Polytope of Type {4,8,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,8,30}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150654)
Rank : 4
Schlafli Type : {4,8,30}
Number of vertices, edges, etc : 4, 16, 120, 30
Order of s₀s₁s₂s₃ : 120
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4,30}*960
   3-fold quotients : {4,8,10}*640b
   4-fold quotients : {2,4,30}*480a, {4,2,30}*480
   5-fold quotients : {4,8,6}*384b
   6-fold quotients : {4,4,10}*320
   8-fold quotients : {4,2,15}*240, {2,2,30}*240
   10-fold quotients : {4,4,6}*192
   12-fold quotients : {2,4,10}*160, {4,2,10}*160
   15-fold quotients : {4,8,2}*128b
   16-fold quotients : {2,2,15}*120
   20-fold quotients : {2,4,6}*96a, {4,2,6}*96
   24-fold quotients : {4,2,5}*80, {2,2,10}*80
   30-fold quotients : {4,4,2}*64
   40-fold quotients : {4,2,3}*48, {2,2,6}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,4,2}*32, {4,2,2}*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 := (  1,241)(  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)( 61,316)( 62,317)( 63,318)( 64,319)
( 65,320)( 66,321)( 67,322)( 68,323)( 69,324)( 70,325)( 71,326)( 72,327)
( 73,328)( 74,329)( 75,330)( 76,301)( 77,302)( 78,303)( 79,304)( 80,305)
( 81,306)( 82,307)( 83,308)( 84,309)( 85,310)( 86,311)( 87,312)( 88,313)
( 89,314)( 90,315)( 91,346)( 92,347)( 93,348)( 94,349)( 95,350)( 96,351)
( 97,352)( 98,353)( 99,354)(100,355)(101,356)(102,357)(103,358)(104,359)
(105,360)(106,331)(107,332)(108,333)(109,334)(110,335)(111,336)(112,337)
(113,338)(114,339)(115,340)(116,341)(117,342)(118,343)(119,344)(120,345)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)
(177,417)(178,418)(179,419)(180,420)(181,436)(182,437)(183,438)(184,439)
(185,440)(186,441)(187,442)(188,443)(189,444)(190,445)(191,446)(192,447)
(193,448)(194,449)(195,450)(196,421)(197,422)(198,423)(199,424)(200,425)
(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)(208,433)
(209,434)(210,435)(211,466)(212,467)(213,468)(214,469)(215,470)(216,471)
(217,472)(218,473)(219,474)(220,475)(221,476)(222,477)(223,478)(224,479)
(225,480)(226,451)(227,452)(228,453)(229,454)(230,455)(231,456)(232,457)
(233,458)(234,459)(235,460)(236,461)(237,462)(238,463)(239,464)(240,465)
(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)(541,796)(542,797)(543,798)(544,799)
(545,800)(546,801)(547,802)(548,803)(549,804)(550,805)(551,806)(552,807)
(553,808)(554,809)(555,810)(556,781)(557,782)(558,783)(559,784)(560,785)
(561,786)(562,787)(563,788)(564,789)(565,790)(566,791)(567,792)(568,793)
(569,794)(570,795)(571,826)(572,827)(573,828)(574,829)(575,830)(576,831)
(577,832)(578,833)(579,834)(580,835)(581,836)(582,837)(583,838)(584,839)
(585,840)(586,811)(587,812)(588,813)(589,814)(590,815)(591,816)(592,817)
(593,818)(594,819)(595,820)(596,821)(597,822)(598,823)(599,824)(600,825)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)(608,848)
(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)(624,864)
(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)(640,880)
(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)(656,896)
(657,897)(658,898)(659,899)(660,900)(661,916)(662,917)(663,918)(664,919)
(665,920)(666,921)(667,922)(668,923)(669,924)(670,925)(671,926)(672,927)
(673,928)(674,929)(675,930)(676,901)(677,902)(678,903)(679,904)(680,905)
(681,906)(682,907)(683,908)(684,909)(685,910)(686,911)(687,912)(688,913)
(689,914)(690,915)(691,946)(692,947)(693,948)(694,949)(695,950)(696,951)
(697,952)(698,953)(699,954)(700,955)(701,956)(702,957)(703,958)(704,959)
(705,960)(706,931)(707,932)(708,933)(709,934)(710,935)(711,936)(712,937)
(713,938)(714,939)(715,940)(716,941)(717,942)(718,943)(719,944)(720,945);;
s1 := ( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)( 68, 83)
( 69, 84)( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 91,106)
( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)( 99,114)
(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(181,196)(182,197)
(183,198)(184,199)(185,200)(186,201)(187,202)(188,203)(189,204)(190,205)
(191,206)(192,207)(193,208)(194,209)(195,210)(211,226)(212,227)(213,228)
(214,229)(215,230)(216,231)(217,232)(218,233)(219,234)(220,235)(221,236)
(222,237)(223,238)(224,239)(225,240)(241,271)(242,272)(243,273)(244,274)
(245,275)(246,276)(247,277)(248,278)(249,279)(250,280)(251,281)(252,282)
(253,283)(254,284)(255,285)(256,286)(257,287)(258,288)(259,289)(260,290)
(261,291)(262,292)(263,293)(264,294)(265,295)(266,296)(267,297)(268,298)
(269,299)(270,300)(301,346)(302,347)(303,348)(304,349)(305,350)(306,351)
(307,352)(308,353)(309,354)(310,355)(311,356)(312,357)(313,358)(314,359)
(315,360)(316,331)(317,332)(318,333)(319,334)(320,335)(321,336)(322,337)
(323,338)(324,339)(325,340)(326,341)(327,342)(328,343)(329,344)(330,345)
(361,391)(362,392)(363,393)(364,394)(365,395)(366,396)(367,397)(368,398)
(369,399)(370,400)(371,401)(372,402)(373,403)(374,404)(375,405)(376,406)
(377,407)(378,408)(379,409)(380,410)(381,411)(382,412)(383,413)(384,414)
(385,415)(386,416)(387,417)(388,418)(389,419)(390,420)(421,466)(422,467)
(423,468)(424,469)(425,470)(426,471)(427,472)(428,473)(429,474)(430,475)
(431,476)(432,477)(433,478)(434,479)(435,480)(436,451)(437,452)(438,453)
(439,454)(440,455)(441,456)(442,457)(443,458)(444,459)(445,460)(446,461)
(447,462)(448,463)(449,464)(450,465)(481,541)(482,542)(483,543)(484,544)
(485,545)(486,546)(487,547)(488,548)(489,549)(490,550)(491,551)(492,552)
(493,553)(494,554)(495,555)(496,556)(497,557)(498,558)(499,559)(500,560)
(501,561)(502,562)(503,563)(504,564)(505,565)(506,566)(507,567)(508,568)
(509,569)(510,570)(511,571)(512,572)(513,573)(514,574)(515,575)(516,576)
(517,577)(518,578)(519,579)(520,580)(521,581)(522,582)(523,583)(524,584)
(525,585)(526,586)(527,587)(528,588)(529,589)(530,590)(531,591)(532,592)
(533,593)(534,594)(535,595)(536,596)(537,597)(538,598)(539,599)(540,600)
(601,661)(602,662)(603,663)(604,664)(605,665)(606,666)(607,667)(608,668)
(609,669)(610,670)(611,671)(612,672)(613,673)(614,674)(615,675)(616,676)
(617,677)(618,678)(619,679)(620,680)(621,681)(622,682)(623,683)(624,684)
(625,685)(626,686)(627,687)(628,688)(629,689)(630,690)(631,691)(632,692)
(633,693)(634,694)(635,695)(636,696)(637,697)(638,698)(639,699)(640,700)
(641,701)(642,702)(643,703)(644,704)(645,705)(646,706)(647,707)(648,708)
(649,709)(650,710)(651,711)(652,712)(653,713)(654,714)(655,715)(656,716)
(657,717)(658,718)(659,719)(660,720)(721,826)(722,827)(723,828)(724,829)
(725,830)(726,831)(727,832)(728,833)(729,834)(730,835)(731,836)(732,837)
(733,838)(734,839)(735,840)(736,811)(737,812)(738,813)(739,814)(740,815)
(741,816)(742,817)(743,818)(744,819)(745,820)(746,821)(747,822)(748,823)
(749,824)(750,825)(751,796)(752,797)(753,798)(754,799)(755,800)(756,801)
(757,802)(758,803)(759,804)(760,805)(761,806)(762,807)(763,808)(764,809)
(765,810)(766,781)(767,782)(768,783)(769,784)(770,785)(771,786)(772,787)
(773,788)(774,789)(775,790)(776,791)(777,792)(778,793)(779,794)(780,795)
(841,946)(842,947)(843,948)(844,949)(845,950)(846,951)(847,952)(848,953)
(849,954)(850,955)(851,956)(852,957)(853,958)(854,959)(855,960)(856,931)
(857,932)(858,933)(859,934)(860,935)(861,936)(862,937)(863,938)(864,939)
(865,940)(866,941)(867,942)(868,943)(869,944)(870,945)(871,916)(872,917)
(873,918)(874,919)(875,920)(876,921)(877,922)(878,923)(879,924)(880,925)
(881,926)(882,927)(883,928)(884,929)(885,930)(886,901)(887,902)(888,903)
(889,904)(890,905)(891,906)(892,907)(893,908)(894,909)(895,910)(896,911)
(897,912)(898,913)(899,914)(900,915);;
s2 := (  1,601)(  2,605)(  3,604)(  4,603)(  5,602)(  6,611)(  7,615)(  8,614)
(  9,613)( 10,612)( 11,606)( 12,610)( 13,609)( 14,608)( 15,607)( 16,616)
( 17,620)( 18,619)( 19,618)( 20,617)( 21,626)( 22,630)( 23,629)( 24,628)
( 25,627)( 26,621)( 27,625)( 28,624)( 29,623)( 30,622)( 31,646)( 32,650)
( 33,649)( 34,648)( 35,647)( 36,656)( 37,660)( 38,659)( 39,658)( 40,657)
( 41,651)( 42,655)( 43,654)( 44,653)( 45,652)( 46,631)( 47,635)( 48,634)
( 49,633)( 50,632)( 51,641)( 52,645)( 53,644)( 54,643)( 55,642)( 56,636)
( 57,640)( 58,639)( 59,638)( 60,637)( 61,676)( 62,680)( 63,679)( 64,678)
( 65,677)( 66,686)( 67,690)( 68,689)( 69,688)( 70,687)( 71,681)( 72,685)
( 73,684)( 74,683)( 75,682)( 76,661)( 77,665)( 78,664)( 79,663)( 80,662)
( 81,671)( 82,675)( 83,674)( 84,673)( 85,672)( 86,666)( 87,670)( 88,669)
( 89,668)( 90,667)( 91,691)( 92,695)( 93,694)( 94,693)( 95,692)( 96,701)
( 97,705)( 98,704)( 99,703)(100,702)(101,696)(102,700)(103,699)(104,698)
(105,697)(106,706)(107,710)(108,709)(109,708)(110,707)(111,716)(112,720)
(113,719)(114,718)(115,717)(116,711)(117,715)(118,714)(119,713)(120,712)
(121,481)(122,485)(123,484)(124,483)(125,482)(126,491)(127,495)(128,494)
(129,493)(130,492)(131,486)(132,490)(133,489)(134,488)(135,487)(136,496)
(137,500)(138,499)(139,498)(140,497)(141,506)(142,510)(143,509)(144,508)
(145,507)(146,501)(147,505)(148,504)(149,503)(150,502)(151,526)(152,530)
(153,529)(154,528)(155,527)(156,536)(157,540)(158,539)(159,538)(160,537)
(161,531)(162,535)(163,534)(164,533)(165,532)(166,511)(167,515)(168,514)
(169,513)(170,512)(171,521)(172,525)(173,524)(174,523)(175,522)(176,516)
(177,520)(178,519)(179,518)(180,517)(181,556)(182,560)(183,559)(184,558)
(185,557)(186,566)(187,570)(188,569)(189,568)(190,567)(191,561)(192,565)
(193,564)(194,563)(195,562)(196,541)(197,545)(198,544)(199,543)(200,542)
(201,551)(202,555)(203,554)(204,553)(205,552)(206,546)(207,550)(208,549)
(209,548)(210,547)(211,571)(212,575)(213,574)(214,573)(215,572)(216,581)
(217,585)(218,584)(219,583)(220,582)(221,576)(222,580)(223,579)(224,578)
(225,577)(226,586)(227,590)(228,589)(229,588)(230,587)(231,596)(232,600)
(233,599)(234,598)(235,597)(236,591)(237,595)(238,594)(239,593)(240,592)
(241,841)(242,845)(243,844)(244,843)(245,842)(246,851)(247,855)(248,854)
(249,853)(250,852)(251,846)(252,850)(253,849)(254,848)(255,847)(256,856)
(257,860)(258,859)(259,858)(260,857)(261,866)(262,870)(263,869)(264,868)
(265,867)(266,861)(267,865)(268,864)(269,863)(270,862)(271,886)(272,890)
(273,889)(274,888)(275,887)(276,896)(277,900)(278,899)(279,898)(280,897)
(281,891)(282,895)(283,894)(284,893)(285,892)(286,871)(287,875)(288,874)
(289,873)(290,872)(291,881)(292,885)(293,884)(294,883)(295,882)(296,876)
(297,880)(298,879)(299,878)(300,877)(301,916)(302,920)(303,919)(304,918)
(305,917)(306,926)(307,930)(308,929)(309,928)(310,927)(311,921)(312,925)
(313,924)(314,923)(315,922)(316,901)(317,905)(318,904)(319,903)(320,902)
(321,911)(322,915)(323,914)(324,913)(325,912)(326,906)(327,910)(328,909)
(329,908)(330,907)(331,931)(332,935)(333,934)(334,933)(335,932)(336,941)
(337,945)(338,944)(339,943)(340,942)(341,936)(342,940)(343,939)(344,938)
(345,937)(346,946)(347,950)(348,949)(349,948)(350,947)(351,956)(352,960)
(353,959)(354,958)(355,957)(356,951)(357,955)(358,954)(359,953)(360,952)
(361,721)(362,725)(363,724)(364,723)(365,722)(366,731)(367,735)(368,734)
(369,733)(370,732)(371,726)(372,730)(373,729)(374,728)(375,727)(376,736)
(377,740)(378,739)(379,738)(380,737)(381,746)(382,750)(383,749)(384,748)
(385,747)(386,741)(387,745)(388,744)(389,743)(390,742)(391,766)(392,770)
(393,769)(394,768)(395,767)(396,776)(397,780)(398,779)(399,778)(400,777)
(401,771)(402,775)(403,774)(404,773)(405,772)(406,751)(407,755)(408,754)
(409,753)(410,752)(411,761)(412,765)(413,764)(414,763)(415,762)(416,756)
(417,760)(418,759)(419,758)(420,757)(421,796)(422,800)(423,799)(424,798)
(425,797)(426,806)(427,810)(428,809)(429,808)(430,807)(431,801)(432,805)
(433,804)(434,803)(435,802)(436,781)(437,785)(438,784)(439,783)(440,782)
(441,791)(442,795)(443,794)(444,793)(445,792)(446,786)(447,790)(448,789)
(449,788)(450,787)(451,811)(452,815)(453,814)(454,813)(455,812)(456,821)
(457,825)(458,824)(459,823)(460,822)(461,816)(462,820)(463,819)(464,818)
(465,817)(466,826)(467,830)(468,829)(469,828)(470,827)(471,836)(472,840)
(473,839)(474,838)(475,837)(476,831)(477,835)(478,834)(479,833)(480,832);;
s3 := (  1,127)(  2,126)(  3,130)(  4,129)(  5,128)(  6,122)(  7,121)(  8,125)
(  9,124)( 10,123)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,142)
( 17,141)( 18,145)( 19,144)( 20,143)( 21,137)( 22,136)( 23,140)( 24,139)
( 25,138)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,157)( 32,156)
( 33,160)( 34,159)( 35,158)( 36,152)( 37,151)( 38,155)( 39,154)( 40,153)
( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,172)( 47,171)( 48,175)
( 49,174)( 50,173)( 51,167)( 52,166)( 53,170)( 54,169)( 55,168)( 56,177)
( 57,176)( 58,180)( 59,179)( 60,178)( 61,187)( 62,186)( 63,190)( 64,189)
( 65,188)( 66,182)( 67,181)( 68,185)( 69,184)( 70,183)( 71,192)( 72,191)
( 73,195)( 74,194)( 75,193)( 76,202)( 77,201)( 78,205)( 79,204)( 80,203)
( 81,197)( 82,196)( 83,200)( 84,199)( 85,198)( 86,207)( 87,206)( 88,210)
( 89,209)( 90,208)( 91,217)( 92,216)( 93,220)( 94,219)( 95,218)( 96,212)
( 97,211)( 98,215)( 99,214)(100,213)(101,222)(102,221)(103,225)(104,224)
(105,223)(106,232)(107,231)(108,235)(109,234)(110,233)(111,227)(112,226)
(113,230)(114,229)(115,228)(116,237)(117,236)(118,240)(119,239)(120,238)
(241,367)(242,366)(243,370)(244,369)(245,368)(246,362)(247,361)(248,365)
(249,364)(250,363)(251,372)(252,371)(253,375)(254,374)(255,373)(256,382)
(257,381)(258,385)(259,384)(260,383)(261,377)(262,376)(263,380)(264,379)
(265,378)(266,387)(267,386)(268,390)(269,389)(270,388)(271,397)(272,396)
(273,400)(274,399)(275,398)(276,392)(277,391)(278,395)(279,394)(280,393)
(281,402)(282,401)(283,405)(284,404)(285,403)(286,412)(287,411)(288,415)
(289,414)(290,413)(291,407)(292,406)(293,410)(294,409)(295,408)(296,417)
(297,416)(298,420)(299,419)(300,418)(301,427)(302,426)(303,430)(304,429)
(305,428)(306,422)(307,421)(308,425)(309,424)(310,423)(311,432)(312,431)
(313,435)(314,434)(315,433)(316,442)(317,441)(318,445)(319,444)(320,443)
(321,437)(322,436)(323,440)(324,439)(325,438)(326,447)(327,446)(328,450)
(329,449)(330,448)(331,457)(332,456)(333,460)(334,459)(335,458)(336,452)
(337,451)(338,455)(339,454)(340,453)(341,462)(342,461)(343,465)(344,464)
(345,463)(346,472)(347,471)(348,475)(349,474)(350,473)(351,467)(352,466)
(353,470)(354,469)(355,468)(356,477)(357,476)(358,480)(359,479)(360,478)
(481,607)(482,606)(483,610)(484,609)(485,608)(486,602)(487,601)(488,605)
(489,604)(490,603)(491,612)(492,611)(493,615)(494,614)(495,613)(496,622)
(497,621)(498,625)(499,624)(500,623)(501,617)(502,616)(503,620)(504,619)
(505,618)(506,627)(507,626)(508,630)(509,629)(510,628)(511,637)(512,636)
(513,640)(514,639)(515,638)(516,632)(517,631)(518,635)(519,634)(520,633)
(521,642)(522,641)(523,645)(524,644)(525,643)(526,652)(527,651)(528,655)
(529,654)(530,653)(531,647)(532,646)(533,650)(534,649)(535,648)(536,657)
(537,656)(538,660)(539,659)(540,658)(541,667)(542,666)(543,670)(544,669)
(545,668)(546,662)(547,661)(548,665)(549,664)(550,663)(551,672)(552,671)
(553,675)(554,674)(555,673)(556,682)(557,681)(558,685)(559,684)(560,683)
(561,677)(562,676)(563,680)(564,679)(565,678)(566,687)(567,686)(568,690)
(569,689)(570,688)(571,697)(572,696)(573,700)(574,699)(575,698)(576,692)
(577,691)(578,695)(579,694)(580,693)(581,702)(582,701)(583,705)(584,704)
(585,703)(586,712)(587,711)(588,715)(589,714)(590,713)(591,707)(592,706)
(593,710)(594,709)(595,708)(596,717)(597,716)(598,720)(599,719)(600,718)
(721,847)(722,846)(723,850)(724,849)(725,848)(726,842)(727,841)(728,845)
(729,844)(730,843)(731,852)(732,851)(733,855)(734,854)(735,853)(736,862)
(737,861)(738,865)(739,864)(740,863)(741,857)(742,856)(743,860)(744,859)
(745,858)(746,867)(747,866)(748,870)(749,869)(750,868)(751,877)(752,876)
(753,880)(754,879)(755,878)(756,872)(757,871)(758,875)(759,874)(760,873)
(761,882)(762,881)(763,885)(764,884)(765,883)(766,892)(767,891)(768,895)
(769,894)(770,893)(771,887)(772,886)(773,890)(774,889)(775,888)(776,897)
(777,896)(778,900)(779,899)(780,898)(781,907)(782,906)(783,910)(784,909)
(785,908)(786,902)(787,901)(788,905)(789,904)(790,903)(791,912)(792,911)
(793,915)(794,914)(795,913)(796,922)(797,921)(798,925)(799,924)(800,923)
(801,917)(802,916)(803,920)(804,919)(805,918)(806,927)(807,926)(808,930)
(809,929)(810,928)(811,937)(812,936)(813,940)(814,939)(815,938)(816,932)
(817,931)(818,935)(819,934)(820,933)(821,942)(822,941)(823,945)(824,944)
(825,943)(826,952)(827,951)(828,955)(829,954)(830,953)(831,947)(832,946)
(833,950)(834,949)(835,948)(836,957)(837,956)(838,960)(839,959)(840,958);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)( 61,316)( 62,317)( 63,318)
( 64,319)( 65,320)( 66,321)( 67,322)( 68,323)( 69,324)( 70,325)( 71,326)
( 72,327)( 73,328)( 74,329)( 75,330)( 76,301)( 77,302)( 78,303)( 79,304)
( 80,305)( 81,306)( 82,307)( 83,308)( 84,309)( 85,310)( 86,311)( 87,312)
( 88,313)( 89,314)( 90,315)( 91,346)( 92,347)( 93,348)( 94,349)( 95,350)
( 96,351)( 97,352)( 98,353)( 99,354)(100,355)(101,356)(102,357)(103,358)
(104,359)(105,360)(106,331)(107,332)(108,333)(109,334)(110,335)(111,336)
(112,337)(113,338)(114,339)(115,340)(116,341)(117,342)(118,343)(119,344)
(120,345)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)
(176,416)(177,417)(178,418)(179,419)(180,420)(181,436)(182,437)(183,438)
(184,439)(185,440)(186,441)(187,442)(188,443)(189,444)(190,445)(191,446)
(192,447)(193,448)(194,449)(195,450)(196,421)(197,422)(198,423)(199,424)
(200,425)(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)
(208,433)(209,434)(210,435)(211,466)(212,467)(213,468)(214,469)(215,470)
(216,471)(217,472)(218,473)(219,474)(220,475)(221,476)(222,477)(223,478)
(224,479)(225,480)(226,451)(227,452)(228,453)(229,454)(230,455)(231,456)
(232,457)(233,458)(234,459)(235,460)(236,461)(237,462)(238,463)(239,464)
(240,465)(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)(541,796)(542,797)(543,798)
(544,799)(545,800)(546,801)(547,802)(548,803)(549,804)(550,805)(551,806)
(552,807)(553,808)(554,809)(555,810)(556,781)(557,782)(558,783)(559,784)
(560,785)(561,786)(562,787)(563,788)(564,789)(565,790)(566,791)(567,792)
(568,793)(569,794)(570,795)(571,826)(572,827)(573,828)(574,829)(575,830)
(576,831)(577,832)(578,833)(579,834)(580,835)(581,836)(582,837)(583,838)
(584,839)(585,840)(586,811)(587,812)(588,813)(589,814)(590,815)(591,816)
(592,817)(593,818)(594,819)(595,820)(596,821)(597,822)(598,823)(599,824)
(600,825)(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)
(608,848)(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)
(624,864)(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)
(640,880)(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)
(656,896)(657,897)(658,898)(659,899)(660,900)(661,916)(662,917)(663,918)
(664,919)(665,920)(666,921)(667,922)(668,923)(669,924)(670,925)(671,926)
(672,927)(673,928)(674,929)(675,930)(676,901)(677,902)(678,903)(679,904)
(680,905)(681,906)(682,907)(683,908)(684,909)(685,910)(686,911)(687,912)
(688,913)(689,914)(690,915)(691,946)(692,947)(693,948)(694,949)(695,950)
(696,951)(697,952)(698,953)(699,954)(700,955)(701,956)(702,957)(703,958)
(704,959)(705,960)(706,931)(707,932)(708,933)(709,934)(710,935)(711,936)
(712,937)(713,938)(714,939)(715,940)(716,941)(717,942)(718,943)(719,944)
(720,945);
s1 := Sym(960)!( 61, 76)( 62, 77)( 63, 78)( 64, 79)( 65, 80)( 66, 81)( 67, 82)
( 68, 83)( 69, 84)( 70, 85)( 71, 86)( 72, 87)( 73, 88)( 74, 89)( 75, 90)
( 91,106)( 92,107)( 93,108)( 94,109)( 95,110)( 96,111)( 97,112)( 98,113)
( 99,114)(100,115)(101,116)(102,117)(103,118)(104,119)(105,120)(181,196)
(182,197)(183,198)(184,199)(185,200)(186,201)(187,202)(188,203)(189,204)
(190,205)(191,206)(192,207)(193,208)(194,209)(195,210)(211,226)(212,227)
(213,228)(214,229)(215,230)(216,231)(217,232)(218,233)(219,234)(220,235)
(221,236)(222,237)(223,238)(224,239)(225,240)(241,271)(242,272)(243,273)
(244,274)(245,275)(246,276)(247,277)(248,278)(249,279)(250,280)(251,281)
(252,282)(253,283)(254,284)(255,285)(256,286)(257,287)(258,288)(259,289)
(260,290)(261,291)(262,292)(263,293)(264,294)(265,295)(266,296)(267,297)
(268,298)(269,299)(270,300)(301,346)(302,347)(303,348)(304,349)(305,350)
(306,351)(307,352)(308,353)(309,354)(310,355)(311,356)(312,357)(313,358)
(314,359)(315,360)(316,331)(317,332)(318,333)(319,334)(320,335)(321,336)
(322,337)(323,338)(324,339)(325,340)(326,341)(327,342)(328,343)(329,344)
(330,345)(361,391)(362,392)(363,393)(364,394)(365,395)(366,396)(367,397)
(368,398)(369,399)(370,400)(371,401)(372,402)(373,403)(374,404)(375,405)
(376,406)(377,407)(378,408)(379,409)(380,410)(381,411)(382,412)(383,413)
(384,414)(385,415)(386,416)(387,417)(388,418)(389,419)(390,420)(421,466)
(422,467)(423,468)(424,469)(425,470)(426,471)(427,472)(428,473)(429,474)
(430,475)(431,476)(432,477)(433,478)(434,479)(435,480)(436,451)(437,452)
(438,453)(439,454)(440,455)(441,456)(442,457)(443,458)(444,459)(445,460)
(446,461)(447,462)(448,463)(449,464)(450,465)(481,541)(482,542)(483,543)
(484,544)(485,545)(486,546)(487,547)(488,548)(489,549)(490,550)(491,551)
(492,552)(493,553)(494,554)(495,555)(496,556)(497,557)(498,558)(499,559)
(500,560)(501,561)(502,562)(503,563)(504,564)(505,565)(506,566)(507,567)
(508,568)(509,569)(510,570)(511,571)(512,572)(513,573)(514,574)(515,575)
(516,576)(517,577)(518,578)(519,579)(520,580)(521,581)(522,582)(523,583)
(524,584)(525,585)(526,586)(527,587)(528,588)(529,589)(530,590)(531,591)
(532,592)(533,593)(534,594)(535,595)(536,596)(537,597)(538,598)(539,599)
(540,600)(601,661)(602,662)(603,663)(604,664)(605,665)(606,666)(607,667)
(608,668)(609,669)(610,670)(611,671)(612,672)(613,673)(614,674)(615,675)
(616,676)(617,677)(618,678)(619,679)(620,680)(621,681)(622,682)(623,683)
(624,684)(625,685)(626,686)(627,687)(628,688)(629,689)(630,690)(631,691)
(632,692)(633,693)(634,694)(635,695)(636,696)(637,697)(638,698)(639,699)
(640,700)(641,701)(642,702)(643,703)(644,704)(645,705)(646,706)(647,707)
(648,708)(649,709)(650,710)(651,711)(652,712)(653,713)(654,714)(655,715)
(656,716)(657,717)(658,718)(659,719)(660,720)(721,826)(722,827)(723,828)
(724,829)(725,830)(726,831)(727,832)(728,833)(729,834)(730,835)(731,836)
(732,837)(733,838)(734,839)(735,840)(736,811)(737,812)(738,813)(739,814)
(740,815)(741,816)(742,817)(743,818)(744,819)(745,820)(746,821)(747,822)
(748,823)(749,824)(750,825)(751,796)(752,797)(753,798)(754,799)(755,800)
(756,801)(757,802)(758,803)(759,804)(760,805)(761,806)(762,807)(763,808)
(764,809)(765,810)(766,781)(767,782)(768,783)(769,784)(770,785)(771,786)
(772,787)(773,788)(774,789)(775,790)(776,791)(777,792)(778,793)(779,794)
(780,795)(841,946)(842,947)(843,948)(844,949)(845,950)(846,951)(847,952)
(848,953)(849,954)(850,955)(851,956)(852,957)(853,958)(854,959)(855,960)
(856,931)(857,932)(858,933)(859,934)(860,935)(861,936)(862,937)(863,938)
(864,939)(865,940)(866,941)(867,942)(868,943)(869,944)(870,945)(871,916)
(872,917)(873,918)(874,919)(875,920)(876,921)(877,922)(878,923)(879,924)
(880,925)(881,926)(882,927)(883,928)(884,929)(885,930)(886,901)(887,902)
(888,903)(889,904)(890,905)(891,906)(892,907)(893,908)(894,909)(895,910)
(896,911)(897,912)(898,913)(899,914)(900,915);
s2 := Sym(960)!(  1,601)(  2,605)(  3,604)(  4,603)(  5,602)(  6,611)(  7,615)
(  8,614)(  9,613)( 10,612)( 11,606)( 12,610)( 13,609)( 14,608)( 15,607)
( 16,616)( 17,620)( 18,619)( 19,618)( 20,617)( 21,626)( 22,630)( 23,629)
( 24,628)( 25,627)( 26,621)( 27,625)( 28,624)( 29,623)( 30,622)( 31,646)
( 32,650)( 33,649)( 34,648)( 35,647)( 36,656)( 37,660)( 38,659)( 39,658)
( 40,657)( 41,651)( 42,655)( 43,654)( 44,653)( 45,652)( 46,631)( 47,635)
( 48,634)( 49,633)( 50,632)( 51,641)( 52,645)( 53,644)( 54,643)( 55,642)
( 56,636)( 57,640)( 58,639)( 59,638)( 60,637)( 61,676)( 62,680)( 63,679)
( 64,678)( 65,677)( 66,686)( 67,690)( 68,689)( 69,688)( 70,687)( 71,681)
( 72,685)( 73,684)( 74,683)( 75,682)( 76,661)( 77,665)( 78,664)( 79,663)
( 80,662)( 81,671)( 82,675)( 83,674)( 84,673)( 85,672)( 86,666)( 87,670)
( 88,669)( 89,668)( 90,667)( 91,691)( 92,695)( 93,694)( 94,693)( 95,692)
( 96,701)( 97,705)( 98,704)( 99,703)(100,702)(101,696)(102,700)(103,699)
(104,698)(105,697)(106,706)(107,710)(108,709)(109,708)(110,707)(111,716)
(112,720)(113,719)(114,718)(115,717)(116,711)(117,715)(118,714)(119,713)
(120,712)(121,481)(122,485)(123,484)(124,483)(125,482)(126,491)(127,495)
(128,494)(129,493)(130,492)(131,486)(132,490)(133,489)(134,488)(135,487)
(136,496)(137,500)(138,499)(139,498)(140,497)(141,506)(142,510)(143,509)
(144,508)(145,507)(146,501)(147,505)(148,504)(149,503)(150,502)(151,526)
(152,530)(153,529)(154,528)(155,527)(156,536)(157,540)(158,539)(159,538)
(160,537)(161,531)(162,535)(163,534)(164,533)(165,532)(166,511)(167,515)
(168,514)(169,513)(170,512)(171,521)(172,525)(173,524)(174,523)(175,522)
(176,516)(177,520)(178,519)(179,518)(180,517)(181,556)(182,560)(183,559)
(184,558)(185,557)(186,566)(187,570)(188,569)(189,568)(190,567)(191,561)
(192,565)(193,564)(194,563)(195,562)(196,541)(197,545)(198,544)(199,543)
(200,542)(201,551)(202,555)(203,554)(204,553)(205,552)(206,546)(207,550)
(208,549)(209,548)(210,547)(211,571)(212,575)(213,574)(214,573)(215,572)
(216,581)(217,585)(218,584)(219,583)(220,582)(221,576)(222,580)(223,579)
(224,578)(225,577)(226,586)(227,590)(228,589)(229,588)(230,587)(231,596)
(232,600)(233,599)(234,598)(235,597)(236,591)(237,595)(238,594)(239,593)
(240,592)(241,841)(242,845)(243,844)(244,843)(245,842)(246,851)(247,855)
(248,854)(249,853)(250,852)(251,846)(252,850)(253,849)(254,848)(255,847)
(256,856)(257,860)(258,859)(259,858)(260,857)(261,866)(262,870)(263,869)
(264,868)(265,867)(266,861)(267,865)(268,864)(269,863)(270,862)(271,886)
(272,890)(273,889)(274,888)(275,887)(276,896)(277,900)(278,899)(279,898)
(280,897)(281,891)(282,895)(283,894)(284,893)(285,892)(286,871)(287,875)
(288,874)(289,873)(290,872)(291,881)(292,885)(293,884)(294,883)(295,882)
(296,876)(297,880)(298,879)(299,878)(300,877)(301,916)(302,920)(303,919)
(304,918)(305,917)(306,926)(307,930)(308,929)(309,928)(310,927)(311,921)
(312,925)(313,924)(314,923)(315,922)(316,901)(317,905)(318,904)(319,903)
(320,902)(321,911)(322,915)(323,914)(324,913)(325,912)(326,906)(327,910)
(328,909)(329,908)(330,907)(331,931)(332,935)(333,934)(334,933)(335,932)
(336,941)(337,945)(338,944)(339,943)(340,942)(341,936)(342,940)(343,939)
(344,938)(345,937)(346,946)(347,950)(348,949)(349,948)(350,947)(351,956)
(352,960)(353,959)(354,958)(355,957)(356,951)(357,955)(358,954)(359,953)
(360,952)(361,721)(362,725)(363,724)(364,723)(365,722)(366,731)(367,735)
(368,734)(369,733)(370,732)(371,726)(372,730)(373,729)(374,728)(375,727)
(376,736)(377,740)(378,739)(379,738)(380,737)(381,746)(382,750)(383,749)
(384,748)(385,747)(386,741)(387,745)(388,744)(389,743)(390,742)(391,766)
(392,770)(393,769)(394,768)(395,767)(396,776)(397,780)(398,779)(399,778)
(400,777)(401,771)(402,775)(403,774)(404,773)(405,772)(406,751)(407,755)
(408,754)(409,753)(410,752)(411,761)(412,765)(413,764)(414,763)(415,762)
(416,756)(417,760)(418,759)(419,758)(420,757)(421,796)(422,800)(423,799)
(424,798)(425,797)(426,806)(427,810)(428,809)(429,808)(430,807)(431,801)
(432,805)(433,804)(434,803)(435,802)(436,781)(437,785)(438,784)(439,783)
(440,782)(441,791)(442,795)(443,794)(444,793)(445,792)(446,786)(447,790)
(448,789)(449,788)(450,787)(451,811)(452,815)(453,814)(454,813)(455,812)
(456,821)(457,825)(458,824)(459,823)(460,822)(461,816)(462,820)(463,819)
(464,818)(465,817)(466,826)(467,830)(468,829)(469,828)(470,827)(471,836)
(472,840)(473,839)(474,838)(475,837)(476,831)(477,835)(478,834)(479,833)
(480,832);
s3 := Sym(960)!(  1,127)(  2,126)(  3,130)(  4,129)(  5,128)(  6,122)(  7,121)
(  8,125)(  9,124)( 10,123)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)
( 16,142)( 17,141)( 18,145)( 19,144)( 20,143)( 21,137)( 22,136)( 23,140)
( 24,139)( 25,138)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,157)
( 32,156)( 33,160)( 34,159)( 35,158)( 36,152)( 37,151)( 38,155)( 39,154)
( 40,153)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,172)( 47,171)
( 48,175)( 49,174)( 50,173)( 51,167)( 52,166)( 53,170)( 54,169)( 55,168)
( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,187)( 62,186)( 63,190)
( 64,189)( 65,188)( 66,182)( 67,181)( 68,185)( 69,184)( 70,183)( 71,192)
( 72,191)( 73,195)( 74,194)( 75,193)( 76,202)( 77,201)( 78,205)( 79,204)
( 80,203)( 81,197)( 82,196)( 83,200)( 84,199)( 85,198)( 86,207)( 87,206)
( 88,210)( 89,209)( 90,208)( 91,217)( 92,216)( 93,220)( 94,219)( 95,218)
( 96,212)( 97,211)( 98,215)( 99,214)(100,213)(101,222)(102,221)(103,225)
(104,224)(105,223)(106,232)(107,231)(108,235)(109,234)(110,233)(111,227)
(112,226)(113,230)(114,229)(115,228)(116,237)(117,236)(118,240)(119,239)
(120,238)(241,367)(242,366)(243,370)(244,369)(245,368)(246,362)(247,361)
(248,365)(249,364)(250,363)(251,372)(252,371)(253,375)(254,374)(255,373)
(256,382)(257,381)(258,385)(259,384)(260,383)(261,377)(262,376)(263,380)
(264,379)(265,378)(266,387)(267,386)(268,390)(269,389)(270,388)(271,397)
(272,396)(273,400)(274,399)(275,398)(276,392)(277,391)(278,395)(279,394)
(280,393)(281,402)(282,401)(283,405)(284,404)(285,403)(286,412)(287,411)
(288,415)(289,414)(290,413)(291,407)(292,406)(293,410)(294,409)(295,408)
(296,417)(297,416)(298,420)(299,419)(300,418)(301,427)(302,426)(303,430)
(304,429)(305,428)(306,422)(307,421)(308,425)(309,424)(310,423)(311,432)
(312,431)(313,435)(314,434)(315,433)(316,442)(317,441)(318,445)(319,444)
(320,443)(321,437)(322,436)(323,440)(324,439)(325,438)(326,447)(327,446)
(328,450)(329,449)(330,448)(331,457)(332,456)(333,460)(334,459)(335,458)
(336,452)(337,451)(338,455)(339,454)(340,453)(341,462)(342,461)(343,465)
(344,464)(345,463)(346,472)(347,471)(348,475)(349,474)(350,473)(351,467)
(352,466)(353,470)(354,469)(355,468)(356,477)(357,476)(358,480)(359,479)
(360,478)(481,607)(482,606)(483,610)(484,609)(485,608)(486,602)(487,601)
(488,605)(489,604)(490,603)(491,612)(492,611)(493,615)(494,614)(495,613)
(496,622)(497,621)(498,625)(499,624)(500,623)(501,617)(502,616)(503,620)
(504,619)(505,618)(506,627)(507,626)(508,630)(509,629)(510,628)(511,637)
(512,636)(513,640)(514,639)(515,638)(516,632)(517,631)(518,635)(519,634)
(520,633)(521,642)(522,641)(523,645)(524,644)(525,643)(526,652)(527,651)
(528,655)(529,654)(530,653)(531,647)(532,646)(533,650)(534,649)(535,648)
(536,657)(537,656)(538,660)(539,659)(540,658)(541,667)(542,666)(543,670)
(544,669)(545,668)(546,662)(547,661)(548,665)(549,664)(550,663)(551,672)
(552,671)(553,675)(554,674)(555,673)(556,682)(557,681)(558,685)(559,684)
(560,683)(561,677)(562,676)(563,680)(564,679)(565,678)(566,687)(567,686)
(568,690)(569,689)(570,688)(571,697)(572,696)(573,700)(574,699)(575,698)
(576,692)(577,691)(578,695)(579,694)(580,693)(581,702)(582,701)(583,705)
(584,704)(585,703)(586,712)(587,711)(588,715)(589,714)(590,713)(591,707)
(592,706)(593,710)(594,709)(595,708)(596,717)(597,716)(598,720)(599,719)
(600,718)(721,847)(722,846)(723,850)(724,849)(725,848)(726,842)(727,841)
(728,845)(729,844)(730,843)(731,852)(732,851)(733,855)(734,854)(735,853)
(736,862)(737,861)(738,865)(739,864)(740,863)(741,857)(742,856)(743,860)
(744,859)(745,858)(746,867)(747,866)(748,870)(749,869)(750,868)(751,877)
(752,876)(753,880)(754,879)(755,878)(756,872)(757,871)(758,875)(759,874)
(760,873)(761,882)(762,881)(763,885)(764,884)(765,883)(766,892)(767,891)
(768,895)(769,894)(770,893)(771,887)(772,886)(773,890)(774,889)(775,888)
(776,897)(777,896)(778,900)(779,899)(780,898)(781,907)(782,906)(783,910)
(784,909)(785,908)(786,902)(787,901)(788,905)(789,904)(790,903)(791,912)
(792,911)(793,915)(794,914)(795,913)(796,922)(797,921)(798,925)(799,924)
(800,923)(801,917)(802,916)(803,920)(804,919)(805,918)(806,927)(807,926)
(808,930)(809,929)(810,928)(811,937)(812,936)(813,940)(814,939)(815,938)
(816,932)(817,931)(818,935)(819,934)(820,933)(821,942)(822,941)(823,945)
(824,944)(825,943)(826,952)(827,951)(828,955)(829,954)(830,953)(831,947)
(832,946)(833,950)(834,949)(835,948)(836,957)(837,956)(838,960)(839,959)
(840,958);
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

References : None.
to this polytope