Polytope of Type {30,8,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,8,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150654)
Rank : 4
Schlafli Type : {30,8,4}
Number of vertices, edges, etc : 30, 120, 16, 4
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 : {30,4,4}*960
   3-fold quotients : {10,8,4}*640b
   4-fold quotients : {30,2,4}*480, {30,4,2}*480a
   5-fold quotients : {6,8,4}*384b
   6-fold quotients : {10,4,4}*320
   8-fold quotients : {15,2,4}*240, {30,2,2}*240
   10-fold quotients : {6,4,4}*192
   12-fold quotients : {10,2,4}*160, {10,4,2}*160
   15-fold quotients : {2,8,4}*128b
   16-fold quotients : {15,2,2}*120
   20-fold quotients : {6,2,4}*96, {6,4,2}*96a
   24-fold quotients : {5,2,4}*80, {10,2,2}*80
   30-fold quotients : {2,4,4}*64
   40-fold quotients : {3,2,4}*48, {6,2,2}*48
   48-fold quotients : {5,2,2}*40
   60-fold quotients : {2,2,4}*32, {2,4,2}*32
   80-fold quotients : {3,2,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  1,121)(  2,125)(  3,124)(  4,123)(  5,122)(  6,131)(  7,135)(  8,134)
(  9,133)( 10,132)( 11,126)( 12,130)( 13,129)( 14,128)( 15,127)( 16,136)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,146)( 22,150)( 23,149)( 24,148)
( 25,147)( 26,141)( 27,145)( 28,144)( 29,143)( 30,142)( 31,151)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,161)( 37,165)( 38,164)( 39,163)( 40,162)
( 41,156)( 42,160)( 43,159)( 44,158)( 45,157)( 46,166)( 47,170)( 48,169)
( 49,168)( 50,167)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)( 56,171)
( 57,175)( 58,174)( 59,173)( 60,172)( 61,181)( 62,185)( 63,184)( 64,183)
( 65,182)( 66,191)( 67,195)( 68,194)( 69,193)( 70,192)( 71,186)( 72,190)
( 73,189)( 74,188)( 75,187)( 76,196)( 77,200)( 78,199)( 79,198)( 80,197)
( 81,206)( 82,210)( 83,209)( 84,208)( 85,207)( 86,201)( 87,205)( 88,204)
( 89,203)( 90,202)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)( 96,221)
( 97,225)( 98,224)( 99,223)(100,222)(101,216)(102,220)(103,219)(104,218)
(105,217)(106,226)(107,230)(108,229)(109,228)(110,227)(111,236)(112,240)
(113,239)(114,238)(115,237)(116,231)(117,235)(118,234)(119,233)(120,232)
(241,361)(242,365)(243,364)(244,363)(245,362)(246,371)(247,375)(248,374)
(249,373)(250,372)(251,366)(252,370)(253,369)(254,368)(255,367)(256,376)
(257,380)(258,379)(259,378)(260,377)(261,386)(262,390)(263,389)(264,388)
(265,387)(266,381)(267,385)(268,384)(269,383)(270,382)(271,391)(272,395)
(273,394)(274,393)(275,392)(276,401)(277,405)(278,404)(279,403)(280,402)
(281,396)(282,400)(283,399)(284,398)(285,397)(286,406)(287,410)(288,409)
(289,408)(290,407)(291,416)(292,420)(293,419)(294,418)(295,417)(296,411)
(297,415)(298,414)(299,413)(300,412)(301,421)(302,425)(303,424)(304,423)
(305,422)(306,431)(307,435)(308,434)(309,433)(310,432)(311,426)(312,430)
(313,429)(314,428)(315,427)(316,436)(317,440)(318,439)(319,438)(320,437)
(321,446)(322,450)(323,449)(324,448)(325,447)(326,441)(327,445)(328,444)
(329,443)(330,442)(331,451)(332,455)(333,454)(334,453)(335,452)(336,461)
(337,465)(338,464)(339,463)(340,462)(341,456)(342,460)(343,459)(344,458)
(345,457)(346,466)(347,470)(348,469)(349,468)(350,467)(351,476)(352,480)
(353,479)(354,478)(355,477)(356,471)(357,475)(358,474)(359,473)(360,472)
(481,601)(482,605)(483,604)(484,603)(485,602)(486,611)(487,615)(488,614)
(489,613)(490,612)(491,606)(492,610)(493,609)(494,608)(495,607)(496,616)
(497,620)(498,619)(499,618)(500,617)(501,626)(502,630)(503,629)(504,628)
(505,627)(506,621)(507,625)(508,624)(509,623)(510,622)(511,631)(512,635)
(513,634)(514,633)(515,632)(516,641)(517,645)(518,644)(519,643)(520,642)
(521,636)(522,640)(523,639)(524,638)(525,637)(526,646)(527,650)(528,649)
(529,648)(530,647)(531,656)(532,660)(533,659)(534,658)(535,657)(536,651)
(537,655)(538,654)(539,653)(540,652)(541,661)(542,665)(543,664)(544,663)
(545,662)(546,671)(547,675)(548,674)(549,673)(550,672)(551,666)(552,670)
(553,669)(554,668)(555,667)(556,676)(557,680)(558,679)(559,678)(560,677)
(561,686)(562,690)(563,689)(564,688)(565,687)(566,681)(567,685)(568,684)
(569,683)(570,682)(571,691)(572,695)(573,694)(574,693)(575,692)(576,701)
(577,705)(578,704)(579,703)(580,702)(581,696)(582,700)(583,699)(584,698)
(585,697)(586,706)(587,710)(588,709)(589,708)(590,707)(591,716)(592,720)
(593,719)(594,718)(595,717)(596,711)(597,715)(598,714)(599,713)(600,712)
(721,841)(722,845)(723,844)(724,843)(725,842)(726,851)(727,855)(728,854)
(729,853)(730,852)(731,846)(732,850)(733,849)(734,848)(735,847)(736,856)
(737,860)(738,859)(739,858)(740,857)(741,866)(742,870)(743,869)(744,868)
(745,867)(746,861)(747,865)(748,864)(749,863)(750,862)(751,871)(752,875)
(753,874)(754,873)(755,872)(756,881)(757,885)(758,884)(759,883)(760,882)
(761,876)(762,880)(763,879)(764,878)(765,877)(766,886)(767,890)(768,889)
(769,888)(770,887)(771,896)(772,900)(773,899)(774,898)(775,897)(776,891)
(777,895)(778,894)(779,893)(780,892)(781,901)(782,905)(783,904)(784,903)
(785,902)(786,911)(787,915)(788,914)(789,913)(790,912)(791,906)(792,910)
(793,909)(794,908)(795,907)(796,916)(797,920)(798,919)(799,918)(800,917)
(801,926)(802,930)(803,929)(804,928)(805,927)(806,921)(807,925)(808,924)
(809,923)(810,922)(811,931)(812,935)(813,934)(814,933)(815,932)(816,941)
(817,945)(818,944)(819,943)(820,942)(821,936)(822,940)(823,939)(824,938)
(825,937)(826,946)(827,950)(828,949)(829,948)(830,947)(831,956)(832,960)
(833,959)(834,958)(835,957)(836,951)(837,955)(838,954)(839,953)(840,952);;
s1 := (  1,607)(  2,606)(  3,610)(  4,609)(  5,608)(  6,602)(  7,601)(  8,605)
(  9,604)( 10,603)( 11,612)( 12,611)( 13,615)( 14,614)( 15,613)( 16,622)
( 17,621)( 18,625)( 19,624)( 20,623)( 21,617)( 22,616)( 23,620)( 24,619)
( 25,618)( 26,627)( 27,626)( 28,630)( 29,629)( 30,628)( 31,652)( 32,651)
( 33,655)( 34,654)( 35,653)( 36,647)( 37,646)( 38,650)( 39,649)( 40,648)
( 41,657)( 42,656)( 43,660)( 44,659)( 45,658)( 46,637)( 47,636)( 48,640)
( 49,639)( 50,638)( 51,632)( 52,631)( 53,635)( 54,634)( 55,633)( 56,642)
( 57,641)( 58,645)( 59,644)( 60,643)( 61,682)( 62,681)( 63,685)( 64,684)
( 65,683)( 66,677)( 67,676)( 68,680)( 69,679)( 70,678)( 71,687)( 72,686)
( 73,690)( 74,689)( 75,688)( 76,667)( 77,666)( 78,670)( 79,669)( 80,668)
( 81,662)( 82,661)( 83,665)( 84,664)( 85,663)( 86,672)( 87,671)( 88,675)
( 89,674)( 90,673)( 91,697)( 92,696)( 93,700)( 94,699)( 95,698)( 96,692)
( 97,691)( 98,695)( 99,694)(100,693)(101,702)(102,701)(103,705)(104,704)
(105,703)(106,712)(107,711)(108,715)(109,714)(110,713)(111,707)(112,706)
(113,710)(114,709)(115,708)(116,717)(117,716)(118,720)(119,719)(120,718)
(121,487)(122,486)(123,490)(124,489)(125,488)(126,482)(127,481)(128,485)
(129,484)(130,483)(131,492)(132,491)(133,495)(134,494)(135,493)(136,502)
(137,501)(138,505)(139,504)(140,503)(141,497)(142,496)(143,500)(144,499)
(145,498)(146,507)(147,506)(148,510)(149,509)(150,508)(151,532)(152,531)
(153,535)(154,534)(155,533)(156,527)(157,526)(158,530)(159,529)(160,528)
(161,537)(162,536)(163,540)(164,539)(165,538)(166,517)(167,516)(168,520)
(169,519)(170,518)(171,512)(172,511)(173,515)(174,514)(175,513)(176,522)
(177,521)(178,525)(179,524)(180,523)(181,562)(182,561)(183,565)(184,564)
(185,563)(186,557)(187,556)(188,560)(189,559)(190,558)(191,567)(192,566)
(193,570)(194,569)(195,568)(196,547)(197,546)(198,550)(199,549)(200,548)
(201,542)(202,541)(203,545)(204,544)(205,543)(206,552)(207,551)(208,555)
(209,554)(210,553)(211,577)(212,576)(213,580)(214,579)(215,578)(216,572)
(217,571)(218,575)(219,574)(220,573)(221,582)(222,581)(223,585)(224,584)
(225,583)(226,592)(227,591)(228,595)(229,594)(230,593)(231,587)(232,586)
(233,590)(234,589)(235,588)(236,597)(237,596)(238,600)(239,599)(240,598)
(241,847)(242,846)(243,850)(244,849)(245,848)(246,842)(247,841)(248,845)
(249,844)(250,843)(251,852)(252,851)(253,855)(254,854)(255,853)(256,862)
(257,861)(258,865)(259,864)(260,863)(261,857)(262,856)(263,860)(264,859)
(265,858)(266,867)(267,866)(268,870)(269,869)(270,868)(271,892)(272,891)
(273,895)(274,894)(275,893)(276,887)(277,886)(278,890)(279,889)(280,888)
(281,897)(282,896)(283,900)(284,899)(285,898)(286,877)(287,876)(288,880)
(289,879)(290,878)(291,872)(292,871)(293,875)(294,874)(295,873)(296,882)
(297,881)(298,885)(299,884)(300,883)(301,922)(302,921)(303,925)(304,924)
(305,923)(306,917)(307,916)(308,920)(309,919)(310,918)(311,927)(312,926)
(313,930)(314,929)(315,928)(316,907)(317,906)(318,910)(319,909)(320,908)
(321,902)(322,901)(323,905)(324,904)(325,903)(326,912)(327,911)(328,915)
(329,914)(330,913)(331,937)(332,936)(333,940)(334,939)(335,938)(336,932)
(337,931)(338,935)(339,934)(340,933)(341,942)(342,941)(343,945)(344,944)
(345,943)(346,952)(347,951)(348,955)(349,954)(350,953)(351,947)(352,946)
(353,950)(354,949)(355,948)(356,957)(357,956)(358,960)(359,959)(360,958)
(361,727)(362,726)(363,730)(364,729)(365,728)(366,722)(367,721)(368,725)
(369,724)(370,723)(371,732)(372,731)(373,735)(374,734)(375,733)(376,742)
(377,741)(378,745)(379,744)(380,743)(381,737)(382,736)(383,740)(384,739)
(385,738)(386,747)(387,746)(388,750)(389,749)(390,748)(391,772)(392,771)
(393,775)(394,774)(395,773)(396,767)(397,766)(398,770)(399,769)(400,768)
(401,777)(402,776)(403,780)(404,779)(405,778)(406,757)(407,756)(408,760)
(409,759)(410,758)(411,752)(412,751)(413,755)(414,754)(415,753)(416,762)
(417,761)(418,765)(419,764)(420,763)(421,802)(422,801)(423,805)(424,804)
(425,803)(426,797)(427,796)(428,800)(429,799)(430,798)(431,807)(432,806)
(433,810)(434,809)(435,808)(436,787)(437,786)(438,790)(439,789)(440,788)
(441,782)(442,781)(443,785)(444,784)(445,783)(446,792)(447,791)(448,795)
(449,794)(450,793)(451,817)(452,816)(453,820)(454,819)(455,818)(456,812)
(457,811)(458,815)(459,814)(460,813)(461,822)(462,821)(463,825)(464,824)
(465,823)(466,832)(467,831)(468,835)(469,834)(470,833)(471,827)(472,826)
(473,830)(474,829)(475,828)(476,837)(477,836)(478,840)(479,839)(480,838);;
s2 := ( 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);;
s3 := (  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);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(960)!(  1,121)(  2,125)(  3,124)(  4,123)(  5,122)(  6,131)(  7,135)
(  8,134)(  9,133)( 10,132)( 11,126)( 12,130)( 13,129)( 14,128)( 15,127)
( 16,136)( 17,140)( 18,139)( 19,138)( 20,137)( 21,146)( 22,150)( 23,149)
( 24,148)( 25,147)( 26,141)( 27,145)( 28,144)( 29,143)( 30,142)( 31,151)
( 32,155)( 33,154)( 34,153)( 35,152)( 36,161)( 37,165)( 38,164)( 39,163)
( 40,162)( 41,156)( 42,160)( 43,159)( 44,158)( 45,157)( 46,166)( 47,170)
( 48,169)( 49,168)( 50,167)( 51,176)( 52,180)( 53,179)( 54,178)( 55,177)
( 56,171)( 57,175)( 58,174)( 59,173)( 60,172)( 61,181)( 62,185)( 63,184)
( 64,183)( 65,182)( 66,191)( 67,195)( 68,194)( 69,193)( 70,192)( 71,186)
( 72,190)( 73,189)( 74,188)( 75,187)( 76,196)( 77,200)( 78,199)( 79,198)
( 80,197)( 81,206)( 82,210)( 83,209)( 84,208)( 85,207)( 86,201)( 87,205)
( 88,204)( 89,203)( 90,202)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)
( 96,221)( 97,225)( 98,224)( 99,223)(100,222)(101,216)(102,220)(103,219)
(104,218)(105,217)(106,226)(107,230)(108,229)(109,228)(110,227)(111,236)
(112,240)(113,239)(114,238)(115,237)(116,231)(117,235)(118,234)(119,233)
(120,232)(241,361)(242,365)(243,364)(244,363)(245,362)(246,371)(247,375)
(248,374)(249,373)(250,372)(251,366)(252,370)(253,369)(254,368)(255,367)
(256,376)(257,380)(258,379)(259,378)(260,377)(261,386)(262,390)(263,389)
(264,388)(265,387)(266,381)(267,385)(268,384)(269,383)(270,382)(271,391)
(272,395)(273,394)(274,393)(275,392)(276,401)(277,405)(278,404)(279,403)
(280,402)(281,396)(282,400)(283,399)(284,398)(285,397)(286,406)(287,410)
(288,409)(289,408)(290,407)(291,416)(292,420)(293,419)(294,418)(295,417)
(296,411)(297,415)(298,414)(299,413)(300,412)(301,421)(302,425)(303,424)
(304,423)(305,422)(306,431)(307,435)(308,434)(309,433)(310,432)(311,426)
(312,430)(313,429)(314,428)(315,427)(316,436)(317,440)(318,439)(319,438)
(320,437)(321,446)(322,450)(323,449)(324,448)(325,447)(326,441)(327,445)
(328,444)(329,443)(330,442)(331,451)(332,455)(333,454)(334,453)(335,452)
(336,461)(337,465)(338,464)(339,463)(340,462)(341,456)(342,460)(343,459)
(344,458)(345,457)(346,466)(347,470)(348,469)(349,468)(350,467)(351,476)
(352,480)(353,479)(354,478)(355,477)(356,471)(357,475)(358,474)(359,473)
(360,472)(481,601)(482,605)(483,604)(484,603)(485,602)(486,611)(487,615)
(488,614)(489,613)(490,612)(491,606)(492,610)(493,609)(494,608)(495,607)
(496,616)(497,620)(498,619)(499,618)(500,617)(501,626)(502,630)(503,629)
(504,628)(505,627)(506,621)(507,625)(508,624)(509,623)(510,622)(511,631)
(512,635)(513,634)(514,633)(515,632)(516,641)(517,645)(518,644)(519,643)
(520,642)(521,636)(522,640)(523,639)(524,638)(525,637)(526,646)(527,650)
(528,649)(529,648)(530,647)(531,656)(532,660)(533,659)(534,658)(535,657)
(536,651)(537,655)(538,654)(539,653)(540,652)(541,661)(542,665)(543,664)
(544,663)(545,662)(546,671)(547,675)(548,674)(549,673)(550,672)(551,666)
(552,670)(553,669)(554,668)(555,667)(556,676)(557,680)(558,679)(559,678)
(560,677)(561,686)(562,690)(563,689)(564,688)(565,687)(566,681)(567,685)
(568,684)(569,683)(570,682)(571,691)(572,695)(573,694)(574,693)(575,692)
(576,701)(577,705)(578,704)(579,703)(580,702)(581,696)(582,700)(583,699)
(584,698)(585,697)(586,706)(587,710)(588,709)(589,708)(590,707)(591,716)
(592,720)(593,719)(594,718)(595,717)(596,711)(597,715)(598,714)(599,713)
(600,712)(721,841)(722,845)(723,844)(724,843)(725,842)(726,851)(727,855)
(728,854)(729,853)(730,852)(731,846)(732,850)(733,849)(734,848)(735,847)
(736,856)(737,860)(738,859)(739,858)(740,857)(741,866)(742,870)(743,869)
(744,868)(745,867)(746,861)(747,865)(748,864)(749,863)(750,862)(751,871)
(752,875)(753,874)(754,873)(755,872)(756,881)(757,885)(758,884)(759,883)
(760,882)(761,876)(762,880)(763,879)(764,878)(765,877)(766,886)(767,890)
(768,889)(769,888)(770,887)(771,896)(772,900)(773,899)(774,898)(775,897)
(776,891)(777,895)(778,894)(779,893)(780,892)(781,901)(782,905)(783,904)
(784,903)(785,902)(786,911)(787,915)(788,914)(789,913)(790,912)(791,906)
(792,910)(793,909)(794,908)(795,907)(796,916)(797,920)(798,919)(799,918)
(800,917)(801,926)(802,930)(803,929)(804,928)(805,927)(806,921)(807,925)
(808,924)(809,923)(810,922)(811,931)(812,935)(813,934)(814,933)(815,932)
(816,941)(817,945)(818,944)(819,943)(820,942)(821,936)(822,940)(823,939)
(824,938)(825,937)(826,946)(827,950)(828,949)(829,948)(830,947)(831,956)
(832,960)(833,959)(834,958)(835,957)(836,951)(837,955)(838,954)(839,953)
(840,952);
s1 := Sym(960)!(  1,607)(  2,606)(  3,610)(  4,609)(  5,608)(  6,602)(  7,601)
(  8,605)(  9,604)( 10,603)( 11,612)( 12,611)( 13,615)( 14,614)( 15,613)
( 16,622)( 17,621)( 18,625)( 19,624)( 20,623)( 21,617)( 22,616)( 23,620)
( 24,619)( 25,618)( 26,627)( 27,626)( 28,630)( 29,629)( 30,628)( 31,652)
( 32,651)( 33,655)( 34,654)( 35,653)( 36,647)( 37,646)( 38,650)( 39,649)
( 40,648)( 41,657)( 42,656)( 43,660)( 44,659)( 45,658)( 46,637)( 47,636)
( 48,640)( 49,639)( 50,638)( 51,632)( 52,631)( 53,635)( 54,634)( 55,633)
( 56,642)( 57,641)( 58,645)( 59,644)( 60,643)( 61,682)( 62,681)( 63,685)
( 64,684)( 65,683)( 66,677)( 67,676)( 68,680)( 69,679)( 70,678)( 71,687)
( 72,686)( 73,690)( 74,689)( 75,688)( 76,667)( 77,666)( 78,670)( 79,669)
( 80,668)( 81,662)( 82,661)( 83,665)( 84,664)( 85,663)( 86,672)( 87,671)
( 88,675)( 89,674)( 90,673)( 91,697)( 92,696)( 93,700)( 94,699)( 95,698)
( 96,692)( 97,691)( 98,695)( 99,694)(100,693)(101,702)(102,701)(103,705)
(104,704)(105,703)(106,712)(107,711)(108,715)(109,714)(110,713)(111,707)
(112,706)(113,710)(114,709)(115,708)(116,717)(117,716)(118,720)(119,719)
(120,718)(121,487)(122,486)(123,490)(124,489)(125,488)(126,482)(127,481)
(128,485)(129,484)(130,483)(131,492)(132,491)(133,495)(134,494)(135,493)
(136,502)(137,501)(138,505)(139,504)(140,503)(141,497)(142,496)(143,500)
(144,499)(145,498)(146,507)(147,506)(148,510)(149,509)(150,508)(151,532)
(152,531)(153,535)(154,534)(155,533)(156,527)(157,526)(158,530)(159,529)
(160,528)(161,537)(162,536)(163,540)(164,539)(165,538)(166,517)(167,516)
(168,520)(169,519)(170,518)(171,512)(172,511)(173,515)(174,514)(175,513)
(176,522)(177,521)(178,525)(179,524)(180,523)(181,562)(182,561)(183,565)
(184,564)(185,563)(186,557)(187,556)(188,560)(189,559)(190,558)(191,567)
(192,566)(193,570)(194,569)(195,568)(196,547)(197,546)(198,550)(199,549)
(200,548)(201,542)(202,541)(203,545)(204,544)(205,543)(206,552)(207,551)
(208,555)(209,554)(210,553)(211,577)(212,576)(213,580)(214,579)(215,578)
(216,572)(217,571)(218,575)(219,574)(220,573)(221,582)(222,581)(223,585)
(224,584)(225,583)(226,592)(227,591)(228,595)(229,594)(230,593)(231,587)
(232,586)(233,590)(234,589)(235,588)(236,597)(237,596)(238,600)(239,599)
(240,598)(241,847)(242,846)(243,850)(244,849)(245,848)(246,842)(247,841)
(248,845)(249,844)(250,843)(251,852)(252,851)(253,855)(254,854)(255,853)
(256,862)(257,861)(258,865)(259,864)(260,863)(261,857)(262,856)(263,860)
(264,859)(265,858)(266,867)(267,866)(268,870)(269,869)(270,868)(271,892)
(272,891)(273,895)(274,894)(275,893)(276,887)(277,886)(278,890)(279,889)
(280,888)(281,897)(282,896)(283,900)(284,899)(285,898)(286,877)(287,876)
(288,880)(289,879)(290,878)(291,872)(292,871)(293,875)(294,874)(295,873)
(296,882)(297,881)(298,885)(299,884)(300,883)(301,922)(302,921)(303,925)
(304,924)(305,923)(306,917)(307,916)(308,920)(309,919)(310,918)(311,927)
(312,926)(313,930)(314,929)(315,928)(316,907)(317,906)(318,910)(319,909)
(320,908)(321,902)(322,901)(323,905)(324,904)(325,903)(326,912)(327,911)
(328,915)(329,914)(330,913)(331,937)(332,936)(333,940)(334,939)(335,938)
(336,932)(337,931)(338,935)(339,934)(340,933)(341,942)(342,941)(343,945)
(344,944)(345,943)(346,952)(347,951)(348,955)(349,954)(350,953)(351,947)
(352,946)(353,950)(354,949)(355,948)(356,957)(357,956)(358,960)(359,959)
(360,958)(361,727)(362,726)(363,730)(364,729)(365,728)(366,722)(367,721)
(368,725)(369,724)(370,723)(371,732)(372,731)(373,735)(374,734)(375,733)
(376,742)(377,741)(378,745)(379,744)(380,743)(381,737)(382,736)(383,740)
(384,739)(385,738)(386,747)(387,746)(388,750)(389,749)(390,748)(391,772)
(392,771)(393,775)(394,774)(395,773)(396,767)(397,766)(398,770)(399,769)
(400,768)(401,777)(402,776)(403,780)(404,779)(405,778)(406,757)(407,756)
(408,760)(409,759)(410,758)(411,752)(412,751)(413,755)(414,754)(415,753)
(416,762)(417,761)(418,765)(419,764)(420,763)(421,802)(422,801)(423,805)
(424,804)(425,803)(426,797)(427,796)(428,800)(429,799)(430,798)(431,807)
(432,806)(433,810)(434,809)(435,808)(436,787)(437,786)(438,790)(439,789)
(440,788)(441,782)(442,781)(443,785)(444,784)(445,783)(446,792)(447,791)
(448,795)(449,794)(450,793)(451,817)(452,816)(453,820)(454,819)(455,818)
(456,812)(457,811)(458,815)(459,814)(460,813)(461,822)(462,821)(463,825)
(464,824)(465,823)(466,832)(467,831)(468,835)(469,834)(470,833)(471,827)
(472,826)(473,830)(474,829)(475,828)(476,837)(477,836)(478,840)(479,839)
(480,838);
s2 := 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);
s3 := 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);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope