type {4,30,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240291)
Rank : 4
Schlafli Type : {4,30,4}
Number of vertices, edges, etc : 4, 120, 120, 8
Order of s0s1s2s3 : 60
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}*960b, {2,30,4}*960
   4-fold quotients : {4,30,2}*480a, {2,15,4}*480, {2,30,4}*480b, {2,30,4}*480c
   5-fold quotients : {4,6,4}*384a
   8-fold quotients : {2,15,4}*240, {2,30,2}*240
   10-fold quotients : {4,6,4}*192b, {2,6,4}*192
   12-fold quotients : {4,10,2}*160
   16-fold quotients : {2,15,2}*120
   20-fold quotients : {4,6,2}*96a, {2,3,4}*96, {2,6,4}*96b, {2,6,4}*96c
   24-fold quotients : {2,10,2}*80
   40-fold quotients : {2,3,4}*48, {2,6,2}*48
   48-fold quotients : {2,5,2}*40
   60-fold quotients : {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)
(121,421)(122,422)(123,423)(124,424)(125,425)(126,426)(127,427)(128,428)
(129,429)(130,430)(131,431)(132,432)(133,433)(134,434)(135,435)(136,436)
(137,437)(138,438)(139,439)(140,440)(141,441)(142,442)(143,443)(144,444)
(145,445)(146,446)(147,447)(148,448)(149,449)(150,450)(151,451)(152,452)
(153,453)(154,454)(155,455)(156,456)(157,457)(158,458)(159,459)(160,460)
(161,461)(162,462)(163,463)(164,464)(165,465)(166,466)(167,467)(168,468)
(169,469)(170,470)(171,471)(172,472)(173,473)(174,474)(175,475)(176,476)
(177,477)(178,478)(179,479)(180,480)(181,361)(182,362)(183,363)(184,364)
(185,365)(186,366)(187,367)(188,368)(189,369)(190,370)(191,371)(192,372)
(193,373)(194,374)(195,375)(196,376)(197,377)(198,378)(199,379)(200,380)
(201,381)(202,382)(203,383)(204,384)(205,385)(206,386)(207,387)(208,388)
(209,389)(210,390)(211,391)(212,392)(213,393)(214,394)(215,395)(216,396)
(217,397)(218,398)(219,399)(220,400)(221,401)(222,402)(223,403)(224,404)
(225,405)(226,406)(227,407)(228,408)(229,409)(230,410)(231,411)(232,412)
(233,413)(234,414)(235,415)(236,416)(237,417)(238,418)(239,419)(240,420)
(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)
(601,901)(602,902)(603,903)(604,904)(605,905)(606,906)(607,907)(608,908)
(609,909)(610,910)(611,911)(612,912)(613,913)(614,914)(615,915)(616,916)
(617,917)(618,918)(619,919)(620,920)(621,921)(622,922)(623,923)(624,924)
(625,925)(626,926)(627,927)(628,928)(629,929)(630,930)(631,931)(632,932)
(633,933)(634,934)(635,935)(636,936)(637,937)(638,938)(639,939)(640,940)
(641,941)(642,942)(643,943)(644,944)(645,945)(646,946)(647,947)(648,948)
(649,949)(650,950)(651,951)(652,952)(653,953)(654,954)(655,955)(656,956)
(657,957)(658,958)(659,959)(660,960)(661,841)(662,842)(663,843)(664,844)
(665,845)(666,846)(667,847)(668,848)(669,849)(670,850)(671,851)(672,852)
(673,853)(674,854)(675,855)(676,856)(677,857)(678,858)(679,859)(680,860)
(681,861)(682,862)(683,863)(684,864)(685,865)(686,866)(687,867)(688,868)
(689,869)(690,870)(691,871)(692,872)(693,873)(694,874)(695,875)(696,876)
(697,877)(698,878)(699,879)(700,880)(701,881)(702,882)(703,883)(704,884)
(705,885)(706,886)(707,887)(708,888)(709,889)(710,890)(711,891)(712,892)
(713,893)(714,894)(715,895)(716,896)(717,897)(718,898)(719,899)(720,900);;
s1 := (  1,121)(  2,122)(  3,124)(  4,123)(  5,137)(  6,138)(  7,140)(  8,139)
(  9,133)( 10,134)( 11,136)( 12,135)( 13,129)( 14,130)( 15,132)( 16,131)
( 17,125)( 18,126)( 19,128)( 20,127)( 21,161)( 22,162)( 23,164)( 24,163)
( 25,177)( 26,178)( 27,180)( 28,179)( 29,173)( 30,174)( 31,176)( 32,175)
( 33,169)( 34,170)( 35,172)( 36,171)( 37,165)( 38,166)( 39,168)( 40,167)
( 41,141)( 42,142)( 43,144)( 44,143)( 45,157)( 46,158)( 47,160)( 48,159)
( 49,153)( 50,154)( 51,156)( 52,155)( 53,149)( 54,150)( 55,152)( 56,151)
( 57,145)( 58,146)( 59,148)( 60,147)( 61,181)( 62,182)( 63,184)( 64,183)
( 65,197)( 66,198)( 67,200)( 68,199)( 69,193)( 70,194)( 71,196)( 72,195)
( 73,189)( 74,190)( 75,192)( 76,191)( 77,185)( 78,186)( 79,188)( 80,187)
( 81,221)( 82,222)( 83,224)( 84,223)( 85,237)( 86,238)( 87,240)( 88,239)
( 89,233)( 90,234)( 91,236)( 92,235)( 93,229)( 94,230)( 95,232)( 96,231)
( 97,225)( 98,226)( 99,228)(100,227)(101,201)(102,202)(103,204)(104,203)
(105,217)(106,218)(107,220)(108,219)(109,213)(110,214)(111,216)(112,215)
(113,209)(114,210)(115,212)(116,211)(117,205)(118,206)(119,208)(120,207)
(241,361)(242,362)(243,364)(244,363)(245,377)(246,378)(247,380)(248,379)
(249,373)(250,374)(251,376)(252,375)(253,369)(254,370)(255,372)(256,371)
(257,365)(258,366)(259,368)(260,367)(261,401)(262,402)(263,404)(264,403)
(265,417)(266,418)(267,420)(268,419)(269,413)(270,414)(271,416)(272,415)
(273,409)(274,410)(275,412)(276,411)(277,405)(278,406)(279,408)(280,407)
(281,381)(282,382)(283,384)(284,383)(285,397)(286,398)(287,400)(288,399)
(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)(295,392)(296,391)
(297,385)(298,386)(299,388)(300,387)(301,421)(302,422)(303,424)(304,423)
(305,437)(306,438)(307,440)(308,439)(309,433)(310,434)(311,436)(312,435)
(313,429)(314,430)(315,432)(316,431)(317,425)(318,426)(319,428)(320,427)
(321,461)(322,462)(323,464)(324,463)(325,477)(326,478)(327,480)(328,479)
(329,473)(330,474)(331,476)(332,475)(333,469)(334,470)(335,472)(336,471)
(337,465)(338,466)(339,468)(340,467)(341,441)(342,442)(343,444)(344,443)
(345,457)(346,458)(347,460)(348,459)(349,453)(350,454)(351,456)(352,455)
(353,449)(354,450)(355,452)(356,451)(357,445)(358,446)(359,448)(360,447)
(481,601)(482,602)(483,604)(484,603)(485,617)(486,618)(487,620)(488,619)
(489,613)(490,614)(491,616)(492,615)(493,609)(494,610)(495,612)(496,611)
(497,605)(498,606)(499,608)(500,607)(501,641)(502,642)(503,644)(504,643)
(505,657)(506,658)(507,660)(508,659)(509,653)(510,654)(511,656)(512,655)
(513,649)(514,650)(515,652)(516,651)(517,645)(518,646)(519,648)(520,647)
(521,621)(522,622)(523,624)(524,623)(525,637)(526,638)(527,640)(528,639)
(529,633)(530,634)(531,636)(532,635)(533,629)(534,630)(535,632)(536,631)
(537,625)(538,626)(539,628)(540,627)(541,661)(542,662)(543,664)(544,663)
(545,677)(546,678)(547,680)(548,679)(549,673)(550,674)(551,676)(552,675)
(553,669)(554,670)(555,672)(556,671)(557,665)(558,666)(559,668)(560,667)
(561,701)(562,702)(563,704)(564,703)(565,717)(566,718)(567,720)(568,719)
(569,713)(570,714)(571,716)(572,715)(573,709)(574,710)(575,712)(576,711)
(577,705)(578,706)(579,708)(580,707)(581,681)(582,682)(583,684)(584,683)
(585,697)(586,698)(587,700)(588,699)(589,693)(590,694)(591,696)(592,695)
(593,689)(594,690)(595,692)(596,691)(597,685)(598,686)(599,688)(600,687)
(721,841)(722,842)(723,844)(724,843)(725,857)(726,858)(727,860)(728,859)
(729,853)(730,854)(731,856)(732,855)(733,849)(734,850)(735,852)(736,851)
(737,845)(738,846)(739,848)(740,847)(741,881)(742,882)(743,884)(744,883)
(745,897)(746,898)(747,900)(748,899)(749,893)(750,894)(751,896)(752,895)
(753,889)(754,890)(755,892)(756,891)(757,885)(758,886)(759,888)(760,887)
(761,861)(762,862)(763,864)(764,863)(765,877)(766,878)(767,880)(768,879)
(769,873)(770,874)(771,876)(772,875)(773,869)(774,870)(775,872)(776,871)
(777,865)(778,866)(779,868)(780,867)(781,901)(782,902)(783,904)(784,903)
(785,917)(786,918)(787,920)(788,919)(789,913)(790,914)(791,916)(792,915)
(793,909)(794,910)(795,912)(796,911)(797,905)(798,906)(799,908)(800,907)
(801,941)(802,942)(803,944)(804,943)(805,957)(806,958)(807,960)(808,959)
(809,953)(810,954)(811,956)(812,955)(813,949)(814,950)(815,952)(816,951)
(817,945)(818,946)(819,948)(820,947)(821,921)(822,922)(823,924)(824,923)
(825,937)(826,938)(827,940)(828,939)(829,933)(830,934)(831,936)(832,935)
(833,929)(834,930)(835,932)(836,931)(837,925)(838,926)(839,928)(840,927);;
s2 := (  1, 25)(  2, 28)(  3, 27)(  4, 26)(  5, 21)(  6, 24)(  7, 23)(  8, 22)
(  9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)( 16, 34)
( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)( 44, 46)
( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)( 63, 87)
( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)( 71, 99)
( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)( 79, 91)
( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)(111,119)
(112,118)(114,116)(121,145)(122,148)(123,147)(124,146)(125,141)(126,144)
(127,143)(128,142)(129,157)(130,160)(131,159)(132,158)(133,153)(134,156)
(135,155)(136,154)(137,149)(138,152)(139,151)(140,150)(161,165)(162,168)
(163,167)(164,166)(169,177)(170,180)(171,179)(172,178)(174,176)(181,205)
(182,208)(183,207)(184,206)(185,201)(186,204)(187,203)(188,202)(189,217)
(190,220)(191,219)(192,218)(193,213)(194,216)(195,215)(196,214)(197,209)
(198,212)(199,211)(200,210)(221,225)(222,228)(223,227)(224,226)(229,237)
(230,240)(231,239)(232,238)(234,236)(241,265)(242,268)(243,267)(244,266)
(245,261)(246,264)(247,263)(248,262)(249,277)(250,280)(251,279)(252,278)
(253,273)(254,276)(255,275)(256,274)(257,269)(258,272)(259,271)(260,270)
(281,285)(282,288)(283,287)(284,286)(289,297)(290,300)(291,299)(292,298)
(294,296)(301,325)(302,328)(303,327)(304,326)(305,321)(306,324)(307,323)
(308,322)(309,337)(310,340)(311,339)(312,338)(313,333)(314,336)(315,335)
(316,334)(317,329)(318,332)(319,331)(320,330)(341,345)(342,348)(343,347)
(344,346)(349,357)(350,360)(351,359)(352,358)(354,356)(361,385)(362,388)
(363,387)(364,386)(365,381)(366,384)(367,383)(368,382)(369,397)(370,400)
(371,399)(372,398)(373,393)(374,396)(375,395)(376,394)(377,389)(378,392)
(379,391)(380,390)(401,405)(402,408)(403,407)(404,406)(409,417)(410,420)
(411,419)(412,418)(414,416)(421,445)(422,448)(423,447)(424,446)(425,441)
(426,444)(427,443)(428,442)(429,457)(430,460)(431,459)(432,458)(433,453)
(434,456)(435,455)(436,454)(437,449)(438,452)(439,451)(440,450)(461,465)
(462,468)(463,467)(464,466)(469,477)(470,480)(471,479)(472,478)(474,476)
(481,505)(482,508)(483,507)(484,506)(485,501)(486,504)(487,503)(488,502)
(489,517)(490,520)(491,519)(492,518)(493,513)(494,516)(495,515)(496,514)
(497,509)(498,512)(499,511)(500,510)(521,525)(522,528)(523,527)(524,526)
(529,537)(530,540)(531,539)(532,538)(534,536)(541,565)(542,568)(543,567)
(544,566)(545,561)(546,564)(547,563)(548,562)(549,577)(550,580)(551,579)
(552,578)(553,573)(554,576)(555,575)(556,574)(557,569)(558,572)(559,571)
(560,570)(581,585)(582,588)(583,587)(584,586)(589,597)(590,600)(591,599)
(592,598)(594,596)(601,625)(602,628)(603,627)(604,626)(605,621)(606,624)
(607,623)(608,622)(609,637)(610,640)(611,639)(612,638)(613,633)(614,636)
(615,635)(616,634)(617,629)(618,632)(619,631)(620,630)(641,645)(642,648)
(643,647)(644,646)(649,657)(650,660)(651,659)(652,658)(654,656)(661,685)
(662,688)(663,687)(664,686)(665,681)(666,684)(667,683)(668,682)(669,697)
(670,700)(671,699)(672,698)(673,693)(674,696)(675,695)(676,694)(677,689)
(678,692)(679,691)(680,690)(701,705)(702,708)(703,707)(704,706)(709,717)
(710,720)(711,719)(712,718)(714,716)(721,745)(722,748)(723,747)(724,746)
(725,741)(726,744)(727,743)(728,742)(729,757)(730,760)(731,759)(732,758)
(733,753)(734,756)(735,755)(736,754)(737,749)(738,752)(739,751)(740,750)
(761,765)(762,768)(763,767)(764,766)(769,777)(770,780)(771,779)(772,778)
(774,776)(781,805)(782,808)(783,807)(784,806)(785,801)(786,804)(787,803)
(788,802)(789,817)(790,820)(791,819)(792,818)(793,813)(794,816)(795,815)
(796,814)(797,809)(798,812)(799,811)(800,810)(821,825)(822,828)(823,827)
(824,826)(829,837)(830,840)(831,839)(832,838)(834,836)(841,865)(842,868)
(843,867)(844,866)(845,861)(846,864)(847,863)(848,862)(849,877)(850,880)
(851,879)(852,878)(853,873)(854,876)(855,875)(856,874)(857,869)(858,872)
(859,871)(860,870)(881,885)(882,888)(883,887)(884,886)(889,897)(890,900)
(891,899)(892,898)(894,896)(901,925)(902,928)(903,927)(904,926)(905,921)
(906,924)(907,923)(908,922)(909,937)(910,940)(911,939)(912,938)(913,933)
(914,936)(915,935)(916,934)(917,929)(918,932)(919,931)(920,930)(941,945)
(942,948)(943,947)(944,946)(949,957)(950,960)(951,959)(952,958)(954,956);;
s3 := (  1,482)(  2,481)(  3,484)(  4,483)(  5,486)(  6,485)(  7,488)(  8,487)
(  9,490)( 10,489)( 11,492)( 12,491)( 13,494)( 14,493)( 15,496)( 16,495)
( 17,498)( 18,497)( 19,500)( 20,499)( 21,502)( 22,501)( 23,504)( 24,503)
( 25,506)( 26,505)( 27,508)( 28,507)( 29,510)( 30,509)( 31,512)( 32,511)
( 33,514)( 34,513)( 35,516)( 36,515)( 37,518)( 38,517)( 39,520)( 40,519)
( 41,522)( 42,521)( 43,524)( 44,523)( 45,526)( 46,525)( 47,528)( 48,527)
( 49,530)( 50,529)( 51,532)( 52,531)( 53,534)( 54,533)( 55,536)( 56,535)
( 57,538)( 58,537)( 59,540)( 60,539)( 61,542)( 62,541)( 63,544)( 64,543)
( 65,546)( 66,545)( 67,548)( 68,547)( 69,550)( 70,549)( 71,552)( 72,551)
( 73,554)( 74,553)( 75,556)( 76,555)( 77,558)( 78,557)( 79,560)( 80,559)
( 81,562)( 82,561)( 83,564)( 84,563)( 85,566)( 86,565)( 87,568)( 88,567)
( 89,570)( 90,569)( 91,572)( 92,571)( 93,574)( 94,573)( 95,576)( 96,575)
( 97,578)( 98,577)( 99,580)(100,579)(101,582)(102,581)(103,584)(104,583)
(105,586)(106,585)(107,588)(108,587)(109,590)(110,589)(111,592)(112,591)
(113,594)(114,593)(115,596)(116,595)(117,598)(118,597)(119,600)(120,599)
(121,602)(122,601)(123,604)(124,603)(125,606)(126,605)(127,608)(128,607)
(129,610)(130,609)(131,612)(132,611)(133,614)(134,613)(135,616)(136,615)
(137,618)(138,617)(139,620)(140,619)(141,622)(142,621)(143,624)(144,623)
(145,626)(146,625)(147,628)(148,627)(149,630)(150,629)(151,632)(152,631)
(153,634)(154,633)(155,636)(156,635)(157,638)(158,637)(159,640)(160,639)
(161,642)(162,641)(163,644)(164,643)(165,646)(166,645)(167,648)(168,647)
(169,650)(170,649)(171,652)(172,651)(173,654)(174,653)(175,656)(176,655)
(177,658)(178,657)(179,660)(180,659)(181,662)(182,661)(183,664)(184,663)
(185,666)(186,665)(187,668)(188,667)(189,670)(190,669)(191,672)(192,671)
(193,674)(194,673)(195,676)(196,675)(197,678)(198,677)(199,680)(200,679)
(201,682)(202,681)(203,684)(204,683)(205,686)(206,685)(207,688)(208,687)
(209,690)(210,689)(211,692)(212,691)(213,694)(214,693)(215,696)(216,695)
(217,698)(218,697)(219,700)(220,699)(221,702)(222,701)(223,704)(224,703)
(225,706)(226,705)(227,708)(228,707)(229,710)(230,709)(231,712)(232,711)
(233,714)(234,713)(235,716)(236,715)(237,718)(238,717)(239,720)(240,719)
(241,722)(242,721)(243,724)(244,723)(245,726)(246,725)(247,728)(248,727)
(249,730)(250,729)(251,732)(252,731)(253,734)(254,733)(255,736)(256,735)
(257,738)(258,737)(259,740)(260,739)(261,742)(262,741)(263,744)(264,743)
(265,746)(266,745)(267,748)(268,747)(269,750)(270,749)(271,752)(272,751)
(273,754)(274,753)(275,756)(276,755)(277,758)(278,757)(279,760)(280,759)
(281,762)(282,761)(283,764)(284,763)(285,766)(286,765)(287,768)(288,767)
(289,770)(290,769)(291,772)(292,771)(293,774)(294,773)(295,776)(296,775)
(297,778)(298,777)(299,780)(300,779)(301,782)(302,781)(303,784)(304,783)
(305,786)(306,785)(307,788)(308,787)(309,790)(310,789)(311,792)(312,791)
(313,794)(314,793)(315,796)(316,795)(317,798)(318,797)(319,800)(320,799)
(321,802)(322,801)(323,804)(324,803)(325,806)(326,805)(327,808)(328,807)
(329,810)(330,809)(331,812)(332,811)(333,814)(334,813)(335,816)(336,815)
(337,818)(338,817)(339,820)(340,819)(341,822)(342,821)(343,824)(344,823)
(345,826)(346,825)(347,828)(348,827)(349,830)(350,829)(351,832)(352,831)
(353,834)(354,833)(355,836)(356,835)(357,838)(358,837)(359,840)(360,839)
(361,842)(362,841)(363,844)(364,843)(365,846)(366,845)(367,848)(368,847)
(369,850)(370,849)(371,852)(372,851)(373,854)(374,853)(375,856)(376,855)
(377,858)(378,857)(379,860)(380,859)(381,862)(382,861)(383,864)(384,863)
(385,866)(386,865)(387,868)(388,867)(389,870)(390,869)(391,872)(392,871)
(393,874)(394,873)(395,876)(396,875)(397,878)(398,877)(399,880)(400,879)
(401,882)(402,881)(403,884)(404,883)(405,886)(406,885)(407,888)(408,887)
(409,890)(410,889)(411,892)(412,891)(413,894)(414,893)(415,896)(416,895)
(417,898)(418,897)(419,900)(420,899)(421,902)(422,901)(423,904)(424,903)
(425,906)(426,905)(427,908)(428,907)(429,910)(430,909)(431,912)(432,911)
(433,914)(434,913)(435,916)(436,915)(437,918)(438,917)(439,920)(440,919)
(441,922)(442,921)(443,924)(444,923)(445,926)(446,925)(447,928)(448,927)
(449,930)(450,929)(451,932)(452,931)(453,934)(454,933)(455,936)(456,935)
(457,938)(458,937)(459,940)(460,939)(461,942)(462,941)(463,944)(464,943)
(465,946)(466,945)(467,948)(468,947)(469,950)(470,949)(471,952)(472,951)
(473,954)(474,953)(475,956)(476,955)(477,958)(478,957)(479,960)(480,959);;
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)(121,421)(122,422)(123,423)(124,424)(125,425)(126,426)(127,427)
(128,428)(129,429)(130,430)(131,431)(132,432)(133,433)(134,434)(135,435)
(136,436)(137,437)(138,438)(139,439)(140,440)(141,441)(142,442)(143,443)
(144,444)(145,445)(146,446)(147,447)(148,448)(149,449)(150,450)(151,451)
(152,452)(153,453)(154,454)(155,455)(156,456)(157,457)(158,458)(159,459)
(160,460)(161,461)(162,462)(163,463)(164,464)(165,465)(166,466)(167,467)
(168,468)(169,469)(170,470)(171,471)(172,472)(173,473)(174,474)(175,475)
(176,476)(177,477)(178,478)(179,479)(180,480)(181,361)(182,362)(183,363)
(184,364)(185,365)(186,366)(187,367)(188,368)(189,369)(190,370)(191,371)
(192,372)(193,373)(194,374)(195,375)(196,376)(197,377)(198,378)(199,379)
(200,380)(201,381)(202,382)(203,383)(204,384)(205,385)(206,386)(207,387)
(208,388)(209,389)(210,390)(211,391)(212,392)(213,393)(214,394)(215,395)
(216,396)(217,397)(218,398)(219,399)(220,400)(221,401)(222,402)(223,403)
(224,404)(225,405)(226,406)(227,407)(228,408)(229,409)(230,410)(231,411)
(232,412)(233,413)(234,414)(235,415)(236,416)(237,417)(238,418)(239,419)
(240,420)(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)(601,901)(602,902)(603,903)(604,904)(605,905)(606,906)(607,907)
(608,908)(609,909)(610,910)(611,911)(612,912)(613,913)(614,914)(615,915)
(616,916)(617,917)(618,918)(619,919)(620,920)(621,921)(622,922)(623,923)
(624,924)(625,925)(626,926)(627,927)(628,928)(629,929)(630,930)(631,931)
(632,932)(633,933)(634,934)(635,935)(636,936)(637,937)(638,938)(639,939)
(640,940)(641,941)(642,942)(643,943)(644,944)(645,945)(646,946)(647,947)
(648,948)(649,949)(650,950)(651,951)(652,952)(653,953)(654,954)(655,955)
(656,956)(657,957)(658,958)(659,959)(660,960)(661,841)(662,842)(663,843)
(664,844)(665,845)(666,846)(667,847)(668,848)(669,849)(670,850)(671,851)
(672,852)(673,853)(674,854)(675,855)(676,856)(677,857)(678,858)(679,859)
(680,860)(681,861)(682,862)(683,863)(684,864)(685,865)(686,866)(687,867)
(688,868)(689,869)(690,870)(691,871)(692,872)(693,873)(694,874)(695,875)
(696,876)(697,877)(698,878)(699,879)(700,880)(701,881)(702,882)(703,883)
(704,884)(705,885)(706,886)(707,887)(708,888)(709,889)(710,890)(711,891)
(712,892)(713,893)(714,894)(715,895)(716,896)(717,897)(718,898)(719,899)
(720,900);
s1 := Sym(960)!(  1,121)(  2,122)(  3,124)(  4,123)(  5,137)(  6,138)(  7,140)
(  8,139)(  9,133)( 10,134)( 11,136)( 12,135)( 13,129)( 14,130)( 15,132)
( 16,131)( 17,125)( 18,126)( 19,128)( 20,127)( 21,161)( 22,162)( 23,164)
( 24,163)( 25,177)( 26,178)( 27,180)( 28,179)( 29,173)( 30,174)( 31,176)
( 32,175)( 33,169)( 34,170)( 35,172)( 36,171)( 37,165)( 38,166)( 39,168)
( 40,167)( 41,141)( 42,142)( 43,144)( 44,143)( 45,157)( 46,158)( 47,160)
( 48,159)( 49,153)( 50,154)( 51,156)( 52,155)( 53,149)( 54,150)( 55,152)
( 56,151)( 57,145)( 58,146)( 59,148)( 60,147)( 61,181)( 62,182)( 63,184)
( 64,183)( 65,197)( 66,198)( 67,200)( 68,199)( 69,193)( 70,194)( 71,196)
( 72,195)( 73,189)( 74,190)( 75,192)( 76,191)( 77,185)( 78,186)( 79,188)
( 80,187)( 81,221)( 82,222)( 83,224)( 84,223)( 85,237)( 86,238)( 87,240)
( 88,239)( 89,233)( 90,234)( 91,236)( 92,235)( 93,229)( 94,230)( 95,232)
( 96,231)( 97,225)( 98,226)( 99,228)(100,227)(101,201)(102,202)(103,204)
(104,203)(105,217)(106,218)(107,220)(108,219)(109,213)(110,214)(111,216)
(112,215)(113,209)(114,210)(115,212)(116,211)(117,205)(118,206)(119,208)
(120,207)(241,361)(242,362)(243,364)(244,363)(245,377)(246,378)(247,380)
(248,379)(249,373)(250,374)(251,376)(252,375)(253,369)(254,370)(255,372)
(256,371)(257,365)(258,366)(259,368)(260,367)(261,401)(262,402)(263,404)
(264,403)(265,417)(266,418)(267,420)(268,419)(269,413)(270,414)(271,416)
(272,415)(273,409)(274,410)(275,412)(276,411)(277,405)(278,406)(279,408)
(280,407)(281,381)(282,382)(283,384)(284,383)(285,397)(286,398)(287,400)
(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)(295,392)
(296,391)(297,385)(298,386)(299,388)(300,387)(301,421)(302,422)(303,424)
(304,423)(305,437)(306,438)(307,440)(308,439)(309,433)(310,434)(311,436)
(312,435)(313,429)(314,430)(315,432)(316,431)(317,425)(318,426)(319,428)
(320,427)(321,461)(322,462)(323,464)(324,463)(325,477)(326,478)(327,480)
(328,479)(329,473)(330,474)(331,476)(332,475)(333,469)(334,470)(335,472)
(336,471)(337,465)(338,466)(339,468)(340,467)(341,441)(342,442)(343,444)
(344,443)(345,457)(346,458)(347,460)(348,459)(349,453)(350,454)(351,456)
(352,455)(353,449)(354,450)(355,452)(356,451)(357,445)(358,446)(359,448)
(360,447)(481,601)(482,602)(483,604)(484,603)(485,617)(486,618)(487,620)
(488,619)(489,613)(490,614)(491,616)(492,615)(493,609)(494,610)(495,612)
(496,611)(497,605)(498,606)(499,608)(500,607)(501,641)(502,642)(503,644)
(504,643)(505,657)(506,658)(507,660)(508,659)(509,653)(510,654)(511,656)
(512,655)(513,649)(514,650)(515,652)(516,651)(517,645)(518,646)(519,648)
(520,647)(521,621)(522,622)(523,624)(524,623)(525,637)(526,638)(527,640)
(528,639)(529,633)(530,634)(531,636)(532,635)(533,629)(534,630)(535,632)
(536,631)(537,625)(538,626)(539,628)(540,627)(541,661)(542,662)(543,664)
(544,663)(545,677)(546,678)(547,680)(548,679)(549,673)(550,674)(551,676)
(552,675)(553,669)(554,670)(555,672)(556,671)(557,665)(558,666)(559,668)
(560,667)(561,701)(562,702)(563,704)(564,703)(565,717)(566,718)(567,720)
(568,719)(569,713)(570,714)(571,716)(572,715)(573,709)(574,710)(575,712)
(576,711)(577,705)(578,706)(579,708)(580,707)(581,681)(582,682)(583,684)
(584,683)(585,697)(586,698)(587,700)(588,699)(589,693)(590,694)(591,696)
(592,695)(593,689)(594,690)(595,692)(596,691)(597,685)(598,686)(599,688)
(600,687)(721,841)(722,842)(723,844)(724,843)(725,857)(726,858)(727,860)
(728,859)(729,853)(730,854)(731,856)(732,855)(733,849)(734,850)(735,852)
(736,851)(737,845)(738,846)(739,848)(740,847)(741,881)(742,882)(743,884)
(744,883)(745,897)(746,898)(747,900)(748,899)(749,893)(750,894)(751,896)
(752,895)(753,889)(754,890)(755,892)(756,891)(757,885)(758,886)(759,888)
(760,887)(761,861)(762,862)(763,864)(764,863)(765,877)(766,878)(767,880)
(768,879)(769,873)(770,874)(771,876)(772,875)(773,869)(774,870)(775,872)
(776,871)(777,865)(778,866)(779,868)(780,867)(781,901)(782,902)(783,904)
(784,903)(785,917)(786,918)(787,920)(788,919)(789,913)(790,914)(791,916)
(792,915)(793,909)(794,910)(795,912)(796,911)(797,905)(798,906)(799,908)
(800,907)(801,941)(802,942)(803,944)(804,943)(805,957)(806,958)(807,960)
(808,959)(809,953)(810,954)(811,956)(812,955)(813,949)(814,950)(815,952)
(816,951)(817,945)(818,946)(819,948)(820,947)(821,921)(822,922)(823,924)
(824,923)(825,937)(826,938)(827,940)(828,939)(829,933)(830,934)(831,936)
(832,935)(833,929)(834,930)(835,932)(836,931)(837,925)(838,926)(839,928)
(840,927);
s2 := Sym(960)!(  1, 25)(  2, 28)(  3, 27)(  4, 26)(  5, 21)(  6, 24)(  7, 23)
(  8, 22)(  9, 37)( 10, 40)( 11, 39)( 12, 38)( 13, 33)( 14, 36)( 15, 35)
( 16, 34)( 17, 29)( 18, 32)( 19, 31)( 20, 30)( 41, 45)( 42, 48)( 43, 47)
( 44, 46)( 49, 57)( 50, 60)( 51, 59)( 52, 58)( 54, 56)( 61, 85)( 62, 88)
( 63, 87)( 64, 86)( 65, 81)( 66, 84)( 67, 83)( 68, 82)( 69, 97)( 70,100)
( 71, 99)( 72, 98)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 89)( 78, 92)
( 79, 91)( 80, 90)(101,105)(102,108)(103,107)(104,106)(109,117)(110,120)
(111,119)(112,118)(114,116)(121,145)(122,148)(123,147)(124,146)(125,141)
(126,144)(127,143)(128,142)(129,157)(130,160)(131,159)(132,158)(133,153)
(134,156)(135,155)(136,154)(137,149)(138,152)(139,151)(140,150)(161,165)
(162,168)(163,167)(164,166)(169,177)(170,180)(171,179)(172,178)(174,176)
(181,205)(182,208)(183,207)(184,206)(185,201)(186,204)(187,203)(188,202)
(189,217)(190,220)(191,219)(192,218)(193,213)(194,216)(195,215)(196,214)
(197,209)(198,212)(199,211)(200,210)(221,225)(222,228)(223,227)(224,226)
(229,237)(230,240)(231,239)(232,238)(234,236)(241,265)(242,268)(243,267)
(244,266)(245,261)(246,264)(247,263)(248,262)(249,277)(250,280)(251,279)
(252,278)(253,273)(254,276)(255,275)(256,274)(257,269)(258,272)(259,271)
(260,270)(281,285)(282,288)(283,287)(284,286)(289,297)(290,300)(291,299)
(292,298)(294,296)(301,325)(302,328)(303,327)(304,326)(305,321)(306,324)
(307,323)(308,322)(309,337)(310,340)(311,339)(312,338)(313,333)(314,336)
(315,335)(316,334)(317,329)(318,332)(319,331)(320,330)(341,345)(342,348)
(343,347)(344,346)(349,357)(350,360)(351,359)(352,358)(354,356)(361,385)
(362,388)(363,387)(364,386)(365,381)(366,384)(367,383)(368,382)(369,397)
(370,400)(371,399)(372,398)(373,393)(374,396)(375,395)(376,394)(377,389)
(378,392)(379,391)(380,390)(401,405)(402,408)(403,407)(404,406)(409,417)
(410,420)(411,419)(412,418)(414,416)(421,445)(422,448)(423,447)(424,446)
(425,441)(426,444)(427,443)(428,442)(429,457)(430,460)(431,459)(432,458)
(433,453)(434,456)(435,455)(436,454)(437,449)(438,452)(439,451)(440,450)
(461,465)(462,468)(463,467)(464,466)(469,477)(470,480)(471,479)(472,478)
(474,476)(481,505)(482,508)(483,507)(484,506)(485,501)(486,504)(487,503)
(488,502)(489,517)(490,520)(491,519)(492,518)(493,513)(494,516)(495,515)
(496,514)(497,509)(498,512)(499,511)(500,510)(521,525)(522,528)(523,527)
(524,526)(529,537)(530,540)(531,539)(532,538)(534,536)(541,565)(542,568)
(543,567)(544,566)(545,561)(546,564)(547,563)(548,562)(549,577)(550,580)
(551,579)(552,578)(553,573)(554,576)(555,575)(556,574)(557,569)(558,572)
(559,571)(560,570)(581,585)(582,588)(583,587)(584,586)(589,597)(590,600)
(591,599)(592,598)(594,596)(601,625)(602,628)(603,627)(604,626)(605,621)
(606,624)(607,623)(608,622)(609,637)(610,640)(611,639)(612,638)(613,633)
(614,636)(615,635)(616,634)(617,629)(618,632)(619,631)(620,630)(641,645)
(642,648)(643,647)(644,646)(649,657)(650,660)(651,659)(652,658)(654,656)
(661,685)(662,688)(663,687)(664,686)(665,681)(666,684)(667,683)(668,682)
(669,697)(670,700)(671,699)(672,698)(673,693)(674,696)(675,695)(676,694)
(677,689)(678,692)(679,691)(680,690)(701,705)(702,708)(703,707)(704,706)
(709,717)(710,720)(711,719)(712,718)(714,716)(721,745)(722,748)(723,747)
(724,746)(725,741)(726,744)(727,743)(728,742)(729,757)(730,760)(731,759)
(732,758)(733,753)(734,756)(735,755)(736,754)(737,749)(738,752)(739,751)
(740,750)(761,765)(762,768)(763,767)(764,766)(769,777)(770,780)(771,779)
(772,778)(774,776)(781,805)(782,808)(783,807)(784,806)(785,801)(786,804)
(787,803)(788,802)(789,817)(790,820)(791,819)(792,818)(793,813)(794,816)
(795,815)(796,814)(797,809)(798,812)(799,811)(800,810)(821,825)(822,828)
(823,827)(824,826)(829,837)(830,840)(831,839)(832,838)(834,836)(841,865)
(842,868)(843,867)(844,866)(845,861)(846,864)(847,863)(848,862)(849,877)
(850,880)(851,879)(852,878)(853,873)(854,876)(855,875)(856,874)(857,869)
(858,872)(859,871)(860,870)(881,885)(882,888)(883,887)(884,886)(889,897)
(890,900)(891,899)(892,898)(894,896)(901,925)(902,928)(903,927)(904,926)
(905,921)(906,924)(907,923)(908,922)(909,937)(910,940)(911,939)(912,938)
(913,933)(914,936)(915,935)(916,934)(917,929)(918,932)(919,931)(920,930)
(941,945)(942,948)(943,947)(944,946)(949,957)(950,960)(951,959)(952,958)
(954,956);
s3 := Sym(960)!(  1,482)(  2,481)(  3,484)(  4,483)(  5,486)(  6,485)(  7,488)
(  8,487)(  9,490)( 10,489)( 11,492)( 12,491)( 13,494)( 14,493)( 15,496)
( 16,495)( 17,498)( 18,497)( 19,500)( 20,499)( 21,502)( 22,501)( 23,504)
( 24,503)( 25,506)( 26,505)( 27,508)( 28,507)( 29,510)( 30,509)( 31,512)
( 32,511)( 33,514)( 34,513)( 35,516)( 36,515)( 37,518)( 38,517)( 39,520)
( 40,519)( 41,522)( 42,521)( 43,524)( 44,523)( 45,526)( 46,525)( 47,528)
( 48,527)( 49,530)( 50,529)( 51,532)( 52,531)( 53,534)( 54,533)( 55,536)
( 56,535)( 57,538)( 58,537)( 59,540)( 60,539)( 61,542)( 62,541)( 63,544)
( 64,543)( 65,546)( 66,545)( 67,548)( 68,547)( 69,550)( 70,549)( 71,552)
( 72,551)( 73,554)( 74,553)( 75,556)( 76,555)( 77,558)( 78,557)( 79,560)
( 80,559)( 81,562)( 82,561)( 83,564)( 84,563)( 85,566)( 86,565)( 87,568)
( 88,567)( 89,570)( 90,569)( 91,572)( 92,571)( 93,574)( 94,573)( 95,576)
( 96,575)( 97,578)( 98,577)( 99,580)(100,579)(101,582)(102,581)(103,584)
(104,583)(105,586)(106,585)(107,588)(108,587)(109,590)(110,589)(111,592)
(112,591)(113,594)(114,593)(115,596)(116,595)(117,598)(118,597)(119,600)
(120,599)(121,602)(122,601)(123,604)(124,603)(125,606)(126,605)(127,608)
(128,607)(129,610)(130,609)(131,612)(132,611)(133,614)(134,613)(135,616)
(136,615)(137,618)(138,617)(139,620)(140,619)(141,622)(142,621)(143,624)
(144,623)(145,626)(146,625)(147,628)(148,627)(149,630)(150,629)(151,632)
(152,631)(153,634)(154,633)(155,636)(156,635)(157,638)(158,637)(159,640)
(160,639)(161,642)(162,641)(163,644)(164,643)(165,646)(166,645)(167,648)
(168,647)(169,650)(170,649)(171,652)(172,651)(173,654)(174,653)(175,656)
(176,655)(177,658)(178,657)(179,660)(180,659)(181,662)(182,661)(183,664)
(184,663)(185,666)(186,665)(187,668)(188,667)(189,670)(190,669)(191,672)
(192,671)(193,674)(194,673)(195,676)(196,675)(197,678)(198,677)(199,680)
(200,679)(201,682)(202,681)(203,684)(204,683)(205,686)(206,685)(207,688)
(208,687)(209,690)(210,689)(211,692)(212,691)(213,694)(214,693)(215,696)
(216,695)(217,698)(218,697)(219,700)(220,699)(221,702)(222,701)(223,704)
(224,703)(225,706)(226,705)(227,708)(228,707)(229,710)(230,709)(231,712)
(232,711)(233,714)(234,713)(235,716)(236,715)(237,718)(238,717)(239,720)
(240,719)(241,722)(242,721)(243,724)(244,723)(245,726)(246,725)(247,728)
(248,727)(249,730)(250,729)(251,732)(252,731)(253,734)(254,733)(255,736)
(256,735)(257,738)(258,737)(259,740)(260,739)(261,742)(262,741)(263,744)
(264,743)(265,746)(266,745)(267,748)(268,747)(269,750)(270,749)(271,752)
(272,751)(273,754)(274,753)(275,756)(276,755)(277,758)(278,757)(279,760)
(280,759)(281,762)(282,761)(283,764)(284,763)(285,766)(286,765)(287,768)
(288,767)(289,770)(290,769)(291,772)(292,771)(293,774)(294,773)(295,776)
(296,775)(297,778)(298,777)(299,780)(300,779)(301,782)(302,781)(303,784)
(304,783)(305,786)(306,785)(307,788)(308,787)(309,790)(310,789)(311,792)
(312,791)(313,794)(314,793)(315,796)(316,795)(317,798)(318,797)(319,800)
(320,799)(321,802)(322,801)(323,804)(324,803)(325,806)(326,805)(327,808)
(328,807)(329,810)(330,809)(331,812)(332,811)(333,814)(334,813)(335,816)
(336,815)(337,818)(338,817)(339,820)(340,819)(341,822)(342,821)(343,824)
(344,823)(345,826)(346,825)(347,828)(348,827)(349,830)(350,829)(351,832)
(352,831)(353,834)(354,833)(355,836)(356,835)(357,838)(358,837)(359,840)
(360,839)(361,842)(362,841)(363,844)(364,843)(365,846)(366,845)(367,848)
(368,847)(369,850)(370,849)(371,852)(372,851)(373,854)(374,853)(375,856)
(376,855)(377,858)(378,857)(379,860)(380,859)(381,862)(382,861)(383,864)
(384,863)(385,866)(386,865)(387,868)(388,867)(389,870)(390,869)(391,872)
(392,871)(393,874)(394,873)(395,876)(396,875)(397,878)(398,877)(399,880)
(400,879)(401,882)(402,881)(403,884)(404,883)(405,886)(406,885)(407,888)
(408,887)(409,890)(410,889)(411,892)(412,891)(413,894)(414,893)(415,896)
(416,895)(417,898)(418,897)(419,900)(420,899)(421,902)(422,901)(423,904)
(424,903)(425,906)(426,905)(427,908)(428,907)(429,910)(430,909)(431,912)
(432,911)(433,914)(434,913)(435,916)(436,915)(437,918)(438,917)(439,920)
(440,919)(441,922)(442,921)(443,924)(444,923)(445,926)(446,925)(447,928)
(448,927)(449,930)(450,929)(451,932)(452,931)(453,934)(454,933)(455,936)
(456,935)(457,938)(458,937)(459,940)(460,939)(461,942)(462,941)(463,944)
(464,943)(465,946)(466,945)(467,948)(468,947)(469,950)(470,949)(471,952)
(472,951)(473,954)(474,953)(475,956)(476,955)(477,958)(478,957)(479,960)
(480,959);
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope