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Polytope of Type {8,4,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,30}*1920a
Also Known As : {{8,4|2},{4,30|2}}. if this polytope has another name.
Group : SmallGroup(1920,148872)
Rank : 4
Schlafli Type : {8,4,30}
Number of vertices, edges, etc : 8, 16, 60, 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, {8,2,30}*960
   3-fold quotients : {8,4,10}*640a
   4-fold quotients : {8,2,15}*480, {2,4,30}*480a, {4,2,30}*480
   5-fold quotients : {8,4,6}*384a
   6-fold quotients : {4,4,10}*320, {8,2,10}*320
   8-fold quotients : {4,2,15}*240, {2,2,30}*240
   10-fold quotients : {4,4,6}*192, {8,2,6}*192
   12-fold quotients : {8,2,5}*160, {2,4,10}*160, {4,2,10}*160
   15-fold quotients : {8,4,2}*128a
   16-fold quotients : {2,2,15}*120
   20-fold quotients : {8,2,3}*96, {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, {8,2,2}*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 := (  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,486)(  7,487)(  8,488)
(  9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)
( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)( 24,504)
( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,511)( 32,512)
( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)( 40,520)
( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)( 48,528)
( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)( 56,536)
( 57,537)( 58,538)( 59,539)( 60,540)( 61,556)( 62,557)( 63,558)( 64,559)
( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)( 72,567)
( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)( 80,545)
( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)( 88,553)
( 89,554)( 90,555)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,591)
( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)(104,599)
(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)(112,577)
(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)(120,585)
(121,601)(122,602)(123,603)(124,604)(125,605)(126,606)(127,607)(128,608)
(129,609)(130,610)(131,611)(132,612)(133,613)(134,614)(135,615)(136,616)
(137,617)(138,618)(139,619)(140,620)(141,621)(142,622)(143,623)(144,624)
(145,625)(146,626)(147,627)(148,628)(149,629)(150,630)(151,631)(152,632)
(153,633)(154,634)(155,635)(156,636)(157,637)(158,638)(159,639)(160,640)
(161,641)(162,642)(163,643)(164,644)(165,645)(166,646)(167,647)(168,648)
(169,649)(170,650)(171,651)(172,652)(173,653)(174,654)(175,655)(176,656)
(177,657)(178,658)(179,659)(180,660)(181,676)(182,677)(183,678)(184,679)
(185,680)(186,681)(187,682)(188,683)(189,684)(190,685)(191,686)(192,687)
(193,688)(194,689)(195,690)(196,661)(197,662)(198,663)(199,664)(200,665)
(201,666)(202,667)(203,668)(204,669)(205,670)(206,671)(207,672)(208,673)
(209,674)(210,675)(211,706)(212,707)(213,708)(214,709)(215,710)(216,711)
(217,712)(218,713)(219,714)(220,715)(221,716)(222,717)(223,718)(224,719)
(225,720)(226,691)(227,692)(228,693)(229,694)(230,695)(231,696)(232,697)
(233,698)(234,699)(235,700)(236,701)(237,702)(238,703)(239,704)(240,705)
(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)(248,728)
(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)(256,736)
(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)(264,744)
(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,751)(272,752)
(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)(280,760)
(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)(288,768)
(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)(296,776)
(297,777)(298,778)(299,779)(300,780)(301,796)(302,797)(303,798)(304,799)
(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)(312,807)
(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)(320,785)
(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)(328,793)
(329,794)(330,795)(331,826)(332,827)(333,828)(334,829)(335,830)(336,831)
(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)(344,839)
(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)(352,817)
(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)(360,825)
(361,841)(362,842)(363,843)(364,844)(365,845)(366,846)(367,847)(368,848)
(369,849)(370,850)(371,851)(372,852)(373,853)(374,854)(375,855)(376,856)
(377,857)(378,858)(379,859)(380,860)(381,861)(382,862)(383,863)(384,864)
(385,865)(386,866)(387,867)(388,868)(389,869)(390,870)(391,871)(392,872)
(393,873)(394,874)(395,875)(396,876)(397,877)(398,878)(399,879)(400,880)
(401,881)(402,882)(403,883)(404,884)(405,885)(406,886)(407,887)(408,888)
(409,889)(410,890)(411,891)(412,892)(413,893)(414,894)(415,895)(416,896)
(417,897)(418,898)(419,899)(420,900)(421,916)(422,917)(423,918)(424,919)
(425,920)(426,921)(427,922)(428,923)(429,924)(430,925)(431,926)(432,927)
(433,928)(434,929)(435,930)(436,901)(437,902)(438,903)(439,904)(440,905)
(441,906)(442,907)(443,908)(444,909)(445,910)(446,911)(447,912)(448,913)
(449,914)(450,915)(451,946)(452,947)(453,948)(454,949)(455,950)(456,951)
(457,952)(458,953)(459,954)(460,955)(461,956)(462,957)(463,958)(464,959)
(465,960)(466,931)(467,932)(468,933)(469,934)(470,935)(471,936)(472,937)
(473,938)(474,939)(475,940)(476,941)(477,942)(478,943)(479,944)(480,945);;
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)(721,811)(722,812)(723,813)(724,814)
(725,815)(726,816)(727,817)(728,818)(729,819)(730,820)(731,821)(732,822)
(733,823)(734,824)(735,825)(736,826)(737,827)(738,828)(739,829)(740,830)
(741,831)(742,832)(743,833)(744,834)(745,835)(746,836)(747,837)(748,838)
(749,839)(750,840)(751,781)(752,782)(753,783)(754,784)(755,785)(756,786)
(757,787)(758,788)(759,789)(760,790)(761,791)(762,792)(763,793)(764,794)
(765,795)(766,796)(767,797)(768,798)(769,799)(770,800)(771,801)(772,802)
(773,803)(774,804)(775,805)(776,806)(777,807)(778,808)(779,809)(780,810)
(841,931)(842,932)(843,933)(844,934)(845,935)(846,936)(847,937)(848,938)
(849,939)(850,940)(851,941)(852,942)(853,943)(854,944)(855,945)(856,946)
(857,947)(858,948)(859,949)(860,950)(861,951)(862,952)(863,953)(864,954)
(865,955)(866,956)(867,957)(868,958)(869,959)(870,960)(871,901)(872,902)
(873,903)(874,904)(875,905)(876,906)(877,907)(878,908)(879,909)(880,910)
(881,911)(882,912)(883,913)(884,914)(885,915)(886,916)(887,917)(888,918)
(889,919)(890,920)(891,921)(892,922)(893,923)(894,924)(895,925)(896,926)
(897,927)(898,928)(899,929)(900,930);;
s2 := (  1,361)(  2,365)(  3,364)(  4,363)(  5,362)(  6,371)(  7,375)(  8,374)
(  9,373)( 10,372)( 11,366)( 12,370)( 13,369)( 14,368)( 15,367)( 16,376)
( 17,380)( 18,379)( 19,378)( 20,377)( 21,386)( 22,390)( 23,389)( 24,388)
( 25,387)( 26,381)( 27,385)( 28,384)( 29,383)( 30,382)( 31,391)( 32,395)
( 33,394)( 34,393)( 35,392)( 36,401)( 37,405)( 38,404)( 39,403)( 40,402)
( 41,396)( 42,400)( 43,399)( 44,398)( 45,397)( 46,406)( 47,410)( 48,409)
( 49,408)( 50,407)( 51,416)( 52,420)( 53,419)( 54,418)( 55,417)( 56,411)
( 57,415)( 58,414)( 59,413)( 60,412)( 61,421)( 62,425)( 63,424)( 64,423)
( 65,422)( 66,431)( 67,435)( 68,434)( 69,433)( 70,432)( 71,426)( 72,430)
( 73,429)( 74,428)( 75,427)( 76,436)( 77,440)( 78,439)( 79,438)( 80,437)
( 81,446)( 82,450)( 83,449)( 84,448)( 85,447)( 86,441)( 87,445)( 88,444)
( 89,443)( 90,442)( 91,451)( 92,455)( 93,454)( 94,453)( 95,452)( 96,461)
( 97,465)( 98,464)( 99,463)(100,462)(101,456)(102,460)(103,459)(104,458)
(105,457)(106,466)(107,470)(108,469)(109,468)(110,467)(111,476)(112,480)
(113,479)(114,478)(115,477)(116,471)(117,475)(118,474)(119,473)(120,472)
(121,241)(122,245)(123,244)(124,243)(125,242)(126,251)(127,255)(128,254)
(129,253)(130,252)(131,246)(132,250)(133,249)(134,248)(135,247)(136,256)
(137,260)(138,259)(139,258)(140,257)(141,266)(142,270)(143,269)(144,268)
(145,267)(146,261)(147,265)(148,264)(149,263)(150,262)(151,271)(152,275)
(153,274)(154,273)(155,272)(156,281)(157,285)(158,284)(159,283)(160,282)
(161,276)(162,280)(163,279)(164,278)(165,277)(166,286)(167,290)(168,289)
(169,288)(170,287)(171,296)(172,300)(173,299)(174,298)(175,297)(176,291)
(177,295)(178,294)(179,293)(180,292)(181,301)(182,305)(183,304)(184,303)
(185,302)(186,311)(187,315)(188,314)(189,313)(190,312)(191,306)(192,310)
(193,309)(194,308)(195,307)(196,316)(197,320)(198,319)(199,318)(200,317)
(201,326)(202,330)(203,329)(204,328)(205,327)(206,321)(207,325)(208,324)
(209,323)(210,322)(211,331)(212,335)(213,334)(214,333)(215,332)(216,341)
(217,345)(218,344)(219,343)(220,342)(221,336)(222,340)(223,339)(224,338)
(225,337)(226,346)(227,350)(228,349)(229,348)(230,347)(231,356)(232,360)
(233,359)(234,358)(235,357)(236,351)(237,355)(238,354)(239,353)(240,352)
(481,841)(482,845)(483,844)(484,843)(485,842)(486,851)(487,855)(488,854)
(489,853)(490,852)(491,846)(492,850)(493,849)(494,848)(495,847)(496,856)
(497,860)(498,859)(499,858)(500,857)(501,866)(502,870)(503,869)(504,868)
(505,867)(506,861)(507,865)(508,864)(509,863)(510,862)(511,871)(512,875)
(513,874)(514,873)(515,872)(516,881)(517,885)(518,884)(519,883)(520,882)
(521,876)(522,880)(523,879)(524,878)(525,877)(526,886)(527,890)(528,889)
(529,888)(530,887)(531,896)(532,900)(533,899)(534,898)(535,897)(536,891)
(537,895)(538,894)(539,893)(540,892)(541,901)(542,905)(543,904)(544,903)
(545,902)(546,911)(547,915)(548,914)(549,913)(550,912)(551,906)(552,910)
(553,909)(554,908)(555,907)(556,916)(557,920)(558,919)(559,918)(560,917)
(561,926)(562,930)(563,929)(564,928)(565,927)(566,921)(567,925)(568,924)
(569,923)(570,922)(571,931)(572,935)(573,934)(574,933)(575,932)(576,941)
(577,945)(578,944)(579,943)(580,942)(581,936)(582,940)(583,939)(584,938)
(585,937)(586,946)(587,950)(588,949)(589,948)(590,947)(591,956)(592,960)
(593,959)(594,958)(595,957)(596,951)(597,955)(598,954)(599,953)(600,952)
(601,721)(602,725)(603,724)(604,723)(605,722)(606,731)(607,735)(608,734)
(609,733)(610,732)(611,726)(612,730)(613,729)(614,728)(615,727)(616,736)
(617,740)(618,739)(619,738)(620,737)(621,746)(622,750)(623,749)(624,748)
(625,747)(626,741)(627,745)(628,744)(629,743)(630,742)(631,751)(632,755)
(633,754)(634,753)(635,752)(636,761)(637,765)(638,764)(639,763)(640,762)
(641,756)(642,760)(643,759)(644,758)(645,757)(646,766)(647,770)(648,769)
(649,768)(650,767)(651,776)(652,780)(653,779)(654,778)(655,777)(656,771)
(657,775)(658,774)(659,773)(660,772)(661,781)(662,785)(663,784)(664,783)
(665,782)(666,791)(667,795)(668,794)(669,793)(670,792)(671,786)(672,790)
(673,789)(674,788)(675,787)(676,796)(677,800)(678,799)(679,798)(680,797)
(681,806)(682,810)(683,809)(684,808)(685,807)(686,801)(687,805)(688,804)
(689,803)(690,802)(691,811)(692,815)(693,814)(694,813)(695,812)(696,821)
(697,825)(698,824)(699,823)(700,822)(701,816)(702,820)(703,819)(704,818)
(705,817)(706,826)(707,830)(708,829)(709,828)(710,827)(711,836)(712,840)
(713,839)(714,838)(715,837)(716,831)(717,835)(718,834)(719,833)(720,832);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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)!(  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,486)(  7,487)
(  8,488)(  9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)
( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)
( 24,504)( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,511)
( 32,512)( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)
( 40,520)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)
( 48,528)( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)
( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 61,556)( 62,557)( 63,558)
( 64,559)( 65,560)( 66,561)( 67,562)( 68,563)( 69,564)( 70,565)( 71,566)
( 72,567)( 73,568)( 74,569)( 75,570)( 76,541)( 77,542)( 78,543)( 79,544)
( 80,545)( 81,546)( 82,547)( 83,548)( 84,549)( 85,550)( 86,551)( 87,552)
( 88,553)( 89,554)( 90,555)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)
( 96,591)( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)
(104,599)(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)
(112,577)(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)
(120,585)(121,601)(122,602)(123,603)(124,604)(125,605)(126,606)(127,607)
(128,608)(129,609)(130,610)(131,611)(132,612)(133,613)(134,614)(135,615)
(136,616)(137,617)(138,618)(139,619)(140,620)(141,621)(142,622)(143,623)
(144,624)(145,625)(146,626)(147,627)(148,628)(149,629)(150,630)(151,631)
(152,632)(153,633)(154,634)(155,635)(156,636)(157,637)(158,638)(159,639)
(160,640)(161,641)(162,642)(163,643)(164,644)(165,645)(166,646)(167,647)
(168,648)(169,649)(170,650)(171,651)(172,652)(173,653)(174,654)(175,655)
(176,656)(177,657)(178,658)(179,659)(180,660)(181,676)(182,677)(183,678)
(184,679)(185,680)(186,681)(187,682)(188,683)(189,684)(190,685)(191,686)
(192,687)(193,688)(194,689)(195,690)(196,661)(197,662)(198,663)(199,664)
(200,665)(201,666)(202,667)(203,668)(204,669)(205,670)(206,671)(207,672)
(208,673)(209,674)(210,675)(211,706)(212,707)(213,708)(214,709)(215,710)
(216,711)(217,712)(218,713)(219,714)(220,715)(221,716)(222,717)(223,718)
(224,719)(225,720)(226,691)(227,692)(228,693)(229,694)(230,695)(231,696)
(232,697)(233,698)(234,699)(235,700)(236,701)(237,702)(238,703)(239,704)
(240,705)(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)
(248,728)(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)
(256,736)(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)
(264,744)(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,751)
(272,752)(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)
(280,760)(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)
(288,768)(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)
(296,776)(297,777)(298,778)(299,779)(300,780)(301,796)(302,797)(303,798)
(304,799)(305,800)(306,801)(307,802)(308,803)(309,804)(310,805)(311,806)
(312,807)(313,808)(314,809)(315,810)(316,781)(317,782)(318,783)(319,784)
(320,785)(321,786)(322,787)(323,788)(324,789)(325,790)(326,791)(327,792)
(328,793)(329,794)(330,795)(331,826)(332,827)(333,828)(334,829)(335,830)
(336,831)(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)
(344,839)(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)
(352,817)(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)
(360,825)(361,841)(362,842)(363,843)(364,844)(365,845)(366,846)(367,847)
(368,848)(369,849)(370,850)(371,851)(372,852)(373,853)(374,854)(375,855)
(376,856)(377,857)(378,858)(379,859)(380,860)(381,861)(382,862)(383,863)
(384,864)(385,865)(386,866)(387,867)(388,868)(389,869)(390,870)(391,871)
(392,872)(393,873)(394,874)(395,875)(396,876)(397,877)(398,878)(399,879)
(400,880)(401,881)(402,882)(403,883)(404,884)(405,885)(406,886)(407,887)
(408,888)(409,889)(410,890)(411,891)(412,892)(413,893)(414,894)(415,895)
(416,896)(417,897)(418,898)(419,899)(420,900)(421,916)(422,917)(423,918)
(424,919)(425,920)(426,921)(427,922)(428,923)(429,924)(430,925)(431,926)
(432,927)(433,928)(434,929)(435,930)(436,901)(437,902)(438,903)(439,904)
(440,905)(441,906)(442,907)(443,908)(444,909)(445,910)(446,911)(447,912)
(448,913)(449,914)(450,915)(451,946)(452,947)(453,948)(454,949)(455,950)
(456,951)(457,952)(458,953)(459,954)(460,955)(461,956)(462,957)(463,958)
(464,959)(465,960)(466,931)(467,932)(468,933)(469,934)(470,935)(471,936)
(472,937)(473,938)(474,939)(475,940)(476,941)(477,942)(478,943)(479,944)
(480,945);
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)(721,811)(722,812)(723,813)
(724,814)(725,815)(726,816)(727,817)(728,818)(729,819)(730,820)(731,821)
(732,822)(733,823)(734,824)(735,825)(736,826)(737,827)(738,828)(739,829)
(740,830)(741,831)(742,832)(743,833)(744,834)(745,835)(746,836)(747,837)
(748,838)(749,839)(750,840)(751,781)(752,782)(753,783)(754,784)(755,785)
(756,786)(757,787)(758,788)(759,789)(760,790)(761,791)(762,792)(763,793)
(764,794)(765,795)(766,796)(767,797)(768,798)(769,799)(770,800)(771,801)
(772,802)(773,803)(774,804)(775,805)(776,806)(777,807)(778,808)(779,809)
(780,810)(841,931)(842,932)(843,933)(844,934)(845,935)(846,936)(847,937)
(848,938)(849,939)(850,940)(851,941)(852,942)(853,943)(854,944)(855,945)
(856,946)(857,947)(858,948)(859,949)(860,950)(861,951)(862,952)(863,953)
(864,954)(865,955)(866,956)(867,957)(868,958)(869,959)(870,960)(871,901)
(872,902)(873,903)(874,904)(875,905)(876,906)(877,907)(878,908)(879,909)
(880,910)(881,911)(882,912)(883,913)(884,914)(885,915)(886,916)(887,917)
(888,918)(889,919)(890,920)(891,921)(892,922)(893,923)(894,924)(895,925)
(896,926)(897,927)(898,928)(899,929)(900,930);
s2 := Sym(960)!(  1,361)(  2,365)(  3,364)(  4,363)(  5,362)(  6,371)(  7,375)
(  8,374)(  9,373)( 10,372)( 11,366)( 12,370)( 13,369)( 14,368)( 15,367)
( 16,376)( 17,380)( 18,379)( 19,378)( 20,377)( 21,386)( 22,390)( 23,389)
( 24,388)( 25,387)( 26,381)( 27,385)( 28,384)( 29,383)( 30,382)( 31,391)
( 32,395)( 33,394)( 34,393)( 35,392)( 36,401)( 37,405)( 38,404)( 39,403)
( 40,402)( 41,396)( 42,400)( 43,399)( 44,398)( 45,397)( 46,406)( 47,410)
( 48,409)( 49,408)( 50,407)( 51,416)( 52,420)( 53,419)( 54,418)( 55,417)
( 56,411)( 57,415)( 58,414)( 59,413)( 60,412)( 61,421)( 62,425)( 63,424)
( 64,423)( 65,422)( 66,431)( 67,435)( 68,434)( 69,433)( 70,432)( 71,426)
( 72,430)( 73,429)( 74,428)( 75,427)( 76,436)( 77,440)( 78,439)( 79,438)
( 80,437)( 81,446)( 82,450)( 83,449)( 84,448)( 85,447)( 86,441)( 87,445)
( 88,444)( 89,443)( 90,442)( 91,451)( 92,455)( 93,454)( 94,453)( 95,452)
( 96,461)( 97,465)( 98,464)( 99,463)(100,462)(101,456)(102,460)(103,459)
(104,458)(105,457)(106,466)(107,470)(108,469)(109,468)(110,467)(111,476)
(112,480)(113,479)(114,478)(115,477)(116,471)(117,475)(118,474)(119,473)
(120,472)(121,241)(122,245)(123,244)(124,243)(125,242)(126,251)(127,255)
(128,254)(129,253)(130,252)(131,246)(132,250)(133,249)(134,248)(135,247)
(136,256)(137,260)(138,259)(139,258)(140,257)(141,266)(142,270)(143,269)
(144,268)(145,267)(146,261)(147,265)(148,264)(149,263)(150,262)(151,271)
(152,275)(153,274)(154,273)(155,272)(156,281)(157,285)(158,284)(159,283)
(160,282)(161,276)(162,280)(163,279)(164,278)(165,277)(166,286)(167,290)
(168,289)(169,288)(170,287)(171,296)(172,300)(173,299)(174,298)(175,297)
(176,291)(177,295)(178,294)(179,293)(180,292)(181,301)(182,305)(183,304)
(184,303)(185,302)(186,311)(187,315)(188,314)(189,313)(190,312)(191,306)
(192,310)(193,309)(194,308)(195,307)(196,316)(197,320)(198,319)(199,318)
(200,317)(201,326)(202,330)(203,329)(204,328)(205,327)(206,321)(207,325)
(208,324)(209,323)(210,322)(211,331)(212,335)(213,334)(214,333)(215,332)
(216,341)(217,345)(218,344)(219,343)(220,342)(221,336)(222,340)(223,339)
(224,338)(225,337)(226,346)(227,350)(228,349)(229,348)(230,347)(231,356)
(232,360)(233,359)(234,358)(235,357)(236,351)(237,355)(238,354)(239,353)
(240,352)(481,841)(482,845)(483,844)(484,843)(485,842)(486,851)(487,855)
(488,854)(489,853)(490,852)(491,846)(492,850)(493,849)(494,848)(495,847)
(496,856)(497,860)(498,859)(499,858)(500,857)(501,866)(502,870)(503,869)
(504,868)(505,867)(506,861)(507,865)(508,864)(509,863)(510,862)(511,871)
(512,875)(513,874)(514,873)(515,872)(516,881)(517,885)(518,884)(519,883)
(520,882)(521,876)(522,880)(523,879)(524,878)(525,877)(526,886)(527,890)
(528,889)(529,888)(530,887)(531,896)(532,900)(533,899)(534,898)(535,897)
(536,891)(537,895)(538,894)(539,893)(540,892)(541,901)(542,905)(543,904)
(544,903)(545,902)(546,911)(547,915)(548,914)(549,913)(550,912)(551,906)
(552,910)(553,909)(554,908)(555,907)(556,916)(557,920)(558,919)(559,918)
(560,917)(561,926)(562,930)(563,929)(564,928)(565,927)(566,921)(567,925)
(568,924)(569,923)(570,922)(571,931)(572,935)(573,934)(574,933)(575,932)
(576,941)(577,945)(578,944)(579,943)(580,942)(581,936)(582,940)(583,939)
(584,938)(585,937)(586,946)(587,950)(588,949)(589,948)(590,947)(591,956)
(592,960)(593,959)(594,958)(595,957)(596,951)(597,955)(598,954)(599,953)
(600,952)(601,721)(602,725)(603,724)(604,723)(605,722)(606,731)(607,735)
(608,734)(609,733)(610,732)(611,726)(612,730)(613,729)(614,728)(615,727)
(616,736)(617,740)(618,739)(619,738)(620,737)(621,746)(622,750)(623,749)
(624,748)(625,747)(626,741)(627,745)(628,744)(629,743)(630,742)(631,751)
(632,755)(633,754)(634,753)(635,752)(636,761)(637,765)(638,764)(639,763)
(640,762)(641,756)(642,760)(643,759)(644,758)(645,757)(646,766)(647,770)
(648,769)(649,768)(650,767)(651,776)(652,780)(653,779)(654,778)(655,777)
(656,771)(657,775)(658,774)(659,773)(660,772)(661,781)(662,785)(663,784)
(664,783)(665,782)(666,791)(667,795)(668,794)(669,793)(670,792)(671,786)
(672,790)(673,789)(674,788)(675,787)(676,796)(677,800)(678,799)(679,798)
(680,797)(681,806)(682,810)(683,809)(684,808)(685,807)(686,801)(687,805)
(688,804)(689,803)(690,802)(691,811)(692,815)(693,814)(694,813)(695,812)
(696,821)(697,825)(698,824)(699,823)(700,822)(701,816)(702,820)(703,819)
(704,818)(705,817)(706,826)(707,830)(708,829)(709,828)(710,827)(711,836)
(712,840)(713,839)(714,838)(715,837)(716,831)(717,835)(718,834)(719,833)
(720,832);
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*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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