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Polytope of Type {40,4,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,4,6}*1920a
Also Known As : {{40,4|2},{4,6|2}}. if this polytope has another name.
Group : SmallGroup(1920,148902)
Rank : 4
Schlafli Type : {40,4,6}
Number of vertices, edges, etc : 40, 80, 12, 6
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 : {20,4,6}*960, {40,2,6}*960
   3-fold quotients : {40,4,2}*640a
   4-fold quotients : {40,2,3}*480, {20,2,6}*480, {10,4,6}*480
   5-fold quotients : {8,4,6}*384a
   6-fold quotients : {20,4,2}*320, {40,2,2}*320
   8-fold quotients : {20,2,3}*240, {10,2,6}*240
   10-fold quotients : {4,4,6}*192, {8,2,6}*192
   12-fold quotients : {20,2,2}*160, {10,4,2}*160
   15-fold quotients : {8,4,2}*128a
   16-fold quotients : {5,2,6}*120, {10,2,3}*120
   20-fold quotients : {8,2,3}*96, {2,4,6}*96a, {4,2,6}*96
   24-fold quotients : {10,2,2}*80
   30-fold quotients : {4,4,2}*64, {8,2,2}*64
   32-fold quotients : {5,2,3}*60
   40-fold quotients : {4,2,3}*48, {2,2,6}*48
   48-fold quotients : {5,2,2}*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)(  2,485)(  3,484)(  4,483)(  5,482)(  6,486)(  7,490)(  8,489)
(  9,488)( 10,487)( 11,491)( 12,495)( 13,494)( 14,493)( 15,492)( 16,496)
( 17,500)( 18,499)( 19,498)( 20,497)( 21,501)( 22,505)( 23,504)( 24,503)
( 25,502)( 26,506)( 27,510)( 28,509)( 29,508)( 30,507)( 31,511)( 32,515)
( 33,514)( 34,513)( 35,512)( 36,516)( 37,520)( 38,519)( 39,518)( 40,517)
( 41,521)( 42,525)( 43,524)( 44,523)( 45,522)( 46,526)( 47,530)( 48,529)
( 49,528)( 50,527)( 51,531)( 52,535)( 53,534)( 54,533)( 55,532)( 56,536)
( 57,540)( 58,539)( 59,538)( 60,537)( 61,556)( 62,560)( 63,559)( 64,558)
( 65,557)( 66,561)( 67,565)( 68,564)( 69,563)( 70,562)( 71,566)( 72,570)
( 73,569)( 74,568)( 75,567)( 76,541)( 77,545)( 78,544)( 79,543)( 80,542)
( 81,546)( 82,550)( 83,549)( 84,548)( 85,547)( 86,551)( 87,555)( 88,554)
( 89,553)( 90,552)( 91,586)( 92,590)( 93,589)( 94,588)( 95,587)( 96,591)
( 97,595)( 98,594)( 99,593)(100,592)(101,596)(102,600)(103,599)(104,598)
(105,597)(106,571)(107,575)(108,574)(109,573)(110,572)(111,576)(112,580)
(113,579)(114,578)(115,577)(116,581)(117,585)(118,584)(119,583)(120,582)
(121,601)(122,605)(123,604)(124,603)(125,602)(126,606)(127,610)(128,609)
(129,608)(130,607)(131,611)(132,615)(133,614)(134,613)(135,612)(136,616)
(137,620)(138,619)(139,618)(140,617)(141,621)(142,625)(143,624)(144,623)
(145,622)(146,626)(147,630)(148,629)(149,628)(150,627)(151,631)(152,635)
(153,634)(154,633)(155,632)(156,636)(157,640)(158,639)(159,638)(160,637)
(161,641)(162,645)(163,644)(164,643)(165,642)(166,646)(167,650)(168,649)
(169,648)(170,647)(171,651)(172,655)(173,654)(174,653)(175,652)(176,656)
(177,660)(178,659)(179,658)(180,657)(181,676)(182,680)(183,679)(184,678)
(185,677)(186,681)(187,685)(188,684)(189,683)(190,682)(191,686)(192,690)
(193,689)(194,688)(195,687)(196,661)(197,665)(198,664)(199,663)(200,662)
(201,666)(202,670)(203,669)(204,668)(205,667)(206,671)(207,675)(208,674)
(209,673)(210,672)(211,706)(212,710)(213,709)(214,708)(215,707)(216,711)
(217,715)(218,714)(219,713)(220,712)(221,716)(222,720)(223,719)(224,718)
(225,717)(226,691)(227,695)(228,694)(229,693)(230,692)(231,696)(232,700)
(233,699)(234,698)(235,697)(236,701)(237,705)(238,704)(239,703)(240,702)
(241,721)(242,725)(243,724)(244,723)(245,722)(246,726)(247,730)(248,729)
(249,728)(250,727)(251,731)(252,735)(253,734)(254,733)(255,732)(256,736)
(257,740)(258,739)(259,738)(260,737)(261,741)(262,745)(263,744)(264,743)
(265,742)(266,746)(267,750)(268,749)(269,748)(270,747)(271,751)(272,755)
(273,754)(274,753)(275,752)(276,756)(277,760)(278,759)(279,758)(280,757)
(281,761)(282,765)(283,764)(284,763)(285,762)(286,766)(287,770)(288,769)
(289,768)(290,767)(291,771)(292,775)(293,774)(294,773)(295,772)(296,776)
(297,780)(298,779)(299,778)(300,777)(301,796)(302,800)(303,799)(304,798)
(305,797)(306,801)(307,805)(308,804)(309,803)(310,802)(311,806)(312,810)
(313,809)(314,808)(315,807)(316,781)(317,785)(318,784)(319,783)(320,782)
(321,786)(322,790)(323,789)(324,788)(325,787)(326,791)(327,795)(328,794)
(329,793)(330,792)(331,826)(332,830)(333,829)(334,828)(335,827)(336,831)
(337,835)(338,834)(339,833)(340,832)(341,836)(342,840)(343,839)(344,838)
(345,837)(346,811)(347,815)(348,814)(349,813)(350,812)(351,816)(352,820)
(353,819)(354,818)(355,817)(356,821)(357,825)(358,824)(359,823)(360,822)
(361,841)(362,845)(363,844)(364,843)(365,842)(366,846)(367,850)(368,849)
(369,848)(370,847)(371,851)(372,855)(373,854)(374,853)(375,852)(376,856)
(377,860)(378,859)(379,858)(380,857)(381,861)(382,865)(383,864)(384,863)
(385,862)(386,866)(387,870)(388,869)(389,868)(390,867)(391,871)(392,875)
(393,874)(394,873)(395,872)(396,876)(397,880)(398,879)(399,878)(400,877)
(401,881)(402,885)(403,884)(404,883)(405,882)(406,886)(407,890)(408,889)
(409,888)(410,887)(411,891)(412,895)(413,894)(414,893)(415,892)(416,896)
(417,900)(418,899)(419,898)(420,897)(421,916)(422,920)(423,919)(424,918)
(425,917)(426,921)(427,925)(428,924)(429,923)(430,922)(431,926)(432,930)
(433,929)(434,928)(435,927)(436,901)(437,905)(438,904)(439,903)(440,902)
(441,906)(442,910)(443,909)(444,908)(445,907)(446,911)(447,915)(448,914)
(449,913)(450,912)(451,946)(452,950)(453,949)(454,948)(455,947)(456,951)
(457,955)(458,954)(459,953)(460,952)(461,956)(462,960)(463,959)(464,958)
(465,957)(466,931)(467,935)(468,934)(469,933)(470,932)(471,936)(472,940)
(473,939)(474,938)(475,937)(476,941)(477,945)(478,944)(479,943)(480,942);;
s1 := (  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)( 18, 20)
( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)( 38, 40)
( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)( 58, 60)
( 61, 77)( 62, 76)( 63, 80)( 64, 79)( 65, 78)( 66, 82)( 67, 81)( 68, 85)
( 69, 84)( 70, 83)( 71, 87)( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 91,107)
( 92,106)( 93,110)( 94,109)( 95,108)( 96,112)( 97,111)( 98,115)( 99,114)
(100,113)(101,117)(102,116)(103,120)(104,119)(105,118)(121,122)(123,125)
(126,127)(128,130)(131,132)(133,135)(136,137)(138,140)(141,142)(143,145)
(146,147)(148,150)(151,152)(153,155)(156,157)(158,160)(161,162)(163,165)
(166,167)(168,170)(171,172)(173,175)(176,177)(178,180)(181,197)(182,196)
(183,200)(184,199)(185,198)(186,202)(187,201)(188,205)(189,204)(190,203)
(191,207)(192,206)(193,210)(194,209)(195,208)(211,227)(212,226)(213,230)
(214,229)(215,228)(216,232)(217,231)(218,235)(219,234)(220,233)(221,237)
(222,236)(223,240)(224,239)(225,238)(241,272)(242,271)(243,275)(244,274)
(245,273)(246,277)(247,276)(248,280)(249,279)(250,278)(251,282)(252,281)
(253,285)(254,284)(255,283)(256,287)(257,286)(258,290)(259,289)(260,288)
(261,292)(262,291)(263,295)(264,294)(265,293)(266,297)(267,296)(268,300)
(269,299)(270,298)(301,347)(302,346)(303,350)(304,349)(305,348)(306,352)
(307,351)(308,355)(309,354)(310,353)(311,357)(312,356)(313,360)(314,359)
(315,358)(316,332)(317,331)(318,335)(319,334)(320,333)(321,337)(322,336)
(323,340)(324,339)(325,338)(326,342)(327,341)(328,345)(329,344)(330,343)
(361,392)(362,391)(363,395)(364,394)(365,393)(366,397)(367,396)(368,400)
(369,399)(370,398)(371,402)(372,401)(373,405)(374,404)(375,403)(376,407)
(377,406)(378,410)(379,409)(380,408)(381,412)(382,411)(383,415)(384,414)
(385,413)(386,417)(387,416)(388,420)(389,419)(390,418)(421,467)(422,466)
(423,470)(424,469)(425,468)(426,472)(427,471)(428,475)(429,474)(430,473)
(431,477)(432,476)(433,480)(434,479)(435,478)(436,452)(437,451)(438,455)
(439,454)(440,453)(441,457)(442,456)(443,460)(444,459)(445,458)(446,462)
(447,461)(448,465)(449,464)(450,463)(481,542)(482,541)(483,545)(484,544)
(485,543)(486,547)(487,546)(488,550)(489,549)(490,548)(491,552)(492,551)
(493,555)(494,554)(495,553)(496,557)(497,556)(498,560)(499,559)(500,558)
(501,562)(502,561)(503,565)(504,564)(505,563)(506,567)(507,566)(508,570)
(509,569)(510,568)(511,572)(512,571)(513,575)(514,574)(515,573)(516,577)
(517,576)(518,580)(519,579)(520,578)(521,582)(522,581)(523,585)(524,584)
(525,583)(526,587)(527,586)(528,590)(529,589)(530,588)(531,592)(532,591)
(533,595)(534,594)(535,593)(536,597)(537,596)(538,600)(539,599)(540,598)
(601,662)(602,661)(603,665)(604,664)(605,663)(606,667)(607,666)(608,670)
(609,669)(610,668)(611,672)(612,671)(613,675)(614,674)(615,673)(616,677)
(617,676)(618,680)(619,679)(620,678)(621,682)(622,681)(623,685)(624,684)
(625,683)(626,687)(627,686)(628,690)(629,689)(630,688)(631,692)(632,691)
(633,695)(634,694)(635,693)(636,697)(637,696)(638,700)(639,699)(640,698)
(641,702)(642,701)(643,705)(644,704)(645,703)(646,707)(647,706)(648,710)
(649,709)(650,708)(651,712)(652,711)(653,715)(654,714)(655,713)(656,717)
(657,716)(658,720)(659,719)(660,718)(721,812)(722,811)(723,815)(724,814)
(725,813)(726,817)(727,816)(728,820)(729,819)(730,818)(731,822)(732,821)
(733,825)(734,824)(735,823)(736,827)(737,826)(738,830)(739,829)(740,828)
(741,832)(742,831)(743,835)(744,834)(745,833)(746,837)(747,836)(748,840)
(749,839)(750,838)(751,782)(752,781)(753,785)(754,784)(755,783)(756,787)
(757,786)(758,790)(759,789)(760,788)(761,792)(762,791)(763,795)(764,794)
(765,793)(766,797)(767,796)(768,800)(769,799)(770,798)(771,802)(772,801)
(773,805)(774,804)(775,803)(776,807)(777,806)(778,810)(779,809)(780,808)
(841,932)(842,931)(843,935)(844,934)(845,933)(846,937)(847,936)(848,940)
(849,939)(850,938)(851,942)(852,941)(853,945)(854,944)(855,943)(856,947)
(857,946)(858,950)(859,949)(860,948)(861,952)(862,951)(863,955)(864,954)
(865,953)(866,957)(867,956)(868,960)(869,959)(870,958)(871,902)(872,901)
(873,905)(874,904)(875,903)(876,907)(877,906)(878,910)(879,909)(880,908)
(881,912)(882,911)(883,915)(884,914)(885,913)(886,917)(887,916)(888,920)
(889,919)(890,918)(891,922)(892,921)(893,925)(894,924)(895,923)(896,927)
(897,926)(898,930)(899,929)(900,928);;
s2 := (  1,361)(  2,362)(  3,363)(  4,364)(  5,365)(  6,371)(  7,372)(  8,373)
(  9,374)( 10,375)( 11,366)( 12,367)( 13,368)( 14,369)( 15,370)( 16,376)
( 17,377)( 18,378)( 19,379)( 20,380)( 21,386)( 22,387)( 23,388)( 24,389)
( 25,390)( 26,381)( 27,382)( 28,383)( 29,384)( 30,385)( 31,391)( 32,392)
( 33,393)( 34,394)( 35,395)( 36,401)( 37,402)( 38,403)( 39,404)( 40,405)
( 41,396)( 42,397)( 43,398)( 44,399)( 45,400)( 46,406)( 47,407)( 48,408)
( 49,409)( 50,410)( 51,416)( 52,417)( 53,418)( 54,419)( 55,420)( 56,411)
( 57,412)( 58,413)( 59,414)( 60,415)( 61,421)( 62,422)( 63,423)( 64,424)
( 65,425)( 66,431)( 67,432)( 68,433)( 69,434)( 70,435)( 71,426)( 72,427)
( 73,428)( 74,429)( 75,430)( 76,436)( 77,437)( 78,438)( 79,439)( 80,440)
( 81,446)( 82,447)( 83,448)( 84,449)( 85,450)( 86,441)( 87,442)( 88,443)
( 89,444)( 90,445)( 91,451)( 92,452)( 93,453)( 94,454)( 95,455)( 96,461)
( 97,462)( 98,463)( 99,464)(100,465)(101,456)(102,457)(103,458)(104,459)
(105,460)(106,466)(107,467)(108,468)(109,469)(110,470)(111,476)(112,477)
(113,478)(114,479)(115,480)(116,471)(117,472)(118,473)(119,474)(120,475)
(121,241)(122,242)(123,243)(124,244)(125,245)(126,251)(127,252)(128,253)
(129,254)(130,255)(131,246)(132,247)(133,248)(134,249)(135,250)(136,256)
(137,257)(138,258)(139,259)(140,260)(141,266)(142,267)(143,268)(144,269)
(145,270)(146,261)(147,262)(148,263)(149,264)(150,265)(151,271)(152,272)
(153,273)(154,274)(155,275)(156,281)(157,282)(158,283)(159,284)(160,285)
(161,276)(162,277)(163,278)(164,279)(165,280)(166,286)(167,287)(168,288)
(169,289)(170,290)(171,296)(172,297)(173,298)(174,299)(175,300)(176,291)
(177,292)(178,293)(179,294)(180,295)(181,301)(182,302)(183,303)(184,304)
(185,305)(186,311)(187,312)(188,313)(189,314)(190,315)(191,306)(192,307)
(193,308)(194,309)(195,310)(196,316)(197,317)(198,318)(199,319)(200,320)
(201,326)(202,327)(203,328)(204,329)(205,330)(206,321)(207,322)(208,323)
(209,324)(210,325)(211,331)(212,332)(213,333)(214,334)(215,335)(216,341)
(217,342)(218,343)(219,344)(220,345)(221,336)(222,337)(223,338)(224,339)
(225,340)(226,346)(227,347)(228,348)(229,349)(230,350)(231,356)(232,357)
(233,358)(234,359)(235,360)(236,351)(237,352)(238,353)(239,354)(240,355)
(481,841)(482,842)(483,843)(484,844)(485,845)(486,851)(487,852)(488,853)
(489,854)(490,855)(491,846)(492,847)(493,848)(494,849)(495,850)(496,856)
(497,857)(498,858)(499,859)(500,860)(501,866)(502,867)(503,868)(504,869)
(505,870)(506,861)(507,862)(508,863)(509,864)(510,865)(511,871)(512,872)
(513,873)(514,874)(515,875)(516,881)(517,882)(518,883)(519,884)(520,885)
(521,876)(522,877)(523,878)(524,879)(525,880)(526,886)(527,887)(528,888)
(529,889)(530,890)(531,896)(532,897)(533,898)(534,899)(535,900)(536,891)
(537,892)(538,893)(539,894)(540,895)(541,901)(542,902)(543,903)(544,904)
(545,905)(546,911)(547,912)(548,913)(549,914)(550,915)(551,906)(552,907)
(553,908)(554,909)(555,910)(556,916)(557,917)(558,918)(559,919)(560,920)
(561,926)(562,927)(563,928)(564,929)(565,930)(566,921)(567,922)(568,923)
(569,924)(570,925)(571,931)(572,932)(573,933)(574,934)(575,935)(576,941)
(577,942)(578,943)(579,944)(580,945)(581,936)(582,937)(583,938)(584,939)
(585,940)(586,946)(587,947)(588,948)(589,949)(590,950)(591,956)(592,957)
(593,958)(594,959)(595,960)(596,951)(597,952)(598,953)(599,954)(600,955)
(601,721)(602,722)(603,723)(604,724)(605,725)(606,731)(607,732)(608,733)
(609,734)(610,735)(611,726)(612,727)(613,728)(614,729)(615,730)(616,736)
(617,737)(618,738)(619,739)(620,740)(621,746)(622,747)(623,748)(624,749)
(625,750)(626,741)(627,742)(628,743)(629,744)(630,745)(631,751)(632,752)
(633,753)(634,754)(635,755)(636,761)(637,762)(638,763)(639,764)(640,765)
(641,756)(642,757)(643,758)(644,759)(645,760)(646,766)(647,767)(648,768)
(649,769)(650,770)(651,776)(652,777)(653,778)(654,779)(655,780)(656,771)
(657,772)(658,773)(659,774)(660,775)(661,781)(662,782)(663,783)(664,784)
(665,785)(666,791)(667,792)(668,793)(669,794)(670,795)(671,786)(672,787)
(673,788)(674,789)(675,790)(676,796)(677,797)(678,798)(679,799)(680,800)
(681,806)(682,807)(683,808)(684,809)(685,810)(686,801)(687,802)(688,803)
(689,804)(690,805)(691,811)(692,812)(693,813)(694,814)(695,815)(696,821)
(697,822)(698,823)(699,824)(700,825)(701,816)(702,817)(703,818)(704,819)
(705,820)(706,826)(707,827)(708,828)(709,829)(710,830)(711,836)(712,837)
(713,838)(714,839)(715,840)(716,831)(717,832)(718,833)(719,834)(720,835);;
s3 := (  1,126)(  2,127)(  3,128)(  4,129)(  5,130)(  6,121)(  7,122)(  8,123)
(  9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,141)
( 17,142)( 18,143)( 19,144)( 20,145)( 21,136)( 22,137)( 23,138)( 24,139)
( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,156)( 32,157)
( 33,158)( 34,159)( 35,160)( 36,151)( 37,152)( 38,153)( 39,154)( 40,155)
( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,171)( 47,172)( 48,173)
( 49,174)( 50,175)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)( 56,176)
( 57,177)( 58,178)( 59,179)( 60,180)( 61,186)( 62,187)( 63,188)( 64,189)
( 65,190)( 66,181)( 67,182)( 68,183)( 69,184)( 70,185)( 71,191)( 72,192)
( 73,193)( 74,194)( 75,195)( 76,201)( 77,202)( 78,203)( 79,204)( 80,205)
( 81,196)( 82,197)( 83,198)( 84,199)( 85,200)( 86,206)( 87,207)( 88,208)
( 89,209)( 90,210)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)( 96,211)
( 97,212)( 98,213)( 99,214)(100,215)(101,221)(102,222)(103,223)(104,224)
(105,225)(106,231)(107,232)(108,233)(109,234)(110,235)(111,226)(112,227)
(113,228)(114,229)(115,230)(116,236)(117,237)(118,238)(119,239)(120,240)
(241,366)(242,367)(243,368)(244,369)(245,370)(246,361)(247,362)(248,363)
(249,364)(250,365)(251,371)(252,372)(253,373)(254,374)(255,375)(256,381)
(257,382)(258,383)(259,384)(260,385)(261,376)(262,377)(263,378)(264,379)
(265,380)(266,386)(267,387)(268,388)(269,389)(270,390)(271,396)(272,397)
(273,398)(274,399)(275,400)(276,391)(277,392)(278,393)(279,394)(280,395)
(281,401)(282,402)(283,403)(284,404)(285,405)(286,411)(287,412)(288,413)
(289,414)(290,415)(291,406)(292,407)(293,408)(294,409)(295,410)(296,416)
(297,417)(298,418)(299,419)(300,420)(301,426)(302,427)(303,428)(304,429)
(305,430)(306,421)(307,422)(308,423)(309,424)(310,425)(311,431)(312,432)
(313,433)(314,434)(315,435)(316,441)(317,442)(318,443)(319,444)(320,445)
(321,436)(322,437)(323,438)(324,439)(325,440)(326,446)(327,447)(328,448)
(329,449)(330,450)(331,456)(332,457)(333,458)(334,459)(335,460)(336,451)
(337,452)(338,453)(339,454)(340,455)(341,461)(342,462)(343,463)(344,464)
(345,465)(346,471)(347,472)(348,473)(349,474)(350,475)(351,466)(352,467)
(353,468)(354,469)(355,470)(356,476)(357,477)(358,478)(359,479)(360,480)
(481,606)(482,607)(483,608)(484,609)(485,610)(486,601)(487,602)(488,603)
(489,604)(490,605)(491,611)(492,612)(493,613)(494,614)(495,615)(496,621)
(497,622)(498,623)(499,624)(500,625)(501,616)(502,617)(503,618)(504,619)
(505,620)(506,626)(507,627)(508,628)(509,629)(510,630)(511,636)(512,637)
(513,638)(514,639)(515,640)(516,631)(517,632)(518,633)(519,634)(520,635)
(521,641)(522,642)(523,643)(524,644)(525,645)(526,651)(527,652)(528,653)
(529,654)(530,655)(531,646)(532,647)(533,648)(534,649)(535,650)(536,656)
(537,657)(538,658)(539,659)(540,660)(541,666)(542,667)(543,668)(544,669)
(545,670)(546,661)(547,662)(548,663)(549,664)(550,665)(551,671)(552,672)
(553,673)(554,674)(555,675)(556,681)(557,682)(558,683)(559,684)(560,685)
(561,676)(562,677)(563,678)(564,679)(565,680)(566,686)(567,687)(568,688)
(569,689)(570,690)(571,696)(572,697)(573,698)(574,699)(575,700)(576,691)
(577,692)(578,693)(579,694)(580,695)(581,701)(582,702)(583,703)(584,704)
(585,705)(586,711)(587,712)(588,713)(589,714)(590,715)(591,706)(592,707)
(593,708)(594,709)(595,710)(596,716)(597,717)(598,718)(599,719)(600,720)
(721,846)(722,847)(723,848)(724,849)(725,850)(726,841)(727,842)(728,843)
(729,844)(730,845)(731,851)(732,852)(733,853)(734,854)(735,855)(736,861)
(737,862)(738,863)(739,864)(740,865)(741,856)(742,857)(743,858)(744,859)
(745,860)(746,866)(747,867)(748,868)(749,869)(750,870)(751,876)(752,877)
(753,878)(754,879)(755,880)(756,871)(757,872)(758,873)(759,874)(760,875)
(761,881)(762,882)(763,883)(764,884)(765,885)(766,891)(767,892)(768,893)
(769,894)(770,895)(771,886)(772,887)(773,888)(774,889)(775,890)(776,896)
(777,897)(778,898)(779,899)(780,900)(781,906)(782,907)(783,908)(784,909)
(785,910)(786,901)(787,902)(788,903)(789,904)(790,905)(791,911)(792,912)
(793,913)(794,914)(795,915)(796,921)(797,922)(798,923)(799,924)(800,925)
(801,916)(802,917)(803,918)(804,919)(805,920)(806,926)(807,927)(808,928)
(809,929)(810,930)(811,936)(812,937)(813,938)(814,939)(815,940)(816,931)
(817,932)(818,933)(819,934)(820,935)(821,941)(822,942)(823,943)(824,944)
(825,945)(826,951)(827,952)(828,953)(829,954)(830,955)(831,946)(832,947)
(833,948)(834,949)(835,950)(836,956)(837,957)(838,958)(839,959)(840,960);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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)!(  1,481)(  2,485)(  3,484)(  4,483)(  5,482)(  6,486)(  7,490)
(  8,489)(  9,488)( 10,487)( 11,491)( 12,495)( 13,494)( 14,493)( 15,492)
( 16,496)( 17,500)( 18,499)( 19,498)( 20,497)( 21,501)( 22,505)( 23,504)
( 24,503)( 25,502)( 26,506)( 27,510)( 28,509)( 29,508)( 30,507)( 31,511)
( 32,515)( 33,514)( 34,513)( 35,512)( 36,516)( 37,520)( 38,519)( 39,518)
( 40,517)( 41,521)( 42,525)( 43,524)( 44,523)( 45,522)( 46,526)( 47,530)
( 48,529)( 49,528)( 50,527)( 51,531)( 52,535)( 53,534)( 54,533)( 55,532)
( 56,536)( 57,540)( 58,539)( 59,538)( 60,537)( 61,556)( 62,560)( 63,559)
( 64,558)( 65,557)( 66,561)( 67,565)( 68,564)( 69,563)( 70,562)( 71,566)
( 72,570)( 73,569)( 74,568)( 75,567)( 76,541)( 77,545)( 78,544)( 79,543)
( 80,542)( 81,546)( 82,550)( 83,549)( 84,548)( 85,547)( 86,551)( 87,555)
( 88,554)( 89,553)( 90,552)( 91,586)( 92,590)( 93,589)( 94,588)( 95,587)
( 96,591)( 97,595)( 98,594)( 99,593)(100,592)(101,596)(102,600)(103,599)
(104,598)(105,597)(106,571)(107,575)(108,574)(109,573)(110,572)(111,576)
(112,580)(113,579)(114,578)(115,577)(116,581)(117,585)(118,584)(119,583)
(120,582)(121,601)(122,605)(123,604)(124,603)(125,602)(126,606)(127,610)
(128,609)(129,608)(130,607)(131,611)(132,615)(133,614)(134,613)(135,612)
(136,616)(137,620)(138,619)(139,618)(140,617)(141,621)(142,625)(143,624)
(144,623)(145,622)(146,626)(147,630)(148,629)(149,628)(150,627)(151,631)
(152,635)(153,634)(154,633)(155,632)(156,636)(157,640)(158,639)(159,638)
(160,637)(161,641)(162,645)(163,644)(164,643)(165,642)(166,646)(167,650)
(168,649)(169,648)(170,647)(171,651)(172,655)(173,654)(174,653)(175,652)
(176,656)(177,660)(178,659)(179,658)(180,657)(181,676)(182,680)(183,679)
(184,678)(185,677)(186,681)(187,685)(188,684)(189,683)(190,682)(191,686)
(192,690)(193,689)(194,688)(195,687)(196,661)(197,665)(198,664)(199,663)
(200,662)(201,666)(202,670)(203,669)(204,668)(205,667)(206,671)(207,675)
(208,674)(209,673)(210,672)(211,706)(212,710)(213,709)(214,708)(215,707)
(216,711)(217,715)(218,714)(219,713)(220,712)(221,716)(222,720)(223,719)
(224,718)(225,717)(226,691)(227,695)(228,694)(229,693)(230,692)(231,696)
(232,700)(233,699)(234,698)(235,697)(236,701)(237,705)(238,704)(239,703)
(240,702)(241,721)(242,725)(243,724)(244,723)(245,722)(246,726)(247,730)
(248,729)(249,728)(250,727)(251,731)(252,735)(253,734)(254,733)(255,732)
(256,736)(257,740)(258,739)(259,738)(260,737)(261,741)(262,745)(263,744)
(264,743)(265,742)(266,746)(267,750)(268,749)(269,748)(270,747)(271,751)
(272,755)(273,754)(274,753)(275,752)(276,756)(277,760)(278,759)(279,758)
(280,757)(281,761)(282,765)(283,764)(284,763)(285,762)(286,766)(287,770)
(288,769)(289,768)(290,767)(291,771)(292,775)(293,774)(294,773)(295,772)
(296,776)(297,780)(298,779)(299,778)(300,777)(301,796)(302,800)(303,799)
(304,798)(305,797)(306,801)(307,805)(308,804)(309,803)(310,802)(311,806)
(312,810)(313,809)(314,808)(315,807)(316,781)(317,785)(318,784)(319,783)
(320,782)(321,786)(322,790)(323,789)(324,788)(325,787)(326,791)(327,795)
(328,794)(329,793)(330,792)(331,826)(332,830)(333,829)(334,828)(335,827)
(336,831)(337,835)(338,834)(339,833)(340,832)(341,836)(342,840)(343,839)
(344,838)(345,837)(346,811)(347,815)(348,814)(349,813)(350,812)(351,816)
(352,820)(353,819)(354,818)(355,817)(356,821)(357,825)(358,824)(359,823)
(360,822)(361,841)(362,845)(363,844)(364,843)(365,842)(366,846)(367,850)
(368,849)(369,848)(370,847)(371,851)(372,855)(373,854)(374,853)(375,852)
(376,856)(377,860)(378,859)(379,858)(380,857)(381,861)(382,865)(383,864)
(384,863)(385,862)(386,866)(387,870)(388,869)(389,868)(390,867)(391,871)
(392,875)(393,874)(394,873)(395,872)(396,876)(397,880)(398,879)(399,878)
(400,877)(401,881)(402,885)(403,884)(404,883)(405,882)(406,886)(407,890)
(408,889)(409,888)(410,887)(411,891)(412,895)(413,894)(414,893)(415,892)
(416,896)(417,900)(418,899)(419,898)(420,897)(421,916)(422,920)(423,919)
(424,918)(425,917)(426,921)(427,925)(428,924)(429,923)(430,922)(431,926)
(432,930)(433,929)(434,928)(435,927)(436,901)(437,905)(438,904)(439,903)
(440,902)(441,906)(442,910)(443,909)(444,908)(445,907)(446,911)(447,915)
(448,914)(449,913)(450,912)(451,946)(452,950)(453,949)(454,948)(455,947)
(456,951)(457,955)(458,954)(459,953)(460,952)(461,956)(462,960)(463,959)
(464,958)(465,957)(466,931)(467,935)(468,934)(469,933)(470,932)(471,936)
(472,940)(473,939)(474,938)(475,937)(476,941)(477,945)(478,944)(479,943)
(480,942);
s1 := Sym(960)!(  1,  2)(  3,  5)(  6,  7)(  8, 10)( 11, 12)( 13, 15)( 16, 17)
( 18, 20)( 21, 22)( 23, 25)( 26, 27)( 28, 30)( 31, 32)( 33, 35)( 36, 37)
( 38, 40)( 41, 42)( 43, 45)( 46, 47)( 48, 50)( 51, 52)( 53, 55)( 56, 57)
( 58, 60)( 61, 77)( 62, 76)( 63, 80)( 64, 79)( 65, 78)( 66, 82)( 67, 81)
( 68, 85)( 69, 84)( 70, 83)( 71, 87)( 72, 86)( 73, 90)( 74, 89)( 75, 88)
( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)( 96,112)( 97,111)( 98,115)
( 99,114)(100,113)(101,117)(102,116)(103,120)(104,119)(105,118)(121,122)
(123,125)(126,127)(128,130)(131,132)(133,135)(136,137)(138,140)(141,142)
(143,145)(146,147)(148,150)(151,152)(153,155)(156,157)(158,160)(161,162)
(163,165)(166,167)(168,170)(171,172)(173,175)(176,177)(178,180)(181,197)
(182,196)(183,200)(184,199)(185,198)(186,202)(187,201)(188,205)(189,204)
(190,203)(191,207)(192,206)(193,210)(194,209)(195,208)(211,227)(212,226)
(213,230)(214,229)(215,228)(216,232)(217,231)(218,235)(219,234)(220,233)
(221,237)(222,236)(223,240)(224,239)(225,238)(241,272)(242,271)(243,275)
(244,274)(245,273)(246,277)(247,276)(248,280)(249,279)(250,278)(251,282)
(252,281)(253,285)(254,284)(255,283)(256,287)(257,286)(258,290)(259,289)
(260,288)(261,292)(262,291)(263,295)(264,294)(265,293)(266,297)(267,296)
(268,300)(269,299)(270,298)(301,347)(302,346)(303,350)(304,349)(305,348)
(306,352)(307,351)(308,355)(309,354)(310,353)(311,357)(312,356)(313,360)
(314,359)(315,358)(316,332)(317,331)(318,335)(319,334)(320,333)(321,337)
(322,336)(323,340)(324,339)(325,338)(326,342)(327,341)(328,345)(329,344)
(330,343)(361,392)(362,391)(363,395)(364,394)(365,393)(366,397)(367,396)
(368,400)(369,399)(370,398)(371,402)(372,401)(373,405)(374,404)(375,403)
(376,407)(377,406)(378,410)(379,409)(380,408)(381,412)(382,411)(383,415)
(384,414)(385,413)(386,417)(387,416)(388,420)(389,419)(390,418)(421,467)
(422,466)(423,470)(424,469)(425,468)(426,472)(427,471)(428,475)(429,474)
(430,473)(431,477)(432,476)(433,480)(434,479)(435,478)(436,452)(437,451)
(438,455)(439,454)(440,453)(441,457)(442,456)(443,460)(444,459)(445,458)
(446,462)(447,461)(448,465)(449,464)(450,463)(481,542)(482,541)(483,545)
(484,544)(485,543)(486,547)(487,546)(488,550)(489,549)(490,548)(491,552)
(492,551)(493,555)(494,554)(495,553)(496,557)(497,556)(498,560)(499,559)
(500,558)(501,562)(502,561)(503,565)(504,564)(505,563)(506,567)(507,566)
(508,570)(509,569)(510,568)(511,572)(512,571)(513,575)(514,574)(515,573)
(516,577)(517,576)(518,580)(519,579)(520,578)(521,582)(522,581)(523,585)
(524,584)(525,583)(526,587)(527,586)(528,590)(529,589)(530,588)(531,592)
(532,591)(533,595)(534,594)(535,593)(536,597)(537,596)(538,600)(539,599)
(540,598)(601,662)(602,661)(603,665)(604,664)(605,663)(606,667)(607,666)
(608,670)(609,669)(610,668)(611,672)(612,671)(613,675)(614,674)(615,673)
(616,677)(617,676)(618,680)(619,679)(620,678)(621,682)(622,681)(623,685)
(624,684)(625,683)(626,687)(627,686)(628,690)(629,689)(630,688)(631,692)
(632,691)(633,695)(634,694)(635,693)(636,697)(637,696)(638,700)(639,699)
(640,698)(641,702)(642,701)(643,705)(644,704)(645,703)(646,707)(647,706)
(648,710)(649,709)(650,708)(651,712)(652,711)(653,715)(654,714)(655,713)
(656,717)(657,716)(658,720)(659,719)(660,718)(721,812)(722,811)(723,815)
(724,814)(725,813)(726,817)(727,816)(728,820)(729,819)(730,818)(731,822)
(732,821)(733,825)(734,824)(735,823)(736,827)(737,826)(738,830)(739,829)
(740,828)(741,832)(742,831)(743,835)(744,834)(745,833)(746,837)(747,836)
(748,840)(749,839)(750,838)(751,782)(752,781)(753,785)(754,784)(755,783)
(756,787)(757,786)(758,790)(759,789)(760,788)(761,792)(762,791)(763,795)
(764,794)(765,793)(766,797)(767,796)(768,800)(769,799)(770,798)(771,802)
(772,801)(773,805)(774,804)(775,803)(776,807)(777,806)(778,810)(779,809)
(780,808)(841,932)(842,931)(843,935)(844,934)(845,933)(846,937)(847,936)
(848,940)(849,939)(850,938)(851,942)(852,941)(853,945)(854,944)(855,943)
(856,947)(857,946)(858,950)(859,949)(860,948)(861,952)(862,951)(863,955)
(864,954)(865,953)(866,957)(867,956)(868,960)(869,959)(870,958)(871,902)
(872,901)(873,905)(874,904)(875,903)(876,907)(877,906)(878,910)(879,909)
(880,908)(881,912)(882,911)(883,915)(884,914)(885,913)(886,917)(887,916)
(888,920)(889,919)(890,918)(891,922)(892,921)(893,925)(894,924)(895,923)
(896,927)(897,926)(898,930)(899,929)(900,928);
s2 := Sym(960)!(  1,361)(  2,362)(  3,363)(  4,364)(  5,365)(  6,371)(  7,372)
(  8,373)(  9,374)( 10,375)( 11,366)( 12,367)( 13,368)( 14,369)( 15,370)
( 16,376)( 17,377)( 18,378)( 19,379)( 20,380)( 21,386)( 22,387)( 23,388)
( 24,389)( 25,390)( 26,381)( 27,382)( 28,383)( 29,384)( 30,385)( 31,391)
( 32,392)( 33,393)( 34,394)( 35,395)( 36,401)( 37,402)( 38,403)( 39,404)
( 40,405)( 41,396)( 42,397)( 43,398)( 44,399)( 45,400)( 46,406)( 47,407)
( 48,408)( 49,409)( 50,410)( 51,416)( 52,417)( 53,418)( 54,419)( 55,420)
( 56,411)( 57,412)( 58,413)( 59,414)( 60,415)( 61,421)( 62,422)( 63,423)
( 64,424)( 65,425)( 66,431)( 67,432)( 68,433)( 69,434)( 70,435)( 71,426)
( 72,427)( 73,428)( 74,429)( 75,430)( 76,436)( 77,437)( 78,438)( 79,439)
( 80,440)( 81,446)( 82,447)( 83,448)( 84,449)( 85,450)( 86,441)( 87,442)
( 88,443)( 89,444)( 90,445)( 91,451)( 92,452)( 93,453)( 94,454)( 95,455)
( 96,461)( 97,462)( 98,463)( 99,464)(100,465)(101,456)(102,457)(103,458)
(104,459)(105,460)(106,466)(107,467)(108,468)(109,469)(110,470)(111,476)
(112,477)(113,478)(114,479)(115,480)(116,471)(117,472)(118,473)(119,474)
(120,475)(121,241)(122,242)(123,243)(124,244)(125,245)(126,251)(127,252)
(128,253)(129,254)(130,255)(131,246)(132,247)(133,248)(134,249)(135,250)
(136,256)(137,257)(138,258)(139,259)(140,260)(141,266)(142,267)(143,268)
(144,269)(145,270)(146,261)(147,262)(148,263)(149,264)(150,265)(151,271)
(152,272)(153,273)(154,274)(155,275)(156,281)(157,282)(158,283)(159,284)
(160,285)(161,276)(162,277)(163,278)(164,279)(165,280)(166,286)(167,287)
(168,288)(169,289)(170,290)(171,296)(172,297)(173,298)(174,299)(175,300)
(176,291)(177,292)(178,293)(179,294)(180,295)(181,301)(182,302)(183,303)
(184,304)(185,305)(186,311)(187,312)(188,313)(189,314)(190,315)(191,306)
(192,307)(193,308)(194,309)(195,310)(196,316)(197,317)(198,318)(199,319)
(200,320)(201,326)(202,327)(203,328)(204,329)(205,330)(206,321)(207,322)
(208,323)(209,324)(210,325)(211,331)(212,332)(213,333)(214,334)(215,335)
(216,341)(217,342)(218,343)(219,344)(220,345)(221,336)(222,337)(223,338)
(224,339)(225,340)(226,346)(227,347)(228,348)(229,349)(230,350)(231,356)
(232,357)(233,358)(234,359)(235,360)(236,351)(237,352)(238,353)(239,354)
(240,355)(481,841)(482,842)(483,843)(484,844)(485,845)(486,851)(487,852)
(488,853)(489,854)(490,855)(491,846)(492,847)(493,848)(494,849)(495,850)
(496,856)(497,857)(498,858)(499,859)(500,860)(501,866)(502,867)(503,868)
(504,869)(505,870)(506,861)(507,862)(508,863)(509,864)(510,865)(511,871)
(512,872)(513,873)(514,874)(515,875)(516,881)(517,882)(518,883)(519,884)
(520,885)(521,876)(522,877)(523,878)(524,879)(525,880)(526,886)(527,887)
(528,888)(529,889)(530,890)(531,896)(532,897)(533,898)(534,899)(535,900)
(536,891)(537,892)(538,893)(539,894)(540,895)(541,901)(542,902)(543,903)
(544,904)(545,905)(546,911)(547,912)(548,913)(549,914)(550,915)(551,906)
(552,907)(553,908)(554,909)(555,910)(556,916)(557,917)(558,918)(559,919)
(560,920)(561,926)(562,927)(563,928)(564,929)(565,930)(566,921)(567,922)
(568,923)(569,924)(570,925)(571,931)(572,932)(573,933)(574,934)(575,935)
(576,941)(577,942)(578,943)(579,944)(580,945)(581,936)(582,937)(583,938)
(584,939)(585,940)(586,946)(587,947)(588,948)(589,949)(590,950)(591,956)
(592,957)(593,958)(594,959)(595,960)(596,951)(597,952)(598,953)(599,954)
(600,955)(601,721)(602,722)(603,723)(604,724)(605,725)(606,731)(607,732)
(608,733)(609,734)(610,735)(611,726)(612,727)(613,728)(614,729)(615,730)
(616,736)(617,737)(618,738)(619,739)(620,740)(621,746)(622,747)(623,748)
(624,749)(625,750)(626,741)(627,742)(628,743)(629,744)(630,745)(631,751)
(632,752)(633,753)(634,754)(635,755)(636,761)(637,762)(638,763)(639,764)
(640,765)(641,756)(642,757)(643,758)(644,759)(645,760)(646,766)(647,767)
(648,768)(649,769)(650,770)(651,776)(652,777)(653,778)(654,779)(655,780)
(656,771)(657,772)(658,773)(659,774)(660,775)(661,781)(662,782)(663,783)
(664,784)(665,785)(666,791)(667,792)(668,793)(669,794)(670,795)(671,786)
(672,787)(673,788)(674,789)(675,790)(676,796)(677,797)(678,798)(679,799)
(680,800)(681,806)(682,807)(683,808)(684,809)(685,810)(686,801)(687,802)
(688,803)(689,804)(690,805)(691,811)(692,812)(693,813)(694,814)(695,815)
(696,821)(697,822)(698,823)(699,824)(700,825)(701,816)(702,817)(703,818)
(704,819)(705,820)(706,826)(707,827)(708,828)(709,829)(710,830)(711,836)
(712,837)(713,838)(714,839)(715,840)(716,831)(717,832)(718,833)(719,834)
(720,835);
s3 := Sym(960)!(  1,126)(  2,127)(  3,128)(  4,129)(  5,130)(  6,121)(  7,122)
(  8,123)(  9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)
( 16,141)( 17,142)( 18,143)( 19,144)( 20,145)( 21,136)( 22,137)( 23,138)
( 24,139)( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,156)
( 32,157)( 33,158)( 34,159)( 35,160)( 36,151)( 37,152)( 38,153)( 39,154)
( 40,155)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,171)( 47,172)
( 48,173)( 49,174)( 50,175)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)
( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,186)( 62,187)( 63,188)
( 64,189)( 65,190)( 66,181)( 67,182)( 68,183)( 69,184)( 70,185)( 71,191)
( 72,192)( 73,193)( 74,194)( 75,195)( 76,201)( 77,202)( 78,203)( 79,204)
( 80,205)( 81,196)( 82,197)( 83,198)( 84,199)( 85,200)( 86,206)( 87,207)
( 88,208)( 89,209)( 90,210)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)
( 96,211)( 97,212)( 98,213)( 99,214)(100,215)(101,221)(102,222)(103,223)
(104,224)(105,225)(106,231)(107,232)(108,233)(109,234)(110,235)(111,226)
(112,227)(113,228)(114,229)(115,230)(116,236)(117,237)(118,238)(119,239)
(120,240)(241,366)(242,367)(243,368)(244,369)(245,370)(246,361)(247,362)
(248,363)(249,364)(250,365)(251,371)(252,372)(253,373)(254,374)(255,375)
(256,381)(257,382)(258,383)(259,384)(260,385)(261,376)(262,377)(263,378)
(264,379)(265,380)(266,386)(267,387)(268,388)(269,389)(270,390)(271,396)
(272,397)(273,398)(274,399)(275,400)(276,391)(277,392)(278,393)(279,394)
(280,395)(281,401)(282,402)(283,403)(284,404)(285,405)(286,411)(287,412)
(288,413)(289,414)(290,415)(291,406)(292,407)(293,408)(294,409)(295,410)
(296,416)(297,417)(298,418)(299,419)(300,420)(301,426)(302,427)(303,428)
(304,429)(305,430)(306,421)(307,422)(308,423)(309,424)(310,425)(311,431)
(312,432)(313,433)(314,434)(315,435)(316,441)(317,442)(318,443)(319,444)
(320,445)(321,436)(322,437)(323,438)(324,439)(325,440)(326,446)(327,447)
(328,448)(329,449)(330,450)(331,456)(332,457)(333,458)(334,459)(335,460)
(336,451)(337,452)(338,453)(339,454)(340,455)(341,461)(342,462)(343,463)
(344,464)(345,465)(346,471)(347,472)(348,473)(349,474)(350,475)(351,466)
(352,467)(353,468)(354,469)(355,470)(356,476)(357,477)(358,478)(359,479)
(360,480)(481,606)(482,607)(483,608)(484,609)(485,610)(486,601)(487,602)
(488,603)(489,604)(490,605)(491,611)(492,612)(493,613)(494,614)(495,615)
(496,621)(497,622)(498,623)(499,624)(500,625)(501,616)(502,617)(503,618)
(504,619)(505,620)(506,626)(507,627)(508,628)(509,629)(510,630)(511,636)
(512,637)(513,638)(514,639)(515,640)(516,631)(517,632)(518,633)(519,634)
(520,635)(521,641)(522,642)(523,643)(524,644)(525,645)(526,651)(527,652)
(528,653)(529,654)(530,655)(531,646)(532,647)(533,648)(534,649)(535,650)
(536,656)(537,657)(538,658)(539,659)(540,660)(541,666)(542,667)(543,668)
(544,669)(545,670)(546,661)(547,662)(548,663)(549,664)(550,665)(551,671)
(552,672)(553,673)(554,674)(555,675)(556,681)(557,682)(558,683)(559,684)
(560,685)(561,676)(562,677)(563,678)(564,679)(565,680)(566,686)(567,687)
(568,688)(569,689)(570,690)(571,696)(572,697)(573,698)(574,699)(575,700)
(576,691)(577,692)(578,693)(579,694)(580,695)(581,701)(582,702)(583,703)
(584,704)(585,705)(586,711)(587,712)(588,713)(589,714)(590,715)(591,706)
(592,707)(593,708)(594,709)(595,710)(596,716)(597,717)(598,718)(599,719)
(600,720)(721,846)(722,847)(723,848)(724,849)(725,850)(726,841)(727,842)
(728,843)(729,844)(730,845)(731,851)(732,852)(733,853)(734,854)(735,855)
(736,861)(737,862)(738,863)(739,864)(740,865)(741,856)(742,857)(743,858)
(744,859)(745,860)(746,866)(747,867)(748,868)(749,869)(750,870)(751,876)
(752,877)(753,878)(754,879)(755,880)(756,871)(757,872)(758,873)(759,874)
(760,875)(761,881)(762,882)(763,883)(764,884)(765,885)(766,891)(767,892)
(768,893)(769,894)(770,895)(771,886)(772,887)(773,888)(774,889)(775,890)
(776,896)(777,897)(778,898)(779,899)(780,900)(781,906)(782,907)(783,908)
(784,909)(785,910)(786,901)(787,902)(788,903)(789,904)(790,905)(791,911)
(792,912)(793,913)(794,914)(795,915)(796,921)(797,922)(798,923)(799,924)
(800,925)(801,916)(802,917)(803,918)(804,919)(805,920)(806,926)(807,927)
(808,928)(809,929)(810,930)(811,936)(812,937)(813,938)(814,939)(815,940)
(816,931)(817,932)(818,933)(819,934)(820,935)(821,941)(822,942)(823,943)
(824,944)(825,945)(826,951)(827,952)(828,953)(829,954)(830,955)(831,946)
(832,947)(833,948)(834,949)(835,950)(836,956)(837,957)(838,958)(839,959)
(840,960);
poly := sub<Sym(960)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
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*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