Polytope of Type {24,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4,10}*1920a
Also Known As : {{24,4|2},{4,10|2}}. if this polytope has another name.
Group : SmallGroup(1920,148900)
Rank : 4
Schlafli Type : {24,4,10}
Number of vertices, edges, etc : 24, 48, 20, 10
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 : {12,4,10}*960, {24,2,10}*960
   3-fold quotients : {8,4,10}*640a
   4-fold quotients : {24,2,5}*480, {12,2,10}*480, {6,4,10}*480
   5-fold quotients : {24,4,2}*384a
   6-fold quotients : {4,4,10}*320, {8,2,10}*320
   8-fold quotients : {12,2,5}*240, {6,2,10}*240
   10-fold quotients : {12,4,2}*192a, {24,2,2}*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 : {3,2,10}*120, {6,2,5}*120
   20-fold quotients : {12,2,2}*96, {6,4,2}*96a
   24-fold quotients : {4,2,5}*80, {2,2,10}*80
   30-fold quotients : {4,4,2}*64, {8,2,2}*64
   32-fold quotients : {3,2,5}*60
   40-fold quotients : {6,2,2}*48
   48-fold quotients : {2,2,5}*40
   60-fold quotients : {2,4,2}*32, {4,2,2}*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 := (  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,491)(  7,492)(  8,493)
(  9,494)( 10,495)( 11,486)( 12,487)( 13,488)( 14,489)( 15,490)( 16,496)
( 17,497)( 18,498)( 19,499)( 20,500)( 21,506)( 22,507)( 23,508)( 24,509)
( 25,510)( 26,501)( 27,502)( 28,503)( 29,504)( 30,505)( 31,511)( 32,512)
( 33,513)( 34,514)( 35,515)( 36,521)( 37,522)( 38,523)( 39,524)( 40,525)
( 41,516)( 42,517)( 43,518)( 44,519)( 45,520)( 46,526)( 47,527)( 48,528)
( 49,529)( 50,530)( 51,536)( 52,537)( 53,538)( 54,539)( 55,540)( 56,531)
( 57,532)( 58,533)( 59,534)( 60,535)( 61,556)( 62,557)( 63,558)( 64,559)
( 65,560)( 66,566)( 67,567)( 68,568)( 69,569)( 70,570)( 71,561)( 72,562)
( 73,563)( 74,564)( 75,565)( 76,541)( 77,542)( 78,543)( 79,544)( 80,545)
( 81,551)( 82,552)( 83,553)( 84,554)( 85,555)( 86,546)( 87,547)( 88,548)
( 89,549)( 90,550)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,596)
( 97,597)( 98,598)( 99,599)(100,600)(101,591)(102,592)(103,593)(104,594)
(105,595)(106,571)(107,572)(108,573)(109,574)(110,575)(111,581)(112,582)
(113,583)(114,584)(115,585)(116,576)(117,577)(118,578)(119,579)(120,580)
(121,601)(122,602)(123,603)(124,604)(125,605)(126,611)(127,612)(128,613)
(129,614)(130,615)(131,606)(132,607)(133,608)(134,609)(135,610)(136,616)
(137,617)(138,618)(139,619)(140,620)(141,626)(142,627)(143,628)(144,629)
(145,630)(146,621)(147,622)(148,623)(149,624)(150,625)(151,631)(152,632)
(153,633)(154,634)(155,635)(156,641)(157,642)(158,643)(159,644)(160,645)
(161,636)(162,637)(163,638)(164,639)(165,640)(166,646)(167,647)(168,648)
(169,649)(170,650)(171,656)(172,657)(173,658)(174,659)(175,660)(176,651)
(177,652)(178,653)(179,654)(180,655)(181,676)(182,677)(183,678)(184,679)
(185,680)(186,686)(187,687)(188,688)(189,689)(190,690)(191,681)(192,682)
(193,683)(194,684)(195,685)(196,661)(197,662)(198,663)(199,664)(200,665)
(201,671)(202,672)(203,673)(204,674)(205,675)(206,666)(207,667)(208,668)
(209,669)(210,670)(211,706)(212,707)(213,708)(214,709)(215,710)(216,716)
(217,717)(218,718)(219,719)(220,720)(221,711)(222,712)(223,713)(224,714)
(225,715)(226,691)(227,692)(228,693)(229,694)(230,695)(231,701)(232,702)
(233,703)(234,704)(235,705)(236,696)(237,697)(238,698)(239,699)(240,700)
(241,721)(242,722)(243,723)(244,724)(245,725)(246,731)(247,732)(248,733)
(249,734)(250,735)(251,726)(252,727)(253,728)(254,729)(255,730)(256,736)
(257,737)(258,738)(259,739)(260,740)(261,746)(262,747)(263,748)(264,749)
(265,750)(266,741)(267,742)(268,743)(269,744)(270,745)(271,751)(272,752)
(273,753)(274,754)(275,755)(276,761)(277,762)(278,763)(279,764)(280,765)
(281,756)(282,757)(283,758)(284,759)(285,760)(286,766)(287,767)(288,768)
(289,769)(290,770)(291,776)(292,777)(293,778)(294,779)(295,780)(296,771)
(297,772)(298,773)(299,774)(300,775)(301,796)(302,797)(303,798)(304,799)
(305,800)(306,806)(307,807)(308,808)(309,809)(310,810)(311,801)(312,802)
(313,803)(314,804)(315,805)(316,781)(317,782)(318,783)(319,784)(320,785)
(321,791)(322,792)(323,793)(324,794)(325,795)(326,786)(327,787)(328,788)
(329,789)(330,790)(331,826)(332,827)(333,828)(334,829)(335,830)(336,836)
(337,837)(338,838)(339,839)(340,840)(341,831)(342,832)(343,833)(344,834)
(345,835)(346,811)(347,812)(348,813)(349,814)(350,815)(351,821)(352,822)
(353,823)(354,824)(355,825)(356,816)(357,817)(358,818)(359,819)(360,820)
(361,841)(362,842)(363,843)(364,844)(365,845)(366,851)(367,852)(368,853)
(369,854)(370,855)(371,846)(372,847)(373,848)(374,849)(375,850)(376,856)
(377,857)(378,858)(379,859)(380,860)(381,866)(382,867)(383,868)(384,869)
(385,870)(386,861)(387,862)(388,863)(389,864)(390,865)(391,871)(392,872)
(393,873)(394,874)(395,875)(396,881)(397,882)(398,883)(399,884)(400,885)
(401,876)(402,877)(403,878)(404,879)(405,880)(406,886)(407,887)(408,888)
(409,889)(410,890)(411,896)(412,897)(413,898)(414,899)(415,900)(416,891)
(417,892)(418,893)(419,894)(420,895)(421,916)(422,917)(423,918)(424,919)
(425,920)(426,926)(427,927)(428,928)(429,929)(430,930)(431,921)(432,922)
(433,923)(434,924)(435,925)(436,901)(437,902)(438,903)(439,904)(440,905)
(441,911)(442,912)(443,913)(444,914)(445,915)(446,906)(447,907)(448,908)
(449,909)(450,910)(451,946)(452,947)(453,948)(454,949)(455,950)(456,956)
(457,957)(458,958)(459,959)(460,960)(461,951)(462,952)(463,953)(464,954)
(465,955)(466,931)(467,932)(468,933)(469,934)(470,935)(471,941)(472,942)
(473,943)(474,944)(475,945)(476,936)(477,937)(478,938)(479,939)(480,940);;
s1 := (  1,  6)(  2,  7)(  3,  8)(  4,  9)(  5, 10)( 16, 21)( 17, 22)( 18, 23)
( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 46, 51)
( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 81)( 62, 82)( 63, 83)( 64, 84)
( 65, 85)( 66, 76)( 67, 77)( 68, 78)( 69, 79)( 70, 80)( 71, 86)( 72, 87)
( 73, 88)( 74, 89)( 75, 90)( 91,111)( 92,112)( 93,113)( 94,114)( 95,115)
( 96,106)( 97,107)( 98,108)( 99,109)(100,110)(101,116)(102,117)(103,118)
(104,119)(105,120)(121,126)(122,127)(123,128)(124,129)(125,130)(136,141)
(137,142)(138,143)(139,144)(140,145)(151,156)(152,157)(153,158)(154,159)
(155,160)(166,171)(167,172)(168,173)(169,174)(170,175)(181,201)(182,202)
(183,203)(184,204)(185,205)(186,196)(187,197)(188,198)(189,199)(190,200)
(191,206)(192,207)(193,208)(194,209)(195,210)(211,231)(212,232)(213,233)
(214,234)(215,235)(216,226)(217,227)(218,228)(219,229)(220,230)(221,236)
(222,237)(223,238)(224,239)(225,240)(241,276)(242,277)(243,278)(244,279)
(245,280)(246,271)(247,272)(248,273)(249,274)(250,275)(251,281)(252,282)
(253,283)(254,284)(255,285)(256,291)(257,292)(258,293)(259,294)(260,295)
(261,286)(262,287)(263,288)(264,289)(265,290)(266,296)(267,297)(268,298)
(269,299)(270,300)(301,351)(302,352)(303,353)(304,354)(305,355)(306,346)
(307,347)(308,348)(309,349)(310,350)(311,356)(312,357)(313,358)(314,359)
(315,360)(316,336)(317,337)(318,338)(319,339)(320,340)(321,331)(322,332)
(323,333)(324,334)(325,335)(326,341)(327,342)(328,343)(329,344)(330,345)
(361,396)(362,397)(363,398)(364,399)(365,400)(366,391)(367,392)(368,393)
(369,394)(370,395)(371,401)(372,402)(373,403)(374,404)(375,405)(376,411)
(377,412)(378,413)(379,414)(380,415)(381,406)(382,407)(383,408)(384,409)
(385,410)(386,416)(387,417)(388,418)(389,419)(390,420)(421,471)(422,472)
(423,473)(424,474)(425,475)(426,466)(427,467)(428,468)(429,469)(430,470)
(431,476)(432,477)(433,478)(434,479)(435,480)(436,456)(437,457)(438,458)
(439,459)(440,460)(441,451)(442,452)(443,453)(444,454)(445,455)(446,461)
(447,462)(448,463)(449,464)(450,465)(481,546)(482,547)(483,548)(484,549)
(485,550)(486,541)(487,542)(488,543)(489,544)(490,545)(491,551)(492,552)
(493,553)(494,554)(495,555)(496,561)(497,562)(498,563)(499,564)(500,565)
(501,556)(502,557)(503,558)(504,559)(505,560)(506,566)(507,567)(508,568)
(509,569)(510,570)(511,576)(512,577)(513,578)(514,579)(515,580)(516,571)
(517,572)(518,573)(519,574)(520,575)(521,581)(522,582)(523,583)(524,584)
(525,585)(526,591)(527,592)(528,593)(529,594)(530,595)(531,586)(532,587)
(533,588)(534,589)(535,590)(536,596)(537,597)(538,598)(539,599)(540,600)
(601,666)(602,667)(603,668)(604,669)(605,670)(606,661)(607,662)(608,663)
(609,664)(610,665)(611,671)(612,672)(613,673)(614,674)(615,675)(616,681)
(617,682)(618,683)(619,684)(620,685)(621,676)(622,677)(623,678)(624,679)
(625,680)(626,686)(627,687)(628,688)(629,689)(630,690)(631,696)(632,697)
(633,698)(634,699)(635,700)(636,691)(637,692)(638,693)(639,694)(640,695)
(641,701)(642,702)(643,703)(644,704)(645,705)(646,711)(647,712)(648,713)
(649,714)(650,715)(651,706)(652,707)(653,708)(654,709)(655,710)(656,716)
(657,717)(658,718)(659,719)(660,720)(721,816)(722,817)(723,818)(724,819)
(725,820)(726,811)(727,812)(728,813)(729,814)(730,815)(731,821)(732,822)
(733,823)(734,824)(735,825)(736,831)(737,832)(738,833)(739,834)(740,835)
(741,826)(742,827)(743,828)(744,829)(745,830)(746,836)(747,837)(748,838)
(749,839)(750,840)(751,786)(752,787)(753,788)(754,789)(755,790)(756,781)
(757,782)(758,783)(759,784)(760,785)(761,791)(762,792)(763,793)(764,794)
(765,795)(766,801)(767,802)(768,803)(769,804)(770,805)(771,796)(772,797)
(773,798)(774,799)(775,800)(776,806)(777,807)(778,808)(779,809)(780,810)
(841,936)(842,937)(843,938)(844,939)(845,940)(846,931)(847,932)(848,933)
(849,934)(850,935)(851,941)(852,942)(853,943)(854,944)(855,945)(856,951)
(857,952)(858,953)(859,954)(860,955)(861,946)(862,947)(863,948)(864,949)
(865,950)(866,956)(867,957)(868,958)(869,959)(870,960)(871,906)(872,907)
(873,908)(874,909)(875,910)(876,901)(877,902)(878,903)(879,904)(880,905)
(881,911)(882,912)(883,913)(884,914)(885,915)(886,921)(887,922)(888,923)
(889,924)(890,925)(891,916)(892,917)(893,918)(894,919)(895,920)(896,926)
(897,927)(898,928)(899,929)(900,930);;
s2 := (  1,361)(  2,365)(  3,364)(  4,363)(  5,362)(  6,366)(  7,370)(  8,369)
(  9,368)( 10,367)( 11,371)( 12,375)( 13,374)( 14,373)( 15,372)( 16,376)
( 17,380)( 18,379)( 19,378)( 20,377)( 21,381)( 22,385)( 23,384)( 24,383)
( 25,382)( 26,386)( 27,390)( 28,389)( 29,388)( 30,387)( 31,391)( 32,395)
( 33,394)( 34,393)( 35,392)( 36,396)( 37,400)( 38,399)( 39,398)( 40,397)
( 41,401)( 42,405)( 43,404)( 44,403)( 45,402)( 46,406)( 47,410)( 48,409)
( 49,408)( 50,407)( 51,411)( 52,415)( 53,414)( 54,413)( 55,412)( 56,416)
( 57,420)( 58,419)( 59,418)( 60,417)( 61,421)( 62,425)( 63,424)( 64,423)
( 65,422)( 66,426)( 67,430)( 68,429)( 69,428)( 70,427)( 71,431)( 72,435)
( 73,434)( 74,433)( 75,432)( 76,436)( 77,440)( 78,439)( 79,438)( 80,437)
( 81,441)( 82,445)( 83,444)( 84,443)( 85,442)( 86,446)( 87,450)( 88,449)
( 89,448)( 90,447)( 91,451)( 92,455)( 93,454)( 94,453)( 95,452)( 96,456)
( 97,460)( 98,459)( 99,458)(100,457)(101,461)(102,465)(103,464)(104,463)
(105,462)(106,466)(107,470)(108,469)(109,468)(110,467)(111,471)(112,475)
(113,474)(114,473)(115,472)(116,476)(117,480)(118,479)(119,478)(120,477)
(121,241)(122,245)(123,244)(124,243)(125,242)(126,246)(127,250)(128,249)
(129,248)(130,247)(131,251)(132,255)(133,254)(134,253)(135,252)(136,256)
(137,260)(138,259)(139,258)(140,257)(141,261)(142,265)(143,264)(144,263)
(145,262)(146,266)(147,270)(148,269)(149,268)(150,267)(151,271)(152,275)
(153,274)(154,273)(155,272)(156,276)(157,280)(158,279)(159,278)(160,277)
(161,281)(162,285)(163,284)(164,283)(165,282)(166,286)(167,290)(168,289)
(169,288)(170,287)(171,291)(172,295)(173,294)(174,293)(175,292)(176,296)
(177,300)(178,299)(179,298)(180,297)(181,301)(182,305)(183,304)(184,303)
(185,302)(186,306)(187,310)(188,309)(189,308)(190,307)(191,311)(192,315)
(193,314)(194,313)(195,312)(196,316)(197,320)(198,319)(199,318)(200,317)
(201,321)(202,325)(203,324)(204,323)(205,322)(206,326)(207,330)(208,329)
(209,328)(210,327)(211,331)(212,335)(213,334)(214,333)(215,332)(216,336)
(217,340)(218,339)(219,338)(220,337)(221,341)(222,345)(223,344)(224,343)
(225,342)(226,346)(227,350)(228,349)(229,348)(230,347)(231,351)(232,355)
(233,354)(234,353)(235,352)(236,356)(237,360)(238,359)(239,358)(240,357)
(481,841)(482,845)(483,844)(484,843)(485,842)(486,846)(487,850)(488,849)
(489,848)(490,847)(491,851)(492,855)(493,854)(494,853)(495,852)(496,856)
(497,860)(498,859)(499,858)(500,857)(501,861)(502,865)(503,864)(504,863)
(505,862)(506,866)(507,870)(508,869)(509,868)(510,867)(511,871)(512,875)
(513,874)(514,873)(515,872)(516,876)(517,880)(518,879)(519,878)(520,877)
(521,881)(522,885)(523,884)(524,883)(525,882)(526,886)(527,890)(528,889)
(529,888)(530,887)(531,891)(532,895)(533,894)(534,893)(535,892)(536,896)
(537,900)(538,899)(539,898)(540,897)(541,901)(542,905)(543,904)(544,903)
(545,902)(546,906)(547,910)(548,909)(549,908)(550,907)(551,911)(552,915)
(553,914)(554,913)(555,912)(556,916)(557,920)(558,919)(559,918)(560,917)
(561,921)(562,925)(563,924)(564,923)(565,922)(566,926)(567,930)(568,929)
(569,928)(570,927)(571,931)(572,935)(573,934)(574,933)(575,932)(576,936)
(577,940)(578,939)(579,938)(580,937)(581,941)(582,945)(583,944)(584,943)
(585,942)(586,946)(587,950)(588,949)(589,948)(590,947)(591,951)(592,955)
(593,954)(594,953)(595,952)(596,956)(597,960)(598,959)(599,958)(600,957)
(601,721)(602,725)(603,724)(604,723)(605,722)(606,726)(607,730)(608,729)
(609,728)(610,727)(611,731)(612,735)(613,734)(614,733)(615,732)(616,736)
(617,740)(618,739)(619,738)(620,737)(621,741)(622,745)(623,744)(624,743)
(625,742)(626,746)(627,750)(628,749)(629,748)(630,747)(631,751)(632,755)
(633,754)(634,753)(635,752)(636,756)(637,760)(638,759)(639,758)(640,757)
(641,761)(642,765)(643,764)(644,763)(645,762)(646,766)(647,770)(648,769)
(649,768)(650,767)(651,771)(652,775)(653,774)(654,773)(655,772)(656,776)
(657,780)(658,779)(659,778)(660,777)(661,781)(662,785)(663,784)(664,783)
(665,782)(666,786)(667,790)(668,789)(669,788)(670,787)(671,791)(672,795)
(673,794)(674,793)(675,792)(676,796)(677,800)(678,799)(679,798)(680,797)
(681,801)(682,805)(683,804)(684,803)(685,802)(686,806)(687,810)(688,809)
(689,808)(690,807)(691,811)(692,815)(693,814)(694,813)(695,812)(696,816)
(697,820)(698,819)(699,818)(700,817)(701,821)(702,825)(703,824)(704,823)
(705,822)(706,826)(707,830)(708,829)(709,828)(710,827)(711,831)(712,835)
(713,834)(714,833)(715,832)(716,836)(717,840)(718,839)(719,838)(720,837);;
s3 := (  1,122)(  2,121)(  3,125)(  4,124)(  5,123)(  6,127)(  7,126)(  8,130)
(  9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,137)
( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)( 24,144)
( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)( 32,151)
( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)( 40,158)
( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)( 48,170)
( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)( 56,177)
( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)( 64,184)
( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)( 72,191)
( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)( 80,198)
( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)( 88,210)
( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)( 96,217)
( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)(104,224)
(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)(112,231)
(113,235)(114,234)(115,233)(116,237)(117,236)(118,240)(119,239)(120,238)
(241,362)(242,361)(243,365)(244,364)(245,363)(246,367)(247,366)(248,370)
(249,369)(250,368)(251,372)(252,371)(253,375)(254,374)(255,373)(256,377)
(257,376)(258,380)(259,379)(260,378)(261,382)(262,381)(263,385)(264,384)
(265,383)(266,387)(267,386)(268,390)(269,389)(270,388)(271,392)(272,391)
(273,395)(274,394)(275,393)(276,397)(277,396)(278,400)(279,399)(280,398)
(281,402)(282,401)(283,405)(284,404)(285,403)(286,407)(287,406)(288,410)
(289,409)(290,408)(291,412)(292,411)(293,415)(294,414)(295,413)(296,417)
(297,416)(298,420)(299,419)(300,418)(301,422)(302,421)(303,425)(304,424)
(305,423)(306,427)(307,426)(308,430)(309,429)(310,428)(311,432)(312,431)
(313,435)(314,434)(315,433)(316,437)(317,436)(318,440)(319,439)(320,438)
(321,442)(322,441)(323,445)(324,444)(325,443)(326,447)(327,446)(328,450)
(329,449)(330,448)(331,452)(332,451)(333,455)(334,454)(335,453)(336,457)
(337,456)(338,460)(339,459)(340,458)(341,462)(342,461)(343,465)(344,464)
(345,463)(346,467)(347,466)(348,470)(349,469)(350,468)(351,472)(352,471)
(353,475)(354,474)(355,473)(356,477)(357,476)(358,480)(359,479)(360,478)
(481,602)(482,601)(483,605)(484,604)(485,603)(486,607)(487,606)(488,610)
(489,609)(490,608)(491,612)(492,611)(493,615)(494,614)(495,613)(496,617)
(497,616)(498,620)(499,619)(500,618)(501,622)(502,621)(503,625)(504,624)
(505,623)(506,627)(507,626)(508,630)(509,629)(510,628)(511,632)(512,631)
(513,635)(514,634)(515,633)(516,637)(517,636)(518,640)(519,639)(520,638)
(521,642)(522,641)(523,645)(524,644)(525,643)(526,647)(527,646)(528,650)
(529,649)(530,648)(531,652)(532,651)(533,655)(534,654)(535,653)(536,657)
(537,656)(538,660)(539,659)(540,658)(541,662)(542,661)(543,665)(544,664)
(545,663)(546,667)(547,666)(548,670)(549,669)(550,668)(551,672)(552,671)
(553,675)(554,674)(555,673)(556,677)(557,676)(558,680)(559,679)(560,678)
(561,682)(562,681)(563,685)(564,684)(565,683)(566,687)(567,686)(568,690)
(569,689)(570,688)(571,692)(572,691)(573,695)(574,694)(575,693)(576,697)
(577,696)(578,700)(579,699)(580,698)(581,702)(582,701)(583,705)(584,704)
(585,703)(586,707)(587,706)(588,710)(589,709)(590,708)(591,712)(592,711)
(593,715)(594,714)(595,713)(596,717)(597,716)(598,720)(599,719)(600,718)
(721,842)(722,841)(723,845)(724,844)(725,843)(726,847)(727,846)(728,850)
(729,849)(730,848)(731,852)(732,851)(733,855)(734,854)(735,853)(736,857)
(737,856)(738,860)(739,859)(740,858)(741,862)(742,861)(743,865)(744,864)
(745,863)(746,867)(747,866)(748,870)(749,869)(750,868)(751,872)(752,871)
(753,875)(754,874)(755,873)(756,877)(757,876)(758,880)(759,879)(760,878)
(761,882)(762,881)(763,885)(764,884)(765,883)(766,887)(767,886)(768,890)
(769,889)(770,888)(771,892)(772,891)(773,895)(774,894)(775,893)(776,897)
(777,896)(778,900)(779,899)(780,898)(781,902)(782,901)(783,905)(784,904)
(785,903)(786,907)(787,906)(788,910)(789,909)(790,908)(791,912)(792,911)
(793,915)(794,914)(795,913)(796,917)(797,916)(798,920)(799,919)(800,918)
(801,922)(802,921)(803,925)(804,924)(805,923)(806,927)(807,926)(808,930)
(809,929)(810,928)(811,932)(812,931)(813,935)(814,934)(815,933)(816,937)
(817,936)(818,940)(819,939)(820,938)(821,942)(822,941)(823,945)(824,944)
(825,943)(826,947)(827,946)(828,950)(829,949)(830,948)(831,952)(832,951)
(833,955)(834,954)(835,953)(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, 
s2*s3*s2*s3*s2*s3*s2*s3*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(960)!(  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,491)(  7,492)
(  8,493)(  9,494)( 10,495)( 11,486)( 12,487)( 13,488)( 14,489)( 15,490)
( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)( 21,506)( 22,507)( 23,508)
( 24,509)( 25,510)( 26,501)( 27,502)( 28,503)( 29,504)( 30,505)( 31,511)
( 32,512)( 33,513)( 34,514)( 35,515)( 36,521)( 37,522)( 38,523)( 39,524)
( 40,525)( 41,516)( 42,517)( 43,518)( 44,519)( 45,520)( 46,526)( 47,527)
( 48,528)( 49,529)( 50,530)( 51,536)( 52,537)( 53,538)( 54,539)( 55,540)
( 56,531)( 57,532)( 58,533)( 59,534)( 60,535)( 61,556)( 62,557)( 63,558)
( 64,559)( 65,560)( 66,566)( 67,567)( 68,568)( 69,569)( 70,570)( 71,561)
( 72,562)( 73,563)( 74,564)( 75,565)( 76,541)( 77,542)( 78,543)( 79,544)
( 80,545)( 81,551)( 82,552)( 83,553)( 84,554)( 85,555)( 86,546)( 87,547)
( 88,548)( 89,549)( 90,550)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)
( 96,596)( 97,597)( 98,598)( 99,599)(100,600)(101,591)(102,592)(103,593)
(104,594)(105,595)(106,571)(107,572)(108,573)(109,574)(110,575)(111,581)
(112,582)(113,583)(114,584)(115,585)(116,576)(117,577)(118,578)(119,579)
(120,580)(121,601)(122,602)(123,603)(124,604)(125,605)(126,611)(127,612)
(128,613)(129,614)(130,615)(131,606)(132,607)(133,608)(134,609)(135,610)
(136,616)(137,617)(138,618)(139,619)(140,620)(141,626)(142,627)(143,628)
(144,629)(145,630)(146,621)(147,622)(148,623)(149,624)(150,625)(151,631)
(152,632)(153,633)(154,634)(155,635)(156,641)(157,642)(158,643)(159,644)
(160,645)(161,636)(162,637)(163,638)(164,639)(165,640)(166,646)(167,647)
(168,648)(169,649)(170,650)(171,656)(172,657)(173,658)(174,659)(175,660)
(176,651)(177,652)(178,653)(179,654)(180,655)(181,676)(182,677)(183,678)
(184,679)(185,680)(186,686)(187,687)(188,688)(189,689)(190,690)(191,681)
(192,682)(193,683)(194,684)(195,685)(196,661)(197,662)(198,663)(199,664)
(200,665)(201,671)(202,672)(203,673)(204,674)(205,675)(206,666)(207,667)
(208,668)(209,669)(210,670)(211,706)(212,707)(213,708)(214,709)(215,710)
(216,716)(217,717)(218,718)(219,719)(220,720)(221,711)(222,712)(223,713)
(224,714)(225,715)(226,691)(227,692)(228,693)(229,694)(230,695)(231,701)
(232,702)(233,703)(234,704)(235,705)(236,696)(237,697)(238,698)(239,699)
(240,700)(241,721)(242,722)(243,723)(244,724)(245,725)(246,731)(247,732)
(248,733)(249,734)(250,735)(251,726)(252,727)(253,728)(254,729)(255,730)
(256,736)(257,737)(258,738)(259,739)(260,740)(261,746)(262,747)(263,748)
(264,749)(265,750)(266,741)(267,742)(268,743)(269,744)(270,745)(271,751)
(272,752)(273,753)(274,754)(275,755)(276,761)(277,762)(278,763)(279,764)
(280,765)(281,756)(282,757)(283,758)(284,759)(285,760)(286,766)(287,767)
(288,768)(289,769)(290,770)(291,776)(292,777)(293,778)(294,779)(295,780)
(296,771)(297,772)(298,773)(299,774)(300,775)(301,796)(302,797)(303,798)
(304,799)(305,800)(306,806)(307,807)(308,808)(309,809)(310,810)(311,801)
(312,802)(313,803)(314,804)(315,805)(316,781)(317,782)(318,783)(319,784)
(320,785)(321,791)(322,792)(323,793)(324,794)(325,795)(326,786)(327,787)
(328,788)(329,789)(330,790)(331,826)(332,827)(333,828)(334,829)(335,830)
(336,836)(337,837)(338,838)(339,839)(340,840)(341,831)(342,832)(343,833)
(344,834)(345,835)(346,811)(347,812)(348,813)(349,814)(350,815)(351,821)
(352,822)(353,823)(354,824)(355,825)(356,816)(357,817)(358,818)(359,819)
(360,820)(361,841)(362,842)(363,843)(364,844)(365,845)(366,851)(367,852)
(368,853)(369,854)(370,855)(371,846)(372,847)(373,848)(374,849)(375,850)
(376,856)(377,857)(378,858)(379,859)(380,860)(381,866)(382,867)(383,868)
(384,869)(385,870)(386,861)(387,862)(388,863)(389,864)(390,865)(391,871)
(392,872)(393,873)(394,874)(395,875)(396,881)(397,882)(398,883)(399,884)
(400,885)(401,876)(402,877)(403,878)(404,879)(405,880)(406,886)(407,887)
(408,888)(409,889)(410,890)(411,896)(412,897)(413,898)(414,899)(415,900)
(416,891)(417,892)(418,893)(419,894)(420,895)(421,916)(422,917)(423,918)
(424,919)(425,920)(426,926)(427,927)(428,928)(429,929)(430,930)(431,921)
(432,922)(433,923)(434,924)(435,925)(436,901)(437,902)(438,903)(439,904)
(440,905)(441,911)(442,912)(443,913)(444,914)(445,915)(446,906)(447,907)
(448,908)(449,909)(450,910)(451,946)(452,947)(453,948)(454,949)(455,950)
(456,956)(457,957)(458,958)(459,959)(460,960)(461,951)(462,952)(463,953)
(464,954)(465,955)(466,931)(467,932)(468,933)(469,934)(470,935)(471,941)
(472,942)(473,943)(474,944)(475,945)(476,936)(477,937)(478,938)(479,939)
(480,940);
s1 := Sym(960)!(  1,  6)(  2,  7)(  3,  8)(  4,  9)(  5, 10)( 16, 21)( 17, 22)
( 18, 23)( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)
( 46, 51)( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 81)( 62, 82)( 63, 83)
( 64, 84)( 65, 85)( 66, 76)( 67, 77)( 68, 78)( 69, 79)( 70, 80)( 71, 86)
( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 91,111)( 92,112)( 93,113)( 94,114)
( 95,115)( 96,106)( 97,107)( 98,108)( 99,109)(100,110)(101,116)(102,117)
(103,118)(104,119)(105,120)(121,126)(122,127)(123,128)(124,129)(125,130)
(136,141)(137,142)(138,143)(139,144)(140,145)(151,156)(152,157)(153,158)
(154,159)(155,160)(166,171)(167,172)(168,173)(169,174)(170,175)(181,201)
(182,202)(183,203)(184,204)(185,205)(186,196)(187,197)(188,198)(189,199)
(190,200)(191,206)(192,207)(193,208)(194,209)(195,210)(211,231)(212,232)
(213,233)(214,234)(215,235)(216,226)(217,227)(218,228)(219,229)(220,230)
(221,236)(222,237)(223,238)(224,239)(225,240)(241,276)(242,277)(243,278)
(244,279)(245,280)(246,271)(247,272)(248,273)(249,274)(250,275)(251,281)
(252,282)(253,283)(254,284)(255,285)(256,291)(257,292)(258,293)(259,294)
(260,295)(261,286)(262,287)(263,288)(264,289)(265,290)(266,296)(267,297)
(268,298)(269,299)(270,300)(301,351)(302,352)(303,353)(304,354)(305,355)
(306,346)(307,347)(308,348)(309,349)(310,350)(311,356)(312,357)(313,358)
(314,359)(315,360)(316,336)(317,337)(318,338)(319,339)(320,340)(321,331)
(322,332)(323,333)(324,334)(325,335)(326,341)(327,342)(328,343)(329,344)
(330,345)(361,396)(362,397)(363,398)(364,399)(365,400)(366,391)(367,392)
(368,393)(369,394)(370,395)(371,401)(372,402)(373,403)(374,404)(375,405)
(376,411)(377,412)(378,413)(379,414)(380,415)(381,406)(382,407)(383,408)
(384,409)(385,410)(386,416)(387,417)(388,418)(389,419)(390,420)(421,471)
(422,472)(423,473)(424,474)(425,475)(426,466)(427,467)(428,468)(429,469)
(430,470)(431,476)(432,477)(433,478)(434,479)(435,480)(436,456)(437,457)
(438,458)(439,459)(440,460)(441,451)(442,452)(443,453)(444,454)(445,455)
(446,461)(447,462)(448,463)(449,464)(450,465)(481,546)(482,547)(483,548)
(484,549)(485,550)(486,541)(487,542)(488,543)(489,544)(490,545)(491,551)
(492,552)(493,553)(494,554)(495,555)(496,561)(497,562)(498,563)(499,564)
(500,565)(501,556)(502,557)(503,558)(504,559)(505,560)(506,566)(507,567)
(508,568)(509,569)(510,570)(511,576)(512,577)(513,578)(514,579)(515,580)
(516,571)(517,572)(518,573)(519,574)(520,575)(521,581)(522,582)(523,583)
(524,584)(525,585)(526,591)(527,592)(528,593)(529,594)(530,595)(531,586)
(532,587)(533,588)(534,589)(535,590)(536,596)(537,597)(538,598)(539,599)
(540,600)(601,666)(602,667)(603,668)(604,669)(605,670)(606,661)(607,662)
(608,663)(609,664)(610,665)(611,671)(612,672)(613,673)(614,674)(615,675)
(616,681)(617,682)(618,683)(619,684)(620,685)(621,676)(622,677)(623,678)
(624,679)(625,680)(626,686)(627,687)(628,688)(629,689)(630,690)(631,696)
(632,697)(633,698)(634,699)(635,700)(636,691)(637,692)(638,693)(639,694)
(640,695)(641,701)(642,702)(643,703)(644,704)(645,705)(646,711)(647,712)
(648,713)(649,714)(650,715)(651,706)(652,707)(653,708)(654,709)(655,710)
(656,716)(657,717)(658,718)(659,719)(660,720)(721,816)(722,817)(723,818)
(724,819)(725,820)(726,811)(727,812)(728,813)(729,814)(730,815)(731,821)
(732,822)(733,823)(734,824)(735,825)(736,831)(737,832)(738,833)(739,834)
(740,835)(741,826)(742,827)(743,828)(744,829)(745,830)(746,836)(747,837)
(748,838)(749,839)(750,840)(751,786)(752,787)(753,788)(754,789)(755,790)
(756,781)(757,782)(758,783)(759,784)(760,785)(761,791)(762,792)(763,793)
(764,794)(765,795)(766,801)(767,802)(768,803)(769,804)(770,805)(771,796)
(772,797)(773,798)(774,799)(775,800)(776,806)(777,807)(778,808)(779,809)
(780,810)(841,936)(842,937)(843,938)(844,939)(845,940)(846,931)(847,932)
(848,933)(849,934)(850,935)(851,941)(852,942)(853,943)(854,944)(855,945)
(856,951)(857,952)(858,953)(859,954)(860,955)(861,946)(862,947)(863,948)
(864,949)(865,950)(866,956)(867,957)(868,958)(869,959)(870,960)(871,906)
(872,907)(873,908)(874,909)(875,910)(876,901)(877,902)(878,903)(879,904)
(880,905)(881,911)(882,912)(883,913)(884,914)(885,915)(886,921)(887,922)
(888,923)(889,924)(890,925)(891,916)(892,917)(893,918)(894,919)(895,920)
(896,926)(897,927)(898,928)(899,929)(900,930);
s2 := Sym(960)!(  1,361)(  2,365)(  3,364)(  4,363)(  5,362)(  6,366)(  7,370)
(  8,369)(  9,368)( 10,367)( 11,371)( 12,375)( 13,374)( 14,373)( 15,372)
( 16,376)( 17,380)( 18,379)( 19,378)( 20,377)( 21,381)( 22,385)( 23,384)
( 24,383)( 25,382)( 26,386)( 27,390)( 28,389)( 29,388)( 30,387)( 31,391)
( 32,395)( 33,394)( 34,393)( 35,392)( 36,396)( 37,400)( 38,399)( 39,398)
( 40,397)( 41,401)( 42,405)( 43,404)( 44,403)( 45,402)( 46,406)( 47,410)
( 48,409)( 49,408)( 50,407)( 51,411)( 52,415)( 53,414)( 54,413)( 55,412)
( 56,416)( 57,420)( 58,419)( 59,418)( 60,417)( 61,421)( 62,425)( 63,424)
( 64,423)( 65,422)( 66,426)( 67,430)( 68,429)( 69,428)( 70,427)( 71,431)
( 72,435)( 73,434)( 74,433)( 75,432)( 76,436)( 77,440)( 78,439)( 79,438)
( 80,437)( 81,441)( 82,445)( 83,444)( 84,443)( 85,442)( 86,446)( 87,450)
( 88,449)( 89,448)( 90,447)( 91,451)( 92,455)( 93,454)( 94,453)( 95,452)
( 96,456)( 97,460)( 98,459)( 99,458)(100,457)(101,461)(102,465)(103,464)
(104,463)(105,462)(106,466)(107,470)(108,469)(109,468)(110,467)(111,471)
(112,475)(113,474)(114,473)(115,472)(116,476)(117,480)(118,479)(119,478)
(120,477)(121,241)(122,245)(123,244)(124,243)(125,242)(126,246)(127,250)
(128,249)(129,248)(130,247)(131,251)(132,255)(133,254)(134,253)(135,252)
(136,256)(137,260)(138,259)(139,258)(140,257)(141,261)(142,265)(143,264)
(144,263)(145,262)(146,266)(147,270)(148,269)(149,268)(150,267)(151,271)
(152,275)(153,274)(154,273)(155,272)(156,276)(157,280)(158,279)(159,278)
(160,277)(161,281)(162,285)(163,284)(164,283)(165,282)(166,286)(167,290)
(168,289)(169,288)(170,287)(171,291)(172,295)(173,294)(174,293)(175,292)
(176,296)(177,300)(178,299)(179,298)(180,297)(181,301)(182,305)(183,304)
(184,303)(185,302)(186,306)(187,310)(188,309)(189,308)(190,307)(191,311)
(192,315)(193,314)(194,313)(195,312)(196,316)(197,320)(198,319)(199,318)
(200,317)(201,321)(202,325)(203,324)(204,323)(205,322)(206,326)(207,330)
(208,329)(209,328)(210,327)(211,331)(212,335)(213,334)(214,333)(215,332)
(216,336)(217,340)(218,339)(219,338)(220,337)(221,341)(222,345)(223,344)
(224,343)(225,342)(226,346)(227,350)(228,349)(229,348)(230,347)(231,351)
(232,355)(233,354)(234,353)(235,352)(236,356)(237,360)(238,359)(239,358)
(240,357)(481,841)(482,845)(483,844)(484,843)(485,842)(486,846)(487,850)
(488,849)(489,848)(490,847)(491,851)(492,855)(493,854)(494,853)(495,852)
(496,856)(497,860)(498,859)(499,858)(500,857)(501,861)(502,865)(503,864)
(504,863)(505,862)(506,866)(507,870)(508,869)(509,868)(510,867)(511,871)
(512,875)(513,874)(514,873)(515,872)(516,876)(517,880)(518,879)(519,878)
(520,877)(521,881)(522,885)(523,884)(524,883)(525,882)(526,886)(527,890)
(528,889)(529,888)(530,887)(531,891)(532,895)(533,894)(534,893)(535,892)
(536,896)(537,900)(538,899)(539,898)(540,897)(541,901)(542,905)(543,904)
(544,903)(545,902)(546,906)(547,910)(548,909)(549,908)(550,907)(551,911)
(552,915)(553,914)(554,913)(555,912)(556,916)(557,920)(558,919)(559,918)
(560,917)(561,921)(562,925)(563,924)(564,923)(565,922)(566,926)(567,930)
(568,929)(569,928)(570,927)(571,931)(572,935)(573,934)(574,933)(575,932)
(576,936)(577,940)(578,939)(579,938)(580,937)(581,941)(582,945)(583,944)
(584,943)(585,942)(586,946)(587,950)(588,949)(589,948)(590,947)(591,951)
(592,955)(593,954)(594,953)(595,952)(596,956)(597,960)(598,959)(599,958)
(600,957)(601,721)(602,725)(603,724)(604,723)(605,722)(606,726)(607,730)
(608,729)(609,728)(610,727)(611,731)(612,735)(613,734)(614,733)(615,732)
(616,736)(617,740)(618,739)(619,738)(620,737)(621,741)(622,745)(623,744)
(624,743)(625,742)(626,746)(627,750)(628,749)(629,748)(630,747)(631,751)
(632,755)(633,754)(634,753)(635,752)(636,756)(637,760)(638,759)(639,758)
(640,757)(641,761)(642,765)(643,764)(644,763)(645,762)(646,766)(647,770)
(648,769)(649,768)(650,767)(651,771)(652,775)(653,774)(654,773)(655,772)
(656,776)(657,780)(658,779)(659,778)(660,777)(661,781)(662,785)(663,784)
(664,783)(665,782)(666,786)(667,790)(668,789)(669,788)(670,787)(671,791)
(672,795)(673,794)(674,793)(675,792)(676,796)(677,800)(678,799)(679,798)
(680,797)(681,801)(682,805)(683,804)(684,803)(685,802)(686,806)(687,810)
(688,809)(689,808)(690,807)(691,811)(692,815)(693,814)(694,813)(695,812)
(696,816)(697,820)(698,819)(699,818)(700,817)(701,821)(702,825)(703,824)
(704,823)(705,822)(706,826)(707,830)(708,829)(709,828)(710,827)(711,831)
(712,835)(713,834)(714,833)(715,832)(716,836)(717,840)(718,839)(719,838)
(720,837);
s3 := Sym(960)!(  1,122)(  2,121)(  3,125)(  4,124)(  5,123)(  6,127)(  7,126)
(  8,130)(  9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)
( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)
( 24,144)( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)
( 32,151)( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)
( 40,158)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)
( 48,170)( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)
( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)
( 64,184)( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)
( 72,191)( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)
( 80,198)( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)
( 88,210)( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)
( 96,217)( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)
(104,224)(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)
(112,231)(113,235)(114,234)(115,233)(116,237)(117,236)(118,240)(119,239)
(120,238)(241,362)(242,361)(243,365)(244,364)(245,363)(246,367)(247,366)
(248,370)(249,369)(250,368)(251,372)(252,371)(253,375)(254,374)(255,373)
(256,377)(257,376)(258,380)(259,379)(260,378)(261,382)(262,381)(263,385)
(264,384)(265,383)(266,387)(267,386)(268,390)(269,389)(270,388)(271,392)
(272,391)(273,395)(274,394)(275,393)(276,397)(277,396)(278,400)(279,399)
(280,398)(281,402)(282,401)(283,405)(284,404)(285,403)(286,407)(287,406)
(288,410)(289,409)(290,408)(291,412)(292,411)(293,415)(294,414)(295,413)
(296,417)(297,416)(298,420)(299,419)(300,418)(301,422)(302,421)(303,425)
(304,424)(305,423)(306,427)(307,426)(308,430)(309,429)(310,428)(311,432)
(312,431)(313,435)(314,434)(315,433)(316,437)(317,436)(318,440)(319,439)
(320,438)(321,442)(322,441)(323,445)(324,444)(325,443)(326,447)(327,446)
(328,450)(329,449)(330,448)(331,452)(332,451)(333,455)(334,454)(335,453)
(336,457)(337,456)(338,460)(339,459)(340,458)(341,462)(342,461)(343,465)
(344,464)(345,463)(346,467)(347,466)(348,470)(349,469)(350,468)(351,472)
(352,471)(353,475)(354,474)(355,473)(356,477)(357,476)(358,480)(359,479)
(360,478)(481,602)(482,601)(483,605)(484,604)(485,603)(486,607)(487,606)
(488,610)(489,609)(490,608)(491,612)(492,611)(493,615)(494,614)(495,613)
(496,617)(497,616)(498,620)(499,619)(500,618)(501,622)(502,621)(503,625)
(504,624)(505,623)(506,627)(507,626)(508,630)(509,629)(510,628)(511,632)
(512,631)(513,635)(514,634)(515,633)(516,637)(517,636)(518,640)(519,639)
(520,638)(521,642)(522,641)(523,645)(524,644)(525,643)(526,647)(527,646)
(528,650)(529,649)(530,648)(531,652)(532,651)(533,655)(534,654)(535,653)
(536,657)(537,656)(538,660)(539,659)(540,658)(541,662)(542,661)(543,665)
(544,664)(545,663)(546,667)(547,666)(548,670)(549,669)(550,668)(551,672)
(552,671)(553,675)(554,674)(555,673)(556,677)(557,676)(558,680)(559,679)
(560,678)(561,682)(562,681)(563,685)(564,684)(565,683)(566,687)(567,686)
(568,690)(569,689)(570,688)(571,692)(572,691)(573,695)(574,694)(575,693)
(576,697)(577,696)(578,700)(579,699)(580,698)(581,702)(582,701)(583,705)
(584,704)(585,703)(586,707)(587,706)(588,710)(589,709)(590,708)(591,712)
(592,711)(593,715)(594,714)(595,713)(596,717)(597,716)(598,720)(599,719)
(600,718)(721,842)(722,841)(723,845)(724,844)(725,843)(726,847)(727,846)
(728,850)(729,849)(730,848)(731,852)(732,851)(733,855)(734,854)(735,853)
(736,857)(737,856)(738,860)(739,859)(740,858)(741,862)(742,861)(743,865)
(744,864)(745,863)(746,867)(747,866)(748,870)(749,869)(750,868)(751,872)
(752,871)(753,875)(754,874)(755,873)(756,877)(757,876)(758,880)(759,879)
(760,878)(761,882)(762,881)(763,885)(764,884)(765,883)(766,887)(767,886)
(768,890)(769,889)(770,888)(771,892)(772,891)(773,895)(774,894)(775,893)
(776,897)(777,896)(778,900)(779,899)(780,898)(781,902)(782,901)(783,905)
(784,904)(785,903)(786,907)(787,906)(788,910)(789,909)(790,908)(791,912)
(792,911)(793,915)(794,914)(795,913)(796,917)(797,916)(798,920)(799,919)
(800,918)(801,922)(802,921)(803,925)(804,924)(805,923)(806,927)(807,926)
(808,930)(809,929)(810,928)(811,932)(812,931)(813,935)(814,934)(815,933)
(816,937)(817,936)(818,940)(819,939)(820,938)(821,942)(822,941)(823,945)
(824,944)(825,943)(826,947)(827,946)(828,950)(829,949)(830,948)(831,952)
(832,951)(833,955)(834,954)(835,953)(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, s2*s3*s2*s3*s2*s3*s2*s3*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 >;
References : None.
to this polytope