Polytope of Type {10,4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,4,24}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150682)
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
   3-fold quotients : {10,4,8}*640b
   4-fold quotients : {10,2,12}*480, {10,4,6}*480
   5-fold quotients : {2,4,24}*384b
   6-fold quotients : {10,4,4}*320
   8-fold quotients : {5,2,12}*240, {10,2,6}*240
   10-fold quotients : {2,4,12}*192a
   12-fold quotients : {10,2,4}*160, {10,4,2}*160
   15-fold quotients : {2,4,8}*128b
   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
   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)( 61,437)( 62,436)( 63,440)( 64,439)
( 65,438)( 66,442)( 67,441)( 68,445)( 69,444)( 70,443)( 71,447)( 72,446)
( 73,450)( 74,449)( 75,448)( 76,422)( 77,421)( 78,425)( 79,424)( 80,423)
( 81,427)( 82,426)( 83,430)( 84,429)( 85,428)( 86,432)( 87,431)( 88,435)
( 89,434)( 90,433)( 91,467)( 92,466)( 93,470)( 94,469)( 95,468)( 96,472)
( 97,471)( 98,475)( 99,474)(100,473)(101,477)(102,476)(103,480)(104,479)
(105,478)(106,452)(107,451)(108,455)(109,454)(110,453)(111,457)(112,456)
(113,460)(114,459)(115,458)(116,462)(117,461)(118,465)(119,464)(120,463)
(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)(181,317)(182,316)(183,320)(184,319)
(185,318)(186,322)(187,321)(188,325)(189,324)(190,323)(191,327)(192,326)
(193,330)(194,329)(195,328)(196,302)(197,301)(198,305)(199,304)(200,303)
(201,307)(202,306)(203,310)(204,309)(205,308)(206,312)(207,311)(208,315)
(209,314)(210,313)(211,347)(212,346)(213,350)(214,349)(215,348)(216,352)
(217,351)(218,355)(219,354)(220,353)(221,357)(222,356)(223,360)(224,359)
(225,358)(226,332)(227,331)(228,335)(229,334)(230,333)(231,337)(232,336)
(233,340)(234,339)(235,338)(236,342)(237,341)(238,345)(239,344)(240,343)
(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)(541,917)(542,916)(543,920)(544,919)
(545,918)(546,922)(547,921)(548,925)(549,924)(550,923)(551,927)(552,926)
(553,930)(554,929)(555,928)(556,902)(557,901)(558,905)(559,904)(560,903)
(561,907)(562,906)(563,910)(564,909)(565,908)(566,912)(567,911)(568,915)
(569,914)(570,913)(571,947)(572,946)(573,950)(574,949)(575,948)(576,952)
(577,951)(578,955)(579,954)(580,953)(581,957)(582,956)(583,960)(584,959)
(585,958)(586,932)(587,931)(588,935)(589,934)(590,933)(591,937)(592,936)
(593,940)(594,939)(595,938)(596,942)(597,941)(598,945)(599,944)(600,943)
(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)(661,797)(662,796)(663,800)(664,799)
(665,798)(666,802)(667,801)(668,805)(669,804)(670,803)(671,807)(672,806)
(673,810)(674,809)(675,808)(676,782)(677,781)(678,785)(679,784)(680,783)
(681,787)(682,786)(683,790)(684,789)(685,788)(686,792)(687,791)(688,795)
(689,794)(690,793)(691,827)(692,826)(693,830)(694,829)(695,828)(696,832)
(697,831)(698,835)(699,834)(700,833)(701,837)(702,836)(703,840)(704,839)
(705,838)(706,812)(707,811)(708,815)(709,814)(710,813)(711,817)(712,816)
(713,820)(714,819)(715,818)(716,822)(717,821)(718,825)(719,824)(720,823);;
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)(721,826)(722,827)(723,828)(724,829)
(725,830)(726,836)(727,837)(728,838)(729,839)(730,840)(731,831)(732,832)
(733,833)(734,834)(735,835)(736,811)(737,812)(738,813)(739,814)(740,815)
(741,821)(742,822)(743,823)(744,824)(745,825)(746,816)(747,817)(748,818)
(749,819)(750,820)(751,796)(752,797)(753,798)(754,799)(755,800)(756,806)
(757,807)(758,808)(759,809)(760,810)(761,801)(762,802)(763,803)(764,804)
(765,805)(766,781)(767,782)(768,783)(769,784)(770,785)(771,791)(772,792)
(773,793)(774,794)(775,795)(776,786)(777,787)(778,788)(779,789)(780,790)
(841,946)(842,947)(843,948)(844,949)(845,950)(846,956)(847,957)(848,958)
(849,959)(850,960)(851,951)(852,952)(853,953)(854,954)(855,955)(856,931)
(857,932)(858,933)(859,934)(860,935)(861,941)(862,942)(863,943)(864,944)
(865,945)(866,936)(867,937)(868,938)(869,939)(870,940)(871,916)(872,917)
(873,918)(874,919)(875,920)(876,926)(877,927)(878,928)(879,929)(880,930)
(881,921)(882,922)(883,923)(884,924)(885,925)(886,901)(887,902)(888,903)
(889,904)(890,905)(891,911)(892,912)(893,913)(894,914)(895,915)(896,906)
(897,907)(898,908)(899,909)(900,910);;
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)( 31,531)( 32,532)
( 33,533)( 34,534)( 35,535)( 36,526)( 37,527)( 38,528)( 39,529)( 40,530)
( 41,536)( 42,537)( 43,538)( 44,539)( 45,540)( 46,516)( 47,517)( 48,518)
( 49,519)( 50,520)( 51,511)( 52,512)( 53,513)( 54,514)( 55,515)( 56,521)
( 57,522)( 58,523)( 59,524)( 60,525)( 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)( 91,576)( 92,577)( 93,578)( 94,579)( 95,580)( 96,571)
( 97,572)( 98,573)( 99,574)(100,575)(101,581)(102,582)(103,583)(104,584)
(105,585)(106,591)(107,592)(108,593)(109,594)(110,595)(111,586)(112,587)
(113,588)(114,589)(115,590)(116,596)(117,597)(118,598)(119,599)(120,600)
(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)(151,651)(152,652)
(153,653)(154,654)(155,655)(156,646)(157,647)(158,648)(159,649)(160,650)
(161,656)(162,657)(163,658)(164,659)(165,660)(166,636)(167,637)(168,638)
(169,639)(170,640)(171,631)(172,632)(173,633)(174,634)(175,635)(176,641)
(177,642)(178,643)(179,644)(180,645)(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)(211,696)(212,697)(213,698)(214,699)(215,700)(216,691)
(217,692)(218,693)(219,694)(220,695)(221,701)(222,702)(223,703)(224,704)
(225,705)(226,711)(227,712)(228,713)(229,714)(230,715)(231,706)(232,707)
(233,708)(234,709)(235,710)(236,716)(237,717)(238,718)(239,719)(240,720)
(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)(271,771)(272,772)
(273,773)(274,774)(275,775)(276,766)(277,767)(278,768)(279,769)(280,770)
(281,776)(282,777)(283,778)(284,779)(285,780)(286,756)(287,757)(288,758)
(289,759)(290,760)(291,751)(292,752)(293,753)(294,754)(295,755)(296,761)
(297,762)(298,763)(299,764)(300,765)(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)(331,816)(332,817)(333,818)(334,819)(335,820)(336,811)
(337,812)(338,813)(339,814)(340,815)(341,821)(342,822)(343,823)(344,824)
(345,825)(346,831)(347,832)(348,833)(349,834)(350,835)(351,826)(352,827)
(353,828)(354,829)(355,830)(356,836)(357,837)(358,838)(359,839)(360,840)
(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)(391,891)(392,892)
(393,893)(394,894)(395,895)(396,886)(397,887)(398,888)(399,889)(400,890)
(401,896)(402,897)(403,898)(404,899)(405,900)(406,876)(407,877)(408,878)
(409,879)(410,880)(411,871)(412,872)(413,873)(414,874)(415,875)(416,881)
(417,882)(418,883)(419,884)(420,885)(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)(451,936)(452,937)(453,938)(454,939)(455,940)(456,931)
(457,932)(458,933)(459,934)(460,935)(461,941)(462,942)(463,943)(464,944)
(465,945)(466,951)(467,952)(468,953)(469,954)(470,955)(471,946)(472,947)
(473,948)(474,949)(475,950)(476,956)(477,957)(478,958)(479,959)(480,960);;
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, s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 ];;
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)( 61,437)( 62,436)( 63,440)
( 64,439)( 65,438)( 66,442)( 67,441)( 68,445)( 69,444)( 70,443)( 71,447)
( 72,446)( 73,450)( 74,449)( 75,448)( 76,422)( 77,421)( 78,425)( 79,424)
( 80,423)( 81,427)( 82,426)( 83,430)( 84,429)( 85,428)( 86,432)( 87,431)
( 88,435)( 89,434)( 90,433)( 91,467)( 92,466)( 93,470)( 94,469)( 95,468)
( 96,472)( 97,471)( 98,475)( 99,474)(100,473)(101,477)(102,476)(103,480)
(104,479)(105,478)(106,452)(107,451)(108,455)(109,454)(110,453)(111,457)
(112,456)(113,460)(114,459)(115,458)(116,462)(117,461)(118,465)(119,464)
(120,463)(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)(181,317)(182,316)(183,320)
(184,319)(185,318)(186,322)(187,321)(188,325)(189,324)(190,323)(191,327)
(192,326)(193,330)(194,329)(195,328)(196,302)(197,301)(198,305)(199,304)
(200,303)(201,307)(202,306)(203,310)(204,309)(205,308)(206,312)(207,311)
(208,315)(209,314)(210,313)(211,347)(212,346)(213,350)(214,349)(215,348)
(216,352)(217,351)(218,355)(219,354)(220,353)(221,357)(222,356)(223,360)
(224,359)(225,358)(226,332)(227,331)(228,335)(229,334)(230,333)(231,337)
(232,336)(233,340)(234,339)(235,338)(236,342)(237,341)(238,345)(239,344)
(240,343)(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)(541,917)(542,916)(543,920)
(544,919)(545,918)(546,922)(547,921)(548,925)(549,924)(550,923)(551,927)
(552,926)(553,930)(554,929)(555,928)(556,902)(557,901)(558,905)(559,904)
(560,903)(561,907)(562,906)(563,910)(564,909)(565,908)(566,912)(567,911)
(568,915)(569,914)(570,913)(571,947)(572,946)(573,950)(574,949)(575,948)
(576,952)(577,951)(578,955)(579,954)(580,953)(581,957)(582,956)(583,960)
(584,959)(585,958)(586,932)(587,931)(588,935)(589,934)(590,933)(591,937)
(592,936)(593,940)(594,939)(595,938)(596,942)(597,941)(598,945)(599,944)
(600,943)(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)(661,797)(662,796)(663,800)
(664,799)(665,798)(666,802)(667,801)(668,805)(669,804)(670,803)(671,807)
(672,806)(673,810)(674,809)(675,808)(676,782)(677,781)(678,785)(679,784)
(680,783)(681,787)(682,786)(683,790)(684,789)(685,788)(686,792)(687,791)
(688,795)(689,794)(690,793)(691,827)(692,826)(693,830)(694,829)(695,828)
(696,832)(697,831)(698,835)(699,834)(700,833)(701,837)(702,836)(703,840)
(704,839)(705,838)(706,812)(707,811)(708,815)(709,814)(710,813)(711,817)
(712,816)(713,820)(714,819)(715,818)(716,822)(717,821)(718,825)(719,824)
(720,823);
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)(721,826)(722,827)(723,828)
(724,829)(725,830)(726,836)(727,837)(728,838)(729,839)(730,840)(731,831)
(732,832)(733,833)(734,834)(735,835)(736,811)(737,812)(738,813)(739,814)
(740,815)(741,821)(742,822)(743,823)(744,824)(745,825)(746,816)(747,817)
(748,818)(749,819)(750,820)(751,796)(752,797)(753,798)(754,799)(755,800)
(756,806)(757,807)(758,808)(759,809)(760,810)(761,801)(762,802)(763,803)
(764,804)(765,805)(766,781)(767,782)(768,783)(769,784)(770,785)(771,791)
(772,792)(773,793)(774,794)(775,795)(776,786)(777,787)(778,788)(779,789)
(780,790)(841,946)(842,947)(843,948)(844,949)(845,950)(846,956)(847,957)
(848,958)(849,959)(850,960)(851,951)(852,952)(853,953)(854,954)(855,955)
(856,931)(857,932)(858,933)(859,934)(860,935)(861,941)(862,942)(863,943)
(864,944)(865,945)(866,936)(867,937)(868,938)(869,939)(870,940)(871,916)
(872,917)(873,918)(874,919)(875,920)(876,926)(877,927)(878,928)(879,929)
(880,930)(881,921)(882,922)(883,923)(884,924)(885,925)(886,901)(887,902)
(888,903)(889,904)(890,905)(891,911)(892,912)(893,913)(894,914)(895,915)
(896,906)(897,907)(898,908)(899,909)(900,910);
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)( 31,531)
( 32,532)( 33,533)( 34,534)( 35,535)( 36,526)( 37,527)( 38,528)( 39,529)
( 40,530)( 41,536)( 42,537)( 43,538)( 44,539)( 45,540)( 46,516)( 47,517)
( 48,518)( 49,519)( 50,520)( 51,511)( 52,512)( 53,513)( 54,514)( 55,515)
( 56,521)( 57,522)( 58,523)( 59,524)( 60,525)( 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)( 91,576)( 92,577)( 93,578)( 94,579)( 95,580)
( 96,571)( 97,572)( 98,573)( 99,574)(100,575)(101,581)(102,582)(103,583)
(104,584)(105,585)(106,591)(107,592)(108,593)(109,594)(110,595)(111,586)
(112,587)(113,588)(114,589)(115,590)(116,596)(117,597)(118,598)(119,599)
(120,600)(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)(151,651)
(152,652)(153,653)(154,654)(155,655)(156,646)(157,647)(158,648)(159,649)
(160,650)(161,656)(162,657)(163,658)(164,659)(165,660)(166,636)(167,637)
(168,638)(169,639)(170,640)(171,631)(172,632)(173,633)(174,634)(175,635)
(176,641)(177,642)(178,643)(179,644)(180,645)(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)(211,696)(212,697)(213,698)(214,699)(215,700)
(216,691)(217,692)(218,693)(219,694)(220,695)(221,701)(222,702)(223,703)
(224,704)(225,705)(226,711)(227,712)(228,713)(229,714)(230,715)(231,706)
(232,707)(233,708)(234,709)(235,710)(236,716)(237,717)(238,718)(239,719)
(240,720)(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)(271,771)
(272,772)(273,773)(274,774)(275,775)(276,766)(277,767)(278,768)(279,769)
(280,770)(281,776)(282,777)(283,778)(284,779)(285,780)(286,756)(287,757)
(288,758)(289,759)(290,760)(291,751)(292,752)(293,753)(294,754)(295,755)
(296,761)(297,762)(298,763)(299,764)(300,765)(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)(331,816)(332,817)(333,818)(334,819)(335,820)
(336,811)(337,812)(338,813)(339,814)(340,815)(341,821)(342,822)(343,823)
(344,824)(345,825)(346,831)(347,832)(348,833)(349,834)(350,835)(351,826)
(352,827)(353,828)(354,829)(355,830)(356,836)(357,837)(358,838)(359,839)
(360,840)(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)(391,891)
(392,892)(393,893)(394,894)(395,895)(396,886)(397,887)(398,888)(399,889)
(400,890)(401,896)(402,897)(403,898)(404,899)(405,900)(406,876)(407,877)
(408,878)(409,879)(410,880)(411,871)(412,872)(413,873)(414,874)(415,875)
(416,881)(417,882)(418,883)(419,884)(420,885)(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)(451,936)(452,937)(453,938)(454,939)(455,940)
(456,931)(457,932)(458,933)(459,934)(460,935)(461,941)(462,942)(463,943)
(464,944)(465,945)(466,951)(467,952)(468,953)(469,954)(470,955)(471,946)
(472,947)(473,948)(474,949)(475,950)(476,956)(477,957)(478,958)(479,959)
(480,960);
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, 
s3*s1*s2*s3*s2*s1*s2*s1*s3*s2*s3*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2 >;

References : None.
to this polytope