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Polytope of Type {10,4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,24}*1920a
Also Known As : {{10,4|2},{4,24|2}}. if this polytope has another name.
Group : SmallGroup(1920,148900)
Rank : 4
Schlafli Type : {10,4,24}
Number of vertices, edges, etc : 10, 20, 48, 24
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 : {10,4,12}*960, {10,2,24}*960
   3-fold quotients : {10,4,8}*640a
   4-fold quotients : {5,2,24}*480, {10,2,12}*480, {10,4,6}*480
   5-fold quotients : {2,4,24}*384a
   6-fold quotients : {10,4,4}*320, {10,2,8}*320
   8-fold quotients : {5,2,12}*240, {10,2,6}*240
   10-fold quotients : {2,4,12}*192a, {2,2,24}*192
   12-fold quotients : {5,2,8}*160, {10,2,4}*160, {10,4,2}*160
   15-fold quotients : {2,4,8}*128a
   16-fold quotients : {5,2,6}*120, {10,2,3}*120
   20-fold quotients : {2,2,12}*96, {2,4,6}*96a
   24-fold quotients : {5,2,4}*80, {10,2,2}*80
   30-fold quotients : {2,4,4}*64, {2,2,8}*64
   32-fold quotients : {5,2,3}*60
   40-fold quotients : {2,2,6}*48
   48-fold quotients : {5,2,2}*40
   60-fold quotients : {2,2,4}*32, {2,4,2}*32
   80-fold quotients : {2,2,3}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,121)(  2,125)(  3,124)(  4,123)(  5,122)(  6,126)(  7,130)(  8,129)
(  9,128)( 10,127)( 11,131)( 12,135)( 13,134)( 14,133)( 15,132)( 16,136)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,141)( 22,145)( 23,144)( 24,143)
( 25,142)( 26,146)( 27,150)( 28,149)( 29,148)( 30,147)( 31,151)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,156)( 37,160)( 38,159)( 39,158)( 40,157)
( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,166)( 47,170)( 48,169)
( 49,168)( 50,167)( 51,171)( 52,175)( 53,174)( 54,173)( 55,172)( 56,176)
( 57,180)( 58,179)( 59,178)( 60,177)( 61,181)( 62,185)( 63,184)( 64,183)
( 65,182)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,191)( 72,195)
( 73,194)( 74,193)( 75,192)( 76,196)( 77,200)( 78,199)( 79,198)( 80,197)
( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,206)( 87,210)( 88,209)
( 89,208)( 90,207)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)( 96,216)
( 97,220)( 98,219)( 99,218)(100,217)(101,221)(102,225)(103,224)(104,223)
(105,222)(106,226)(107,230)(108,229)(109,228)(110,227)(111,231)(112,235)
(113,234)(114,233)(115,232)(116,236)(117,240)(118,239)(119,238)(120,237)
(241,361)(242,365)(243,364)(244,363)(245,362)(246,366)(247,370)(248,369)
(249,368)(250,367)(251,371)(252,375)(253,374)(254,373)(255,372)(256,376)
(257,380)(258,379)(259,378)(260,377)(261,381)(262,385)(263,384)(264,383)
(265,382)(266,386)(267,390)(268,389)(269,388)(270,387)(271,391)(272,395)
(273,394)(274,393)(275,392)(276,396)(277,400)(278,399)(279,398)(280,397)
(281,401)(282,405)(283,404)(284,403)(285,402)(286,406)(287,410)(288,409)
(289,408)(290,407)(291,411)(292,415)(293,414)(294,413)(295,412)(296,416)
(297,420)(298,419)(299,418)(300,417)(301,421)(302,425)(303,424)(304,423)
(305,422)(306,426)(307,430)(308,429)(309,428)(310,427)(311,431)(312,435)
(313,434)(314,433)(315,432)(316,436)(317,440)(318,439)(319,438)(320,437)
(321,441)(322,445)(323,444)(324,443)(325,442)(326,446)(327,450)(328,449)
(329,448)(330,447)(331,451)(332,455)(333,454)(334,453)(335,452)(336,456)
(337,460)(338,459)(339,458)(340,457)(341,461)(342,465)(343,464)(344,463)
(345,462)(346,466)(347,470)(348,469)(349,468)(350,467)(351,471)(352,475)
(353,474)(354,473)(355,472)(356,476)(357,480)(358,479)(359,478)(360,477)
(481,601)(482,605)(483,604)(484,603)(485,602)(486,606)(487,610)(488,609)
(489,608)(490,607)(491,611)(492,615)(493,614)(494,613)(495,612)(496,616)
(497,620)(498,619)(499,618)(500,617)(501,621)(502,625)(503,624)(504,623)
(505,622)(506,626)(507,630)(508,629)(509,628)(510,627)(511,631)(512,635)
(513,634)(514,633)(515,632)(516,636)(517,640)(518,639)(519,638)(520,637)
(521,641)(522,645)(523,644)(524,643)(525,642)(526,646)(527,650)(528,649)
(529,648)(530,647)(531,651)(532,655)(533,654)(534,653)(535,652)(536,656)
(537,660)(538,659)(539,658)(540,657)(541,661)(542,665)(543,664)(544,663)
(545,662)(546,666)(547,670)(548,669)(549,668)(550,667)(551,671)(552,675)
(553,674)(554,673)(555,672)(556,676)(557,680)(558,679)(559,678)(560,677)
(561,681)(562,685)(563,684)(564,683)(565,682)(566,686)(567,690)(568,689)
(569,688)(570,687)(571,691)(572,695)(573,694)(574,693)(575,692)(576,696)
(577,700)(578,699)(579,698)(580,697)(581,701)(582,705)(583,704)(584,703)
(585,702)(586,706)(587,710)(588,709)(589,708)(590,707)(591,711)(592,715)
(593,714)(594,713)(595,712)(596,716)(597,720)(598,719)(599,718)(600,717)
(721,841)(722,845)(723,844)(724,843)(725,842)(726,846)(727,850)(728,849)
(729,848)(730,847)(731,851)(732,855)(733,854)(734,853)(735,852)(736,856)
(737,860)(738,859)(739,858)(740,857)(741,861)(742,865)(743,864)(744,863)
(745,862)(746,866)(747,870)(748,869)(749,868)(750,867)(751,871)(752,875)
(753,874)(754,873)(755,872)(756,876)(757,880)(758,879)(759,878)(760,877)
(761,881)(762,885)(763,884)(764,883)(765,882)(766,886)(767,890)(768,889)
(769,888)(770,887)(771,891)(772,895)(773,894)(774,893)(775,892)(776,896)
(777,900)(778,899)(779,898)(780,897)(781,901)(782,905)(783,904)(784,903)
(785,902)(786,906)(787,910)(788,909)(789,908)(790,907)(791,911)(792,915)
(793,914)(794,913)(795,912)(796,916)(797,920)(798,919)(799,918)(800,917)
(801,921)(802,925)(803,924)(804,923)(805,922)(806,926)(807,930)(808,929)
(809,928)(810,927)(811,931)(812,935)(813,934)(814,933)(815,932)(816,936)
(817,940)(818,939)(819,938)(820,937)(821,941)(822,945)(823,944)(824,943)
(825,942)(826,946)(827,950)(828,949)(829,948)(830,947)(831,951)(832,955)
(833,954)(834,953)(835,952)(836,956)(837,960)(838,959)(839,958)(840,957);;
s1 := (  1,362)(  2,361)(  3,365)(  4,364)(  5,363)(  6,367)(  7,366)(  8,370)
(  9,369)( 10,368)( 11,372)( 12,371)( 13,375)( 14,374)( 15,373)( 16,377)
( 17,376)( 18,380)( 19,379)( 20,378)( 21,382)( 22,381)( 23,385)( 24,384)
( 25,383)( 26,387)( 27,386)( 28,390)( 29,389)( 30,388)( 31,392)( 32,391)
( 33,395)( 34,394)( 35,393)( 36,397)( 37,396)( 38,400)( 39,399)( 40,398)
( 41,402)( 42,401)( 43,405)( 44,404)( 45,403)( 46,407)( 47,406)( 48,410)
( 49,409)( 50,408)( 51,412)( 52,411)( 53,415)( 54,414)( 55,413)( 56,417)
( 57,416)( 58,420)( 59,419)( 60,418)( 61,422)( 62,421)( 63,425)( 64,424)
( 65,423)( 66,427)( 67,426)( 68,430)( 69,429)( 70,428)( 71,432)( 72,431)
( 73,435)( 74,434)( 75,433)( 76,437)( 77,436)( 78,440)( 79,439)( 80,438)
( 81,442)( 82,441)( 83,445)( 84,444)( 85,443)( 86,447)( 87,446)( 88,450)
( 89,449)( 90,448)( 91,452)( 92,451)( 93,455)( 94,454)( 95,453)( 96,457)
( 97,456)( 98,460)( 99,459)(100,458)(101,462)(102,461)(103,465)(104,464)
(105,463)(106,467)(107,466)(108,470)(109,469)(110,468)(111,472)(112,471)
(113,475)(114,474)(115,473)(116,477)(117,476)(118,480)(119,479)(120,478)
(121,242)(122,241)(123,245)(124,244)(125,243)(126,247)(127,246)(128,250)
(129,249)(130,248)(131,252)(132,251)(133,255)(134,254)(135,253)(136,257)
(137,256)(138,260)(139,259)(140,258)(141,262)(142,261)(143,265)(144,264)
(145,263)(146,267)(147,266)(148,270)(149,269)(150,268)(151,272)(152,271)
(153,275)(154,274)(155,273)(156,277)(157,276)(158,280)(159,279)(160,278)
(161,282)(162,281)(163,285)(164,284)(165,283)(166,287)(167,286)(168,290)
(169,289)(170,288)(171,292)(172,291)(173,295)(174,294)(175,293)(176,297)
(177,296)(178,300)(179,299)(180,298)(181,302)(182,301)(183,305)(184,304)
(185,303)(186,307)(187,306)(188,310)(189,309)(190,308)(191,312)(192,311)
(193,315)(194,314)(195,313)(196,317)(197,316)(198,320)(199,319)(200,318)
(201,322)(202,321)(203,325)(204,324)(205,323)(206,327)(207,326)(208,330)
(209,329)(210,328)(211,332)(212,331)(213,335)(214,334)(215,333)(216,337)
(217,336)(218,340)(219,339)(220,338)(221,342)(222,341)(223,345)(224,344)
(225,343)(226,347)(227,346)(228,350)(229,349)(230,348)(231,352)(232,351)
(233,355)(234,354)(235,353)(236,357)(237,356)(238,360)(239,359)(240,358)
(481,842)(482,841)(483,845)(484,844)(485,843)(486,847)(487,846)(488,850)
(489,849)(490,848)(491,852)(492,851)(493,855)(494,854)(495,853)(496,857)
(497,856)(498,860)(499,859)(500,858)(501,862)(502,861)(503,865)(504,864)
(505,863)(506,867)(507,866)(508,870)(509,869)(510,868)(511,872)(512,871)
(513,875)(514,874)(515,873)(516,877)(517,876)(518,880)(519,879)(520,878)
(521,882)(522,881)(523,885)(524,884)(525,883)(526,887)(527,886)(528,890)
(529,889)(530,888)(531,892)(532,891)(533,895)(534,894)(535,893)(536,897)
(537,896)(538,900)(539,899)(540,898)(541,902)(542,901)(543,905)(544,904)
(545,903)(546,907)(547,906)(548,910)(549,909)(550,908)(551,912)(552,911)
(553,915)(554,914)(555,913)(556,917)(557,916)(558,920)(559,919)(560,918)
(561,922)(562,921)(563,925)(564,924)(565,923)(566,927)(567,926)(568,930)
(569,929)(570,928)(571,932)(572,931)(573,935)(574,934)(575,933)(576,937)
(577,936)(578,940)(579,939)(580,938)(581,942)(582,941)(583,945)(584,944)
(585,943)(586,947)(587,946)(588,950)(589,949)(590,948)(591,952)(592,951)
(593,955)(594,954)(595,953)(596,957)(597,956)(598,960)(599,959)(600,958)
(601,722)(602,721)(603,725)(604,724)(605,723)(606,727)(607,726)(608,730)
(609,729)(610,728)(611,732)(612,731)(613,735)(614,734)(615,733)(616,737)
(617,736)(618,740)(619,739)(620,738)(621,742)(622,741)(623,745)(624,744)
(625,743)(626,747)(627,746)(628,750)(629,749)(630,748)(631,752)(632,751)
(633,755)(634,754)(635,753)(636,757)(637,756)(638,760)(639,759)(640,758)
(641,762)(642,761)(643,765)(644,764)(645,763)(646,767)(647,766)(648,770)
(649,769)(650,768)(651,772)(652,771)(653,775)(654,774)(655,773)(656,777)
(657,776)(658,780)(659,779)(660,778)(661,782)(662,781)(663,785)(664,784)
(665,783)(666,787)(667,786)(668,790)(669,789)(670,788)(671,792)(672,791)
(673,795)(674,794)(675,793)(676,797)(677,796)(678,800)(679,799)(680,798)
(681,802)(682,801)(683,805)(684,804)(685,803)(686,807)(687,806)(688,810)
(689,809)(690,808)(691,812)(692,811)(693,815)(694,814)(695,813)(696,817)
(697,816)(698,820)(699,819)(700,818)(701,822)(702,821)(703,825)(704,824)
(705,823)(706,827)(707,826)(708,830)(709,829)(710,828)(711,832)(712,831)
(713,835)(714,834)(715,833)(716,837)(717,836)(718,840)(719,839)(720,838);;
s2 := (  6, 11)(  7, 12)(  8, 13)(  9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)
( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)
( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61, 76)( 62, 77)( 63, 78)( 64, 79)
( 65, 80)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)( 71, 81)( 72, 82)
( 73, 83)( 74, 84)( 75, 85)( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)
( 96,116)( 97,117)( 98,118)( 99,119)(100,120)(101,111)(102,112)(103,113)
(104,114)(105,115)(126,131)(127,132)(128,133)(129,134)(130,135)(141,146)
(142,147)(143,148)(144,149)(145,150)(156,161)(157,162)(158,163)(159,164)
(160,165)(171,176)(172,177)(173,178)(174,179)(175,180)(181,196)(182,197)
(183,198)(184,199)(185,200)(186,206)(187,207)(188,208)(189,209)(190,210)
(191,201)(192,202)(193,203)(194,204)(195,205)(211,226)(212,227)(213,228)
(214,229)(215,230)(216,236)(217,237)(218,238)(219,239)(220,240)(221,231)
(222,232)(223,233)(224,234)(225,235)(241,271)(242,272)(243,273)(244,274)
(245,275)(246,281)(247,282)(248,283)(249,284)(250,285)(251,276)(252,277)
(253,278)(254,279)(255,280)(256,286)(257,287)(258,288)(259,289)(260,290)
(261,296)(262,297)(263,298)(264,299)(265,300)(266,291)(267,292)(268,293)
(269,294)(270,295)(301,346)(302,347)(303,348)(304,349)(305,350)(306,356)
(307,357)(308,358)(309,359)(310,360)(311,351)(312,352)(313,353)(314,354)
(315,355)(316,331)(317,332)(318,333)(319,334)(320,335)(321,341)(322,342)
(323,343)(324,344)(325,345)(326,336)(327,337)(328,338)(329,339)(330,340)
(361,391)(362,392)(363,393)(364,394)(365,395)(366,401)(367,402)(368,403)
(369,404)(370,405)(371,396)(372,397)(373,398)(374,399)(375,400)(376,406)
(377,407)(378,408)(379,409)(380,410)(381,416)(382,417)(383,418)(384,419)
(385,420)(386,411)(387,412)(388,413)(389,414)(390,415)(421,466)(422,467)
(423,468)(424,469)(425,470)(426,476)(427,477)(428,478)(429,479)(430,480)
(431,471)(432,472)(433,473)(434,474)(435,475)(436,451)(437,452)(438,453)
(439,454)(440,455)(441,461)(442,462)(443,463)(444,464)(445,465)(446,456)
(447,457)(448,458)(449,459)(450,460)(481,541)(482,542)(483,543)(484,544)
(485,545)(486,551)(487,552)(488,553)(489,554)(490,555)(491,546)(492,547)
(493,548)(494,549)(495,550)(496,556)(497,557)(498,558)(499,559)(500,560)
(501,566)(502,567)(503,568)(504,569)(505,570)(506,561)(507,562)(508,563)
(509,564)(510,565)(511,571)(512,572)(513,573)(514,574)(515,575)(516,581)
(517,582)(518,583)(519,584)(520,585)(521,576)(522,577)(523,578)(524,579)
(525,580)(526,586)(527,587)(528,588)(529,589)(530,590)(531,596)(532,597)
(533,598)(534,599)(535,600)(536,591)(537,592)(538,593)(539,594)(540,595)
(601,661)(602,662)(603,663)(604,664)(605,665)(606,671)(607,672)(608,673)
(609,674)(610,675)(611,666)(612,667)(613,668)(614,669)(615,670)(616,676)
(617,677)(618,678)(619,679)(620,680)(621,686)(622,687)(623,688)(624,689)
(625,690)(626,681)(627,682)(628,683)(629,684)(630,685)(631,691)(632,692)
(633,693)(634,694)(635,695)(636,701)(637,702)(638,703)(639,704)(640,705)
(641,696)(642,697)(643,698)(644,699)(645,700)(646,706)(647,707)(648,708)
(649,709)(650,710)(651,716)(652,717)(653,718)(654,719)(655,720)(656,711)
(657,712)(658,713)(659,714)(660,715)(721,811)(722,812)(723,813)(724,814)
(725,815)(726,821)(727,822)(728,823)(729,824)(730,825)(731,816)(732,817)
(733,818)(734,819)(735,820)(736,826)(737,827)(738,828)(739,829)(740,830)
(741,836)(742,837)(743,838)(744,839)(745,840)(746,831)(747,832)(748,833)
(749,834)(750,835)(751,781)(752,782)(753,783)(754,784)(755,785)(756,791)
(757,792)(758,793)(759,794)(760,795)(761,786)(762,787)(763,788)(764,789)
(765,790)(766,796)(767,797)(768,798)(769,799)(770,800)(771,806)(772,807)
(773,808)(774,809)(775,810)(776,801)(777,802)(778,803)(779,804)(780,805)
(841,931)(842,932)(843,933)(844,934)(845,935)(846,941)(847,942)(848,943)
(849,944)(850,945)(851,936)(852,937)(853,938)(854,939)(855,940)(856,946)
(857,947)(858,948)(859,949)(860,950)(861,956)(862,957)(863,958)(864,959)
(865,960)(866,951)(867,952)(868,953)(869,954)(870,955)(871,901)(872,902)
(873,903)(874,904)(875,905)(876,911)(877,912)(878,913)(879,914)(880,915)
(881,906)(882,907)(883,908)(884,909)(885,910)(886,916)(887,917)(888,918)
(889,919)(890,920)(891,926)(892,927)(893,928)(894,929)(895,930)(896,921)
(897,922)(898,923)(899,924)(900,925);;
s3 := (  1,486)(  2,487)(  3,488)(  4,489)(  5,490)(  6,481)(  7,482)(  8,483)
(  9,484)( 10,485)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,501)
( 17,502)( 18,503)( 19,504)( 20,505)( 21,496)( 22,497)( 23,498)( 24,499)
( 25,500)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,516)( 32,517)
( 33,518)( 34,519)( 35,520)( 36,511)( 37,512)( 38,513)( 39,514)( 40,515)
( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,531)( 47,532)( 48,533)
( 49,534)( 50,535)( 51,526)( 52,527)( 53,528)( 54,529)( 55,530)( 56,536)
( 57,537)( 58,538)( 59,539)( 60,540)( 61,561)( 62,562)( 63,563)( 64,564)
( 65,565)( 66,556)( 67,557)( 68,558)( 69,559)( 70,560)( 71,566)( 72,567)
( 73,568)( 74,569)( 75,570)( 76,546)( 77,547)( 78,548)( 79,549)( 80,550)
( 81,541)( 82,542)( 83,543)( 84,544)( 85,545)( 86,551)( 87,552)( 88,553)
( 89,554)( 90,555)( 91,591)( 92,592)( 93,593)( 94,594)( 95,595)( 96,586)
( 97,587)( 98,588)( 99,589)(100,590)(101,596)(102,597)(103,598)(104,599)
(105,600)(106,576)(107,577)(108,578)(109,579)(110,580)(111,571)(112,572)
(113,573)(114,574)(115,575)(116,581)(117,582)(118,583)(119,584)(120,585)
(121,606)(122,607)(123,608)(124,609)(125,610)(126,601)(127,602)(128,603)
(129,604)(130,605)(131,611)(132,612)(133,613)(134,614)(135,615)(136,621)
(137,622)(138,623)(139,624)(140,625)(141,616)(142,617)(143,618)(144,619)
(145,620)(146,626)(147,627)(148,628)(149,629)(150,630)(151,636)(152,637)
(153,638)(154,639)(155,640)(156,631)(157,632)(158,633)(159,634)(160,635)
(161,641)(162,642)(163,643)(164,644)(165,645)(166,651)(167,652)(168,653)
(169,654)(170,655)(171,646)(172,647)(173,648)(174,649)(175,650)(176,656)
(177,657)(178,658)(179,659)(180,660)(181,681)(182,682)(183,683)(184,684)
(185,685)(186,676)(187,677)(188,678)(189,679)(190,680)(191,686)(192,687)
(193,688)(194,689)(195,690)(196,666)(197,667)(198,668)(199,669)(200,670)
(201,661)(202,662)(203,663)(204,664)(205,665)(206,671)(207,672)(208,673)
(209,674)(210,675)(211,711)(212,712)(213,713)(214,714)(215,715)(216,706)
(217,707)(218,708)(219,709)(220,710)(221,716)(222,717)(223,718)(224,719)
(225,720)(226,696)(227,697)(228,698)(229,699)(230,700)(231,691)(232,692)
(233,693)(234,694)(235,695)(236,701)(237,702)(238,703)(239,704)(240,705)
(241,726)(242,727)(243,728)(244,729)(245,730)(246,721)(247,722)(248,723)
(249,724)(250,725)(251,731)(252,732)(253,733)(254,734)(255,735)(256,741)
(257,742)(258,743)(259,744)(260,745)(261,736)(262,737)(263,738)(264,739)
(265,740)(266,746)(267,747)(268,748)(269,749)(270,750)(271,756)(272,757)
(273,758)(274,759)(275,760)(276,751)(277,752)(278,753)(279,754)(280,755)
(281,761)(282,762)(283,763)(284,764)(285,765)(286,771)(287,772)(288,773)
(289,774)(290,775)(291,766)(292,767)(293,768)(294,769)(295,770)(296,776)
(297,777)(298,778)(299,779)(300,780)(301,801)(302,802)(303,803)(304,804)
(305,805)(306,796)(307,797)(308,798)(309,799)(310,800)(311,806)(312,807)
(313,808)(314,809)(315,810)(316,786)(317,787)(318,788)(319,789)(320,790)
(321,781)(322,782)(323,783)(324,784)(325,785)(326,791)(327,792)(328,793)
(329,794)(330,795)(331,831)(332,832)(333,833)(334,834)(335,835)(336,826)
(337,827)(338,828)(339,829)(340,830)(341,836)(342,837)(343,838)(344,839)
(345,840)(346,816)(347,817)(348,818)(349,819)(350,820)(351,811)(352,812)
(353,813)(354,814)(355,815)(356,821)(357,822)(358,823)(359,824)(360,825)
(361,846)(362,847)(363,848)(364,849)(365,850)(366,841)(367,842)(368,843)
(369,844)(370,845)(371,851)(372,852)(373,853)(374,854)(375,855)(376,861)
(377,862)(378,863)(379,864)(380,865)(381,856)(382,857)(383,858)(384,859)
(385,860)(386,866)(387,867)(388,868)(389,869)(390,870)(391,876)(392,877)
(393,878)(394,879)(395,880)(396,871)(397,872)(398,873)(399,874)(400,875)
(401,881)(402,882)(403,883)(404,884)(405,885)(406,891)(407,892)(408,893)
(409,894)(410,895)(411,886)(412,887)(413,888)(414,889)(415,890)(416,896)
(417,897)(418,898)(419,899)(420,900)(421,921)(422,922)(423,923)(424,924)
(425,925)(426,916)(427,917)(428,918)(429,919)(430,920)(431,926)(432,927)
(433,928)(434,929)(435,930)(436,906)(437,907)(438,908)(439,909)(440,910)
(441,901)(442,902)(443,903)(444,904)(445,905)(446,911)(447,912)(448,913)
(449,914)(450,915)(451,951)(452,952)(453,953)(454,954)(455,955)(456,946)
(457,947)(458,948)(459,949)(460,950)(461,956)(462,957)(463,958)(464,959)
(465,960)(466,936)(467,937)(468,938)(469,939)(470,940)(471,931)(472,932)
(473,933)(474,934)(475,935)(476,941)(477,942)(478,943)(479,944)(480,945);;
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*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(960)!(  1,121)(  2,125)(  3,124)(  4,123)(  5,122)(  6,126)(  7,130)
(  8,129)(  9,128)( 10,127)( 11,131)( 12,135)( 13,134)( 14,133)( 15,132)
( 16,136)( 17,140)( 18,139)( 19,138)( 20,137)( 21,141)( 22,145)( 23,144)
( 24,143)( 25,142)( 26,146)( 27,150)( 28,149)( 29,148)( 30,147)( 31,151)
( 32,155)( 33,154)( 34,153)( 35,152)( 36,156)( 37,160)( 38,159)( 39,158)
( 40,157)( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,166)( 47,170)
( 48,169)( 49,168)( 50,167)( 51,171)( 52,175)( 53,174)( 54,173)( 55,172)
( 56,176)( 57,180)( 58,179)( 59,178)( 60,177)( 61,181)( 62,185)( 63,184)
( 64,183)( 65,182)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,191)
( 72,195)( 73,194)( 74,193)( 75,192)( 76,196)( 77,200)( 78,199)( 79,198)
( 80,197)( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,206)( 87,210)
( 88,209)( 89,208)( 90,207)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)
( 96,216)( 97,220)( 98,219)( 99,218)(100,217)(101,221)(102,225)(103,224)
(104,223)(105,222)(106,226)(107,230)(108,229)(109,228)(110,227)(111,231)
(112,235)(113,234)(114,233)(115,232)(116,236)(117,240)(118,239)(119,238)
(120,237)(241,361)(242,365)(243,364)(244,363)(245,362)(246,366)(247,370)
(248,369)(249,368)(250,367)(251,371)(252,375)(253,374)(254,373)(255,372)
(256,376)(257,380)(258,379)(259,378)(260,377)(261,381)(262,385)(263,384)
(264,383)(265,382)(266,386)(267,390)(268,389)(269,388)(270,387)(271,391)
(272,395)(273,394)(274,393)(275,392)(276,396)(277,400)(278,399)(279,398)
(280,397)(281,401)(282,405)(283,404)(284,403)(285,402)(286,406)(287,410)
(288,409)(289,408)(290,407)(291,411)(292,415)(293,414)(294,413)(295,412)
(296,416)(297,420)(298,419)(299,418)(300,417)(301,421)(302,425)(303,424)
(304,423)(305,422)(306,426)(307,430)(308,429)(309,428)(310,427)(311,431)
(312,435)(313,434)(314,433)(315,432)(316,436)(317,440)(318,439)(319,438)
(320,437)(321,441)(322,445)(323,444)(324,443)(325,442)(326,446)(327,450)
(328,449)(329,448)(330,447)(331,451)(332,455)(333,454)(334,453)(335,452)
(336,456)(337,460)(338,459)(339,458)(340,457)(341,461)(342,465)(343,464)
(344,463)(345,462)(346,466)(347,470)(348,469)(349,468)(350,467)(351,471)
(352,475)(353,474)(354,473)(355,472)(356,476)(357,480)(358,479)(359,478)
(360,477)(481,601)(482,605)(483,604)(484,603)(485,602)(486,606)(487,610)
(488,609)(489,608)(490,607)(491,611)(492,615)(493,614)(494,613)(495,612)
(496,616)(497,620)(498,619)(499,618)(500,617)(501,621)(502,625)(503,624)
(504,623)(505,622)(506,626)(507,630)(508,629)(509,628)(510,627)(511,631)
(512,635)(513,634)(514,633)(515,632)(516,636)(517,640)(518,639)(519,638)
(520,637)(521,641)(522,645)(523,644)(524,643)(525,642)(526,646)(527,650)
(528,649)(529,648)(530,647)(531,651)(532,655)(533,654)(534,653)(535,652)
(536,656)(537,660)(538,659)(539,658)(540,657)(541,661)(542,665)(543,664)
(544,663)(545,662)(546,666)(547,670)(548,669)(549,668)(550,667)(551,671)
(552,675)(553,674)(554,673)(555,672)(556,676)(557,680)(558,679)(559,678)
(560,677)(561,681)(562,685)(563,684)(564,683)(565,682)(566,686)(567,690)
(568,689)(569,688)(570,687)(571,691)(572,695)(573,694)(574,693)(575,692)
(576,696)(577,700)(578,699)(579,698)(580,697)(581,701)(582,705)(583,704)
(584,703)(585,702)(586,706)(587,710)(588,709)(589,708)(590,707)(591,711)
(592,715)(593,714)(594,713)(595,712)(596,716)(597,720)(598,719)(599,718)
(600,717)(721,841)(722,845)(723,844)(724,843)(725,842)(726,846)(727,850)
(728,849)(729,848)(730,847)(731,851)(732,855)(733,854)(734,853)(735,852)
(736,856)(737,860)(738,859)(739,858)(740,857)(741,861)(742,865)(743,864)
(744,863)(745,862)(746,866)(747,870)(748,869)(749,868)(750,867)(751,871)
(752,875)(753,874)(754,873)(755,872)(756,876)(757,880)(758,879)(759,878)
(760,877)(761,881)(762,885)(763,884)(764,883)(765,882)(766,886)(767,890)
(768,889)(769,888)(770,887)(771,891)(772,895)(773,894)(774,893)(775,892)
(776,896)(777,900)(778,899)(779,898)(780,897)(781,901)(782,905)(783,904)
(784,903)(785,902)(786,906)(787,910)(788,909)(789,908)(790,907)(791,911)
(792,915)(793,914)(794,913)(795,912)(796,916)(797,920)(798,919)(799,918)
(800,917)(801,921)(802,925)(803,924)(804,923)(805,922)(806,926)(807,930)
(808,929)(809,928)(810,927)(811,931)(812,935)(813,934)(814,933)(815,932)
(816,936)(817,940)(818,939)(819,938)(820,937)(821,941)(822,945)(823,944)
(824,943)(825,942)(826,946)(827,950)(828,949)(829,948)(830,947)(831,951)
(832,955)(833,954)(834,953)(835,952)(836,956)(837,960)(838,959)(839,958)
(840,957);
s1 := Sym(960)!(  1,362)(  2,361)(  3,365)(  4,364)(  5,363)(  6,367)(  7,366)
(  8,370)(  9,369)( 10,368)( 11,372)( 12,371)( 13,375)( 14,374)( 15,373)
( 16,377)( 17,376)( 18,380)( 19,379)( 20,378)( 21,382)( 22,381)( 23,385)
( 24,384)( 25,383)( 26,387)( 27,386)( 28,390)( 29,389)( 30,388)( 31,392)
( 32,391)( 33,395)( 34,394)( 35,393)( 36,397)( 37,396)( 38,400)( 39,399)
( 40,398)( 41,402)( 42,401)( 43,405)( 44,404)( 45,403)( 46,407)( 47,406)
( 48,410)( 49,409)( 50,408)( 51,412)( 52,411)( 53,415)( 54,414)( 55,413)
( 56,417)( 57,416)( 58,420)( 59,419)( 60,418)( 61,422)( 62,421)( 63,425)
( 64,424)( 65,423)( 66,427)( 67,426)( 68,430)( 69,429)( 70,428)( 71,432)
( 72,431)( 73,435)( 74,434)( 75,433)( 76,437)( 77,436)( 78,440)( 79,439)
( 80,438)( 81,442)( 82,441)( 83,445)( 84,444)( 85,443)( 86,447)( 87,446)
( 88,450)( 89,449)( 90,448)( 91,452)( 92,451)( 93,455)( 94,454)( 95,453)
( 96,457)( 97,456)( 98,460)( 99,459)(100,458)(101,462)(102,461)(103,465)
(104,464)(105,463)(106,467)(107,466)(108,470)(109,469)(110,468)(111,472)
(112,471)(113,475)(114,474)(115,473)(116,477)(117,476)(118,480)(119,479)
(120,478)(121,242)(122,241)(123,245)(124,244)(125,243)(126,247)(127,246)
(128,250)(129,249)(130,248)(131,252)(132,251)(133,255)(134,254)(135,253)
(136,257)(137,256)(138,260)(139,259)(140,258)(141,262)(142,261)(143,265)
(144,264)(145,263)(146,267)(147,266)(148,270)(149,269)(150,268)(151,272)
(152,271)(153,275)(154,274)(155,273)(156,277)(157,276)(158,280)(159,279)
(160,278)(161,282)(162,281)(163,285)(164,284)(165,283)(166,287)(167,286)
(168,290)(169,289)(170,288)(171,292)(172,291)(173,295)(174,294)(175,293)
(176,297)(177,296)(178,300)(179,299)(180,298)(181,302)(182,301)(183,305)
(184,304)(185,303)(186,307)(187,306)(188,310)(189,309)(190,308)(191,312)
(192,311)(193,315)(194,314)(195,313)(196,317)(197,316)(198,320)(199,319)
(200,318)(201,322)(202,321)(203,325)(204,324)(205,323)(206,327)(207,326)
(208,330)(209,329)(210,328)(211,332)(212,331)(213,335)(214,334)(215,333)
(216,337)(217,336)(218,340)(219,339)(220,338)(221,342)(222,341)(223,345)
(224,344)(225,343)(226,347)(227,346)(228,350)(229,349)(230,348)(231,352)
(232,351)(233,355)(234,354)(235,353)(236,357)(237,356)(238,360)(239,359)
(240,358)(481,842)(482,841)(483,845)(484,844)(485,843)(486,847)(487,846)
(488,850)(489,849)(490,848)(491,852)(492,851)(493,855)(494,854)(495,853)
(496,857)(497,856)(498,860)(499,859)(500,858)(501,862)(502,861)(503,865)
(504,864)(505,863)(506,867)(507,866)(508,870)(509,869)(510,868)(511,872)
(512,871)(513,875)(514,874)(515,873)(516,877)(517,876)(518,880)(519,879)
(520,878)(521,882)(522,881)(523,885)(524,884)(525,883)(526,887)(527,886)
(528,890)(529,889)(530,888)(531,892)(532,891)(533,895)(534,894)(535,893)
(536,897)(537,896)(538,900)(539,899)(540,898)(541,902)(542,901)(543,905)
(544,904)(545,903)(546,907)(547,906)(548,910)(549,909)(550,908)(551,912)
(552,911)(553,915)(554,914)(555,913)(556,917)(557,916)(558,920)(559,919)
(560,918)(561,922)(562,921)(563,925)(564,924)(565,923)(566,927)(567,926)
(568,930)(569,929)(570,928)(571,932)(572,931)(573,935)(574,934)(575,933)
(576,937)(577,936)(578,940)(579,939)(580,938)(581,942)(582,941)(583,945)
(584,944)(585,943)(586,947)(587,946)(588,950)(589,949)(590,948)(591,952)
(592,951)(593,955)(594,954)(595,953)(596,957)(597,956)(598,960)(599,959)
(600,958)(601,722)(602,721)(603,725)(604,724)(605,723)(606,727)(607,726)
(608,730)(609,729)(610,728)(611,732)(612,731)(613,735)(614,734)(615,733)
(616,737)(617,736)(618,740)(619,739)(620,738)(621,742)(622,741)(623,745)
(624,744)(625,743)(626,747)(627,746)(628,750)(629,749)(630,748)(631,752)
(632,751)(633,755)(634,754)(635,753)(636,757)(637,756)(638,760)(639,759)
(640,758)(641,762)(642,761)(643,765)(644,764)(645,763)(646,767)(647,766)
(648,770)(649,769)(650,768)(651,772)(652,771)(653,775)(654,774)(655,773)
(656,777)(657,776)(658,780)(659,779)(660,778)(661,782)(662,781)(663,785)
(664,784)(665,783)(666,787)(667,786)(668,790)(669,789)(670,788)(671,792)
(672,791)(673,795)(674,794)(675,793)(676,797)(677,796)(678,800)(679,799)
(680,798)(681,802)(682,801)(683,805)(684,804)(685,803)(686,807)(687,806)
(688,810)(689,809)(690,808)(691,812)(692,811)(693,815)(694,814)(695,813)
(696,817)(697,816)(698,820)(699,819)(700,818)(701,822)(702,821)(703,825)
(704,824)(705,823)(706,827)(707,826)(708,830)(709,829)(710,828)(711,832)
(712,831)(713,835)(714,834)(715,833)(716,837)(717,836)(718,840)(719,839)
(720,838);
s2 := Sym(960)!(  6, 11)(  7, 12)(  8, 13)(  9, 14)( 10, 15)( 21, 26)( 22, 27)
( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)
( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 61, 76)( 62, 77)( 63, 78)
( 64, 79)( 65, 80)( 66, 86)( 67, 87)( 68, 88)( 69, 89)( 70, 90)( 71, 81)
( 72, 82)( 73, 83)( 74, 84)( 75, 85)( 91,106)( 92,107)( 93,108)( 94,109)
( 95,110)( 96,116)( 97,117)( 98,118)( 99,119)(100,120)(101,111)(102,112)
(103,113)(104,114)(105,115)(126,131)(127,132)(128,133)(129,134)(130,135)
(141,146)(142,147)(143,148)(144,149)(145,150)(156,161)(157,162)(158,163)
(159,164)(160,165)(171,176)(172,177)(173,178)(174,179)(175,180)(181,196)
(182,197)(183,198)(184,199)(185,200)(186,206)(187,207)(188,208)(189,209)
(190,210)(191,201)(192,202)(193,203)(194,204)(195,205)(211,226)(212,227)
(213,228)(214,229)(215,230)(216,236)(217,237)(218,238)(219,239)(220,240)
(221,231)(222,232)(223,233)(224,234)(225,235)(241,271)(242,272)(243,273)
(244,274)(245,275)(246,281)(247,282)(248,283)(249,284)(250,285)(251,276)
(252,277)(253,278)(254,279)(255,280)(256,286)(257,287)(258,288)(259,289)
(260,290)(261,296)(262,297)(263,298)(264,299)(265,300)(266,291)(267,292)
(268,293)(269,294)(270,295)(301,346)(302,347)(303,348)(304,349)(305,350)
(306,356)(307,357)(308,358)(309,359)(310,360)(311,351)(312,352)(313,353)
(314,354)(315,355)(316,331)(317,332)(318,333)(319,334)(320,335)(321,341)
(322,342)(323,343)(324,344)(325,345)(326,336)(327,337)(328,338)(329,339)
(330,340)(361,391)(362,392)(363,393)(364,394)(365,395)(366,401)(367,402)
(368,403)(369,404)(370,405)(371,396)(372,397)(373,398)(374,399)(375,400)
(376,406)(377,407)(378,408)(379,409)(380,410)(381,416)(382,417)(383,418)
(384,419)(385,420)(386,411)(387,412)(388,413)(389,414)(390,415)(421,466)
(422,467)(423,468)(424,469)(425,470)(426,476)(427,477)(428,478)(429,479)
(430,480)(431,471)(432,472)(433,473)(434,474)(435,475)(436,451)(437,452)
(438,453)(439,454)(440,455)(441,461)(442,462)(443,463)(444,464)(445,465)
(446,456)(447,457)(448,458)(449,459)(450,460)(481,541)(482,542)(483,543)
(484,544)(485,545)(486,551)(487,552)(488,553)(489,554)(490,555)(491,546)
(492,547)(493,548)(494,549)(495,550)(496,556)(497,557)(498,558)(499,559)
(500,560)(501,566)(502,567)(503,568)(504,569)(505,570)(506,561)(507,562)
(508,563)(509,564)(510,565)(511,571)(512,572)(513,573)(514,574)(515,575)
(516,581)(517,582)(518,583)(519,584)(520,585)(521,576)(522,577)(523,578)
(524,579)(525,580)(526,586)(527,587)(528,588)(529,589)(530,590)(531,596)
(532,597)(533,598)(534,599)(535,600)(536,591)(537,592)(538,593)(539,594)
(540,595)(601,661)(602,662)(603,663)(604,664)(605,665)(606,671)(607,672)
(608,673)(609,674)(610,675)(611,666)(612,667)(613,668)(614,669)(615,670)
(616,676)(617,677)(618,678)(619,679)(620,680)(621,686)(622,687)(623,688)
(624,689)(625,690)(626,681)(627,682)(628,683)(629,684)(630,685)(631,691)
(632,692)(633,693)(634,694)(635,695)(636,701)(637,702)(638,703)(639,704)
(640,705)(641,696)(642,697)(643,698)(644,699)(645,700)(646,706)(647,707)
(648,708)(649,709)(650,710)(651,716)(652,717)(653,718)(654,719)(655,720)
(656,711)(657,712)(658,713)(659,714)(660,715)(721,811)(722,812)(723,813)
(724,814)(725,815)(726,821)(727,822)(728,823)(729,824)(730,825)(731,816)
(732,817)(733,818)(734,819)(735,820)(736,826)(737,827)(738,828)(739,829)
(740,830)(741,836)(742,837)(743,838)(744,839)(745,840)(746,831)(747,832)
(748,833)(749,834)(750,835)(751,781)(752,782)(753,783)(754,784)(755,785)
(756,791)(757,792)(758,793)(759,794)(760,795)(761,786)(762,787)(763,788)
(764,789)(765,790)(766,796)(767,797)(768,798)(769,799)(770,800)(771,806)
(772,807)(773,808)(774,809)(775,810)(776,801)(777,802)(778,803)(779,804)
(780,805)(841,931)(842,932)(843,933)(844,934)(845,935)(846,941)(847,942)
(848,943)(849,944)(850,945)(851,936)(852,937)(853,938)(854,939)(855,940)
(856,946)(857,947)(858,948)(859,949)(860,950)(861,956)(862,957)(863,958)
(864,959)(865,960)(866,951)(867,952)(868,953)(869,954)(870,955)(871,901)
(872,902)(873,903)(874,904)(875,905)(876,911)(877,912)(878,913)(879,914)
(880,915)(881,906)(882,907)(883,908)(884,909)(885,910)(886,916)(887,917)
(888,918)(889,919)(890,920)(891,926)(892,927)(893,928)(894,929)(895,930)
(896,921)(897,922)(898,923)(899,924)(900,925);
s3 := Sym(960)!(  1,486)(  2,487)(  3,488)(  4,489)(  5,490)(  6,481)(  7,482)
(  8,483)(  9,484)( 10,485)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)
( 16,501)( 17,502)( 18,503)( 19,504)( 20,505)( 21,496)( 22,497)( 23,498)
( 24,499)( 25,500)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,516)
( 32,517)( 33,518)( 34,519)( 35,520)( 36,511)( 37,512)( 38,513)( 39,514)
( 40,515)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,531)( 47,532)
( 48,533)( 49,534)( 50,535)( 51,526)( 52,527)( 53,528)( 54,529)( 55,530)
( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 61,561)( 62,562)( 63,563)
( 64,564)( 65,565)( 66,556)( 67,557)( 68,558)( 69,559)( 70,560)( 71,566)
( 72,567)( 73,568)( 74,569)( 75,570)( 76,546)( 77,547)( 78,548)( 79,549)
( 80,550)( 81,541)( 82,542)( 83,543)( 84,544)( 85,545)( 86,551)( 87,552)
( 88,553)( 89,554)( 90,555)( 91,591)( 92,592)( 93,593)( 94,594)( 95,595)
( 96,586)( 97,587)( 98,588)( 99,589)(100,590)(101,596)(102,597)(103,598)
(104,599)(105,600)(106,576)(107,577)(108,578)(109,579)(110,580)(111,571)
(112,572)(113,573)(114,574)(115,575)(116,581)(117,582)(118,583)(119,584)
(120,585)(121,606)(122,607)(123,608)(124,609)(125,610)(126,601)(127,602)
(128,603)(129,604)(130,605)(131,611)(132,612)(133,613)(134,614)(135,615)
(136,621)(137,622)(138,623)(139,624)(140,625)(141,616)(142,617)(143,618)
(144,619)(145,620)(146,626)(147,627)(148,628)(149,629)(150,630)(151,636)
(152,637)(153,638)(154,639)(155,640)(156,631)(157,632)(158,633)(159,634)
(160,635)(161,641)(162,642)(163,643)(164,644)(165,645)(166,651)(167,652)
(168,653)(169,654)(170,655)(171,646)(172,647)(173,648)(174,649)(175,650)
(176,656)(177,657)(178,658)(179,659)(180,660)(181,681)(182,682)(183,683)
(184,684)(185,685)(186,676)(187,677)(188,678)(189,679)(190,680)(191,686)
(192,687)(193,688)(194,689)(195,690)(196,666)(197,667)(198,668)(199,669)
(200,670)(201,661)(202,662)(203,663)(204,664)(205,665)(206,671)(207,672)
(208,673)(209,674)(210,675)(211,711)(212,712)(213,713)(214,714)(215,715)
(216,706)(217,707)(218,708)(219,709)(220,710)(221,716)(222,717)(223,718)
(224,719)(225,720)(226,696)(227,697)(228,698)(229,699)(230,700)(231,691)
(232,692)(233,693)(234,694)(235,695)(236,701)(237,702)(238,703)(239,704)
(240,705)(241,726)(242,727)(243,728)(244,729)(245,730)(246,721)(247,722)
(248,723)(249,724)(250,725)(251,731)(252,732)(253,733)(254,734)(255,735)
(256,741)(257,742)(258,743)(259,744)(260,745)(261,736)(262,737)(263,738)
(264,739)(265,740)(266,746)(267,747)(268,748)(269,749)(270,750)(271,756)
(272,757)(273,758)(274,759)(275,760)(276,751)(277,752)(278,753)(279,754)
(280,755)(281,761)(282,762)(283,763)(284,764)(285,765)(286,771)(287,772)
(288,773)(289,774)(290,775)(291,766)(292,767)(293,768)(294,769)(295,770)
(296,776)(297,777)(298,778)(299,779)(300,780)(301,801)(302,802)(303,803)
(304,804)(305,805)(306,796)(307,797)(308,798)(309,799)(310,800)(311,806)
(312,807)(313,808)(314,809)(315,810)(316,786)(317,787)(318,788)(319,789)
(320,790)(321,781)(322,782)(323,783)(324,784)(325,785)(326,791)(327,792)
(328,793)(329,794)(330,795)(331,831)(332,832)(333,833)(334,834)(335,835)
(336,826)(337,827)(338,828)(339,829)(340,830)(341,836)(342,837)(343,838)
(344,839)(345,840)(346,816)(347,817)(348,818)(349,819)(350,820)(351,811)
(352,812)(353,813)(354,814)(355,815)(356,821)(357,822)(358,823)(359,824)
(360,825)(361,846)(362,847)(363,848)(364,849)(365,850)(366,841)(367,842)
(368,843)(369,844)(370,845)(371,851)(372,852)(373,853)(374,854)(375,855)
(376,861)(377,862)(378,863)(379,864)(380,865)(381,856)(382,857)(383,858)
(384,859)(385,860)(386,866)(387,867)(388,868)(389,869)(390,870)(391,876)
(392,877)(393,878)(394,879)(395,880)(396,871)(397,872)(398,873)(399,874)
(400,875)(401,881)(402,882)(403,883)(404,884)(405,885)(406,891)(407,892)
(408,893)(409,894)(410,895)(411,886)(412,887)(413,888)(414,889)(415,890)
(416,896)(417,897)(418,898)(419,899)(420,900)(421,921)(422,922)(423,923)
(424,924)(425,925)(426,916)(427,917)(428,918)(429,919)(430,920)(431,926)
(432,927)(433,928)(434,929)(435,930)(436,906)(437,907)(438,908)(439,909)
(440,910)(441,901)(442,902)(443,903)(444,904)(445,905)(446,911)(447,912)
(448,913)(449,914)(450,915)(451,951)(452,952)(453,953)(454,954)(455,955)
(456,946)(457,947)(458,948)(459,949)(460,950)(461,956)(462,957)(463,958)
(464,959)(465,960)(466,936)(467,937)(468,938)(469,939)(470,940)(471,931)
(472,932)(473,933)(474,934)(475,935)(476,941)(477,942)(478,943)(479,944)
(480,945);
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*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 
References : None.
to this polytope