Polytope of Type {10,24,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,24,4}*1920a
Also Known As : {{10,24|2},{24,4|2}}. if this polytope has another name.
Group : SmallGroup(1920,148900)
Rank : 4
Schlafli Type : {10,24,4}
Number of vertices, edges, etc : 10, 120, 48, 4
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,12,4}*960a, {10,24,2}*960
   3-fold quotients : {10,8,4}*640a
   4-fold quotients : {10,12,2}*480, {10,6,4}*480a
   5-fold quotients : {2,24,4}*384a
   6-fold quotients : {10,4,4}*320, {10,8,2}*320
   8-fold quotients : {10,6,2}*240
   10-fold quotients : {2,12,4}*192a, {2,24,2}*192
   12-fold quotients : {10,2,4}*160, {10,4,2}*160
   15-fold quotients : {2,8,4}*128a
   20-fold quotients : {2,12,2}*96, {2,6,4}*96a
   24-fold quotients : {5,2,4}*80, {10,2,2}*80
   30-fold quotients : {2,4,4}*64, {2,8,2}*64
   40-fold quotients : {2,6,2}*48
   48-fold quotients : {5,2,2}*40
   60-fold quotients : {2,2,4}*32, {2,4,2}*32
   80-fold quotients : {2,3,2}*24
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (  1,121)(  2,125)(  3,124)(  4,123)(  5,122)(  6,126)(  7,130)(  8,129)
(  9,128)( 10,127)( 11,131)( 12,135)( 13,134)( 14,133)( 15,132)( 16,136)
( 17,140)( 18,139)( 19,138)( 20,137)( 21,141)( 22,145)( 23,144)( 24,143)
( 25,142)( 26,146)( 27,150)( 28,149)( 29,148)( 30,147)( 31,151)( 32,155)
( 33,154)( 34,153)( 35,152)( 36,156)( 37,160)( 38,159)( 39,158)( 40,157)
( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,166)( 47,170)( 48,169)
( 49,168)( 50,167)( 51,171)( 52,175)( 53,174)( 54,173)( 55,172)( 56,176)
( 57,180)( 58,179)( 59,178)( 60,177)( 61,181)( 62,185)( 63,184)( 64,183)
( 65,182)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,191)( 72,195)
( 73,194)( 74,193)( 75,192)( 76,196)( 77,200)( 78,199)( 79,198)( 80,197)
( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,206)( 87,210)( 88,209)
( 89,208)( 90,207)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)( 96,216)
( 97,220)( 98,219)( 99,218)(100,217)(101,221)(102,225)(103,224)(104,223)
(105,222)(106,226)(107,230)(108,229)(109,228)(110,227)(111,231)(112,235)
(113,234)(114,233)(115,232)(116,236)(117,240)(118,239)(119,238)(120,237)
(241,361)(242,365)(243,364)(244,363)(245,362)(246,366)(247,370)(248,369)
(249,368)(250,367)(251,371)(252,375)(253,374)(254,373)(255,372)(256,376)
(257,380)(258,379)(259,378)(260,377)(261,381)(262,385)(263,384)(264,383)
(265,382)(266,386)(267,390)(268,389)(269,388)(270,387)(271,391)(272,395)
(273,394)(274,393)(275,392)(276,396)(277,400)(278,399)(279,398)(280,397)
(281,401)(282,405)(283,404)(284,403)(285,402)(286,406)(287,410)(288,409)
(289,408)(290,407)(291,411)(292,415)(293,414)(294,413)(295,412)(296,416)
(297,420)(298,419)(299,418)(300,417)(301,421)(302,425)(303,424)(304,423)
(305,422)(306,426)(307,430)(308,429)(309,428)(310,427)(311,431)(312,435)
(313,434)(314,433)(315,432)(316,436)(317,440)(318,439)(319,438)(320,437)
(321,441)(322,445)(323,444)(324,443)(325,442)(326,446)(327,450)(328,449)
(329,448)(330,447)(331,451)(332,455)(333,454)(334,453)(335,452)(336,456)
(337,460)(338,459)(339,458)(340,457)(341,461)(342,465)(343,464)(344,463)
(345,462)(346,466)(347,470)(348,469)(349,468)(350,467)(351,471)(352,475)
(353,474)(354,473)(355,472)(356,476)(357,480)(358,479)(359,478)(360,477)
(481,601)(482,605)(483,604)(484,603)(485,602)(486,606)(487,610)(488,609)
(489,608)(490,607)(491,611)(492,615)(493,614)(494,613)(495,612)(496,616)
(497,620)(498,619)(499,618)(500,617)(501,621)(502,625)(503,624)(504,623)
(505,622)(506,626)(507,630)(508,629)(509,628)(510,627)(511,631)(512,635)
(513,634)(514,633)(515,632)(516,636)(517,640)(518,639)(519,638)(520,637)
(521,641)(522,645)(523,644)(524,643)(525,642)(526,646)(527,650)(528,649)
(529,648)(530,647)(531,651)(532,655)(533,654)(534,653)(535,652)(536,656)
(537,660)(538,659)(539,658)(540,657)(541,661)(542,665)(543,664)(544,663)
(545,662)(546,666)(547,670)(548,669)(549,668)(550,667)(551,671)(552,675)
(553,674)(554,673)(555,672)(556,676)(557,680)(558,679)(559,678)(560,677)
(561,681)(562,685)(563,684)(564,683)(565,682)(566,686)(567,690)(568,689)
(569,688)(570,687)(571,691)(572,695)(573,694)(574,693)(575,692)(576,696)
(577,700)(578,699)(579,698)(580,697)(581,701)(582,705)(583,704)(584,703)
(585,702)(586,706)(587,710)(588,709)(589,708)(590,707)(591,711)(592,715)
(593,714)(594,713)(595,712)(596,716)(597,720)(598,719)(599,718)(600,717)
(721,841)(722,845)(723,844)(724,843)(725,842)(726,846)(727,850)(728,849)
(729,848)(730,847)(731,851)(732,855)(733,854)(734,853)(735,852)(736,856)
(737,860)(738,859)(739,858)(740,857)(741,861)(742,865)(743,864)(744,863)
(745,862)(746,866)(747,870)(748,869)(749,868)(750,867)(751,871)(752,875)
(753,874)(754,873)(755,872)(756,876)(757,880)(758,879)(759,878)(760,877)
(761,881)(762,885)(763,884)(764,883)(765,882)(766,886)(767,890)(768,889)
(769,888)(770,887)(771,891)(772,895)(773,894)(774,893)(775,892)(776,896)
(777,900)(778,899)(779,898)(780,897)(781,901)(782,905)(783,904)(784,903)
(785,902)(786,906)(787,910)(788,909)(789,908)(790,907)(791,911)(792,915)
(793,914)(794,913)(795,912)(796,916)(797,920)(798,919)(799,918)(800,917)
(801,921)(802,925)(803,924)(804,923)(805,922)(806,926)(807,930)(808,929)
(809,928)(810,927)(811,931)(812,935)(813,934)(814,933)(815,932)(816,936)
(817,940)(818,939)(819,938)(820,937)(821,941)(822,945)(823,944)(824,943)
(825,942)(826,946)(827,950)(828,949)(829,948)(830,947)(831,951)(832,955)
(833,954)(834,953)(835,952)(836,956)(837,960)(838,959)(839,958)(840,957);;
s1 := (  1,602)(  2,601)(  3,605)(  4,604)(  5,603)(  6,612)(  7,611)(  8,615)
(  9,614)( 10,613)( 11,607)( 12,606)( 13,610)( 14,609)( 15,608)( 16,617)
( 17,616)( 18,620)( 19,619)( 20,618)( 21,627)( 22,626)( 23,630)( 24,629)
( 25,628)( 26,622)( 27,621)( 28,625)( 29,624)( 30,623)( 31,632)( 32,631)
( 33,635)( 34,634)( 35,633)( 36,642)( 37,641)( 38,645)( 39,644)( 40,643)
( 41,637)( 42,636)( 43,640)( 44,639)( 45,638)( 46,647)( 47,646)( 48,650)
( 49,649)( 50,648)( 51,657)( 52,656)( 53,660)( 54,659)( 55,658)( 56,652)
( 57,651)( 58,655)( 59,654)( 60,653)( 61,677)( 62,676)( 63,680)( 64,679)
( 65,678)( 66,687)( 67,686)( 68,690)( 69,689)( 70,688)( 71,682)( 72,681)
( 73,685)( 74,684)( 75,683)( 76,662)( 77,661)( 78,665)( 79,664)( 80,663)
( 81,672)( 82,671)( 83,675)( 84,674)( 85,673)( 86,667)( 87,666)( 88,670)
( 89,669)( 90,668)( 91,707)( 92,706)( 93,710)( 94,709)( 95,708)( 96,717)
( 97,716)( 98,720)( 99,719)(100,718)(101,712)(102,711)(103,715)(104,714)
(105,713)(106,692)(107,691)(108,695)(109,694)(110,693)(111,702)(112,701)
(113,705)(114,704)(115,703)(116,697)(117,696)(118,700)(119,699)(120,698)
(121,482)(122,481)(123,485)(124,484)(125,483)(126,492)(127,491)(128,495)
(129,494)(130,493)(131,487)(132,486)(133,490)(134,489)(135,488)(136,497)
(137,496)(138,500)(139,499)(140,498)(141,507)(142,506)(143,510)(144,509)
(145,508)(146,502)(147,501)(148,505)(149,504)(150,503)(151,512)(152,511)
(153,515)(154,514)(155,513)(156,522)(157,521)(158,525)(159,524)(160,523)
(161,517)(162,516)(163,520)(164,519)(165,518)(166,527)(167,526)(168,530)
(169,529)(170,528)(171,537)(172,536)(173,540)(174,539)(175,538)(176,532)
(177,531)(178,535)(179,534)(180,533)(181,557)(182,556)(183,560)(184,559)
(185,558)(186,567)(187,566)(188,570)(189,569)(190,568)(191,562)(192,561)
(193,565)(194,564)(195,563)(196,542)(197,541)(198,545)(199,544)(200,543)
(201,552)(202,551)(203,555)(204,554)(205,553)(206,547)(207,546)(208,550)
(209,549)(210,548)(211,587)(212,586)(213,590)(214,589)(215,588)(216,597)
(217,596)(218,600)(219,599)(220,598)(221,592)(222,591)(223,595)(224,594)
(225,593)(226,572)(227,571)(228,575)(229,574)(230,573)(231,582)(232,581)
(233,585)(234,584)(235,583)(236,577)(237,576)(238,580)(239,579)(240,578)
(241,842)(242,841)(243,845)(244,844)(245,843)(246,852)(247,851)(248,855)
(249,854)(250,853)(251,847)(252,846)(253,850)(254,849)(255,848)(256,857)
(257,856)(258,860)(259,859)(260,858)(261,867)(262,866)(263,870)(264,869)
(265,868)(266,862)(267,861)(268,865)(269,864)(270,863)(271,872)(272,871)
(273,875)(274,874)(275,873)(276,882)(277,881)(278,885)(279,884)(280,883)
(281,877)(282,876)(283,880)(284,879)(285,878)(286,887)(287,886)(288,890)
(289,889)(290,888)(291,897)(292,896)(293,900)(294,899)(295,898)(296,892)
(297,891)(298,895)(299,894)(300,893)(301,917)(302,916)(303,920)(304,919)
(305,918)(306,927)(307,926)(308,930)(309,929)(310,928)(311,922)(312,921)
(313,925)(314,924)(315,923)(316,902)(317,901)(318,905)(319,904)(320,903)
(321,912)(322,911)(323,915)(324,914)(325,913)(326,907)(327,906)(328,910)
(329,909)(330,908)(331,947)(332,946)(333,950)(334,949)(335,948)(336,957)
(337,956)(338,960)(339,959)(340,958)(341,952)(342,951)(343,955)(344,954)
(345,953)(346,932)(347,931)(348,935)(349,934)(350,933)(351,942)(352,941)
(353,945)(354,944)(355,943)(356,937)(357,936)(358,940)(359,939)(360,938)
(361,722)(362,721)(363,725)(364,724)(365,723)(366,732)(367,731)(368,735)
(369,734)(370,733)(371,727)(372,726)(373,730)(374,729)(375,728)(376,737)
(377,736)(378,740)(379,739)(380,738)(381,747)(382,746)(383,750)(384,749)
(385,748)(386,742)(387,741)(388,745)(389,744)(390,743)(391,752)(392,751)
(393,755)(394,754)(395,753)(396,762)(397,761)(398,765)(399,764)(400,763)
(401,757)(402,756)(403,760)(404,759)(405,758)(406,767)(407,766)(408,770)
(409,769)(410,768)(411,777)(412,776)(413,780)(414,779)(415,778)(416,772)
(417,771)(418,775)(419,774)(420,773)(421,797)(422,796)(423,800)(424,799)
(425,798)(426,807)(427,806)(428,810)(429,809)(430,808)(431,802)(432,801)
(433,805)(434,804)(435,803)(436,782)(437,781)(438,785)(439,784)(440,783)
(441,792)(442,791)(443,795)(444,794)(445,793)(446,787)(447,786)(448,790)
(449,789)(450,788)(451,827)(452,826)(453,830)(454,829)(455,828)(456,837)
(457,836)(458,840)(459,839)(460,838)(461,832)(462,831)(463,835)(464,834)
(465,833)(466,812)(467,811)(468,815)(469,814)(470,813)(471,822)(472,821)
(473,825)(474,824)(475,823)(476,817)(477,816)(478,820)(479,819)(480,818);;
s2 := (  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);;
s3 := (  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)(  8,248)
(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)( 24,264)
( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)( 40,280)
( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)( 56,296)
( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)( 72,312)
( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)( 88,328)
( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,336)
( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)(104,344)
(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)(112,352)
(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)(120,360)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)(128,368)
(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)(144,384)
(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)(160,400)
(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)(176,416)
(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)(192,432)
(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)(208,448)
(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)(216,456)
(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)(224,464)
(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)(232,472)
(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)(240,480)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)(488,728)
(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)(504,744)
(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)(520,760)
(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)(536,776)
(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)(544,784)
(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)(552,792)
(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)(560,800)
(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)(568,808)
(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)(576,816)
(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)(584,824)
(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)(592,832)
(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)(600,840)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)(608,848)
(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)(624,864)
(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)(640,880)
(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)(656,896)
(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)(672,912)
(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)(688,928)
(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)(696,936)
(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)(704,944)
(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)(712,952)
(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)(720,960);;
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*s3*s2*s1*s2*s3*s2, 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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(960)!(  1,121)(  2,125)(  3,124)(  4,123)(  5,122)(  6,126)(  7,130)
(  8,129)(  9,128)( 10,127)( 11,131)( 12,135)( 13,134)( 14,133)( 15,132)
( 16,136)( 17,140)( 18,139)( 19,138)( 20,137)( 21,141)( 22,145)( 23,144)
( 24,143)( 25,142)( 26,146)( 27,150)( 28,149)( 29,148)( 30,147)( 31,151)
( 32,155)( 33,154)( 34,153)( 35,152)( 36,156)( 37,160)( 38,159)( 39,158)
( 40,157)( 41,161)( 42,165)( 43,164)( 44,163)( 45,162)( 46,166)( 47,170)
( 48,169)( 49,168)( 50,167)( 51,171)( 52,175)( 53,174)( 54,173)( 55,172)
( 56,176)( 57,180)( 58,179)( 59,178)( 60,177)( 61,181)( 62,185)( 63,184)
( 64,183)( 65,182)( 66,186)( 67,190)( 68,189)( 69,188)( 70,187)( 71,191)
( 72,195)( 73,194)( 74,193)( 75,192)( 76,196)( 77,200)( 78,199)( 79,198)
( 80,197)( 81,201)( 82,205)( 83,204)( 84,203)( 85,202)( 86,206)( 87,210)
( 88,209)( 89,208)( 90,207)( 91,211)( 92,215)( 93,214)( 94,213)( 95,212)
( 96,216)( 97,220)( 98,219)( 99,218)(100,217)(101,221)(102,225)(103,224)
(104,223)(105,222)(106,226)(107,230)(108,229)(109,228)(110,227)(111,231)
(112,235)(113,234)(114,233)(115,232)(116,236)(117,240)(118,239)(119,238)
(120,237)(241,361)(242,365)(243,364)(244,363)(245,362)(246,366)(247,370)
(248,369)(249,368)(250,367)(251,371)(252,375)(253,374)(254,373)(255,372)
(256,376)(257,380)(258,379)(259,378)(260,377)(261,381)(262,385)(263,384)
(264,383)(265,382)(266,386)(267,390)(268,389)(269,388)(270,387)(271,391)
(272,395)(273,394)(274,393)(275,392)(276,396)(277,400)(278,399)(279,398)
(280,397)(281,401)(282,405)(283,404)(284,403)(285,402)(286,406)(287,410)
(288,409)(289,408)(290,407)(291,411)(292,415)(293,414)(294,413)(295,412)
(296,416)(297,420)(298,419)(299,418)(300,417)(301,421)(302,425)(303,424)
(304,423)(305,422)(306,426)(307,430)(308,429)(309,428)(310,427)(311,431)
(312,435)(313,434)(314,433)(315,432)(316,436)(317,440)(318,439)(319,438)
(320,437)(321,441)(322,445)(323,444)(324,443)(325,442)(326,446)(327,450)
(328,449)(329,448)(330,447)(331,451)(332,455)(333,454)(334,453)(335,452)
(336,456)(337,460)(338,459)(339,458)(340,457)(341,461)(342,465)(343,464)
(344,463)(345,462)(346,466)(347,470)(348,469)(349,468)(350,467)(351,471)
(352,475)(353,474)(354,473)(355,472)(356,476)(357,480)(358,479)(359,478)
(360,477)(481,601)(482,605)(483,604)(484,603)(485,602)(486,606)(487,610)
(488,609)(489,608)(490,607)(491,611)(492,615)(493,614)(494,613)(495,612)
(496,616)(497,620)(498,619)(499,618)(500,617)(501,621)(502,625)(503,624)
(504,623)(505,622)(506,626)(507,630)(508,629)(509,628)(510,627)(511,631)
(512,635)(513,634)(514,633)(515,632)(516,636)(517,640)(518,639)(519,638)
(520,637)(521,641)(522,645)(523,644)(524,643)(525,642)(526,646)(527,650)
(528,649)(529,648)(530,647)(531,651)(532,655)(533,654)(534,653)(535,652)
(536,656)(537,660)(538,659)(539,658)(540,657)(541,661)(542,665)(543,664)
(544,663)(545,662)(546,666)(547,670)(548,669)(549,668)(550,667)(551,671)
(552,675)(553,674)(554,673)(555,672)(556,676)(557,680)(558,679)(559,678)
(560,677)(561,681)(562,685)(563,684)(564,683)(565,682)(566,686)(567,690)
(568,689)(569,688)(570,687)(571,691)(572,695)(573,694)(574,693)(575,692)
(576,696)(577,700)(578,699)(579,698)(580,697)(581,701)(582,705)(583,704)
(584,703)(585,702)(586,706)(587,710)(588,709)(589,708)(590,707)(591,711)
(592,715)(593,714)(594,713)(595,712)(596,716)(597,720)(598,719)(599,718)
(600,717)(721,841)(722,845)(723,844)(724,843)(725,842)(726,846)(727,850)
(728,849)(729,848)(730,847)(731,851)(732,855)(733,854)(734,853)(735,852)
(736,856)(737,860)(738,859)(739,858)(740,857)(741,861)(742,865)(743,864)
(744,863)(745,862)(746,866)(747,870)(748,869)(749,868)(750,867)(751,871)
(752,875)(753,874)(754,873)(755,872)(756,876)(757,880)(758,879)(759,878)
(760,877)(761,881)(762,885)(763,884)(764,883)(765,882)(766,886)(767,890)
(768,889)(769,888)(770,887)(771,891)(772,895)(773,894)(774,893)(775,892)
(776,896)(777,900)(778,899)(779,898)(780,897)(781,901)(782,905)(783,904)
(784,903)(785,902)(786,906)(787,910)(788,909)(789,908)(790,907)(791,911)
(792,915)(793,914)(794,913)(795,912)(796,916)(797,920)(798,919)(799,918)
(800,917)(801,921)(802,925)(803,924)(804,923)(805,922)(806,926)(807,930)
(808,929)(809,928)(810,927)(811,931)(812,935)(813,934)(814,933)(815,932)
(816,936)(817,940)(818,939)(819,938)(820,937)(821,941)(822,945)(823,944)
(824,943)(825,942)(826,946)(827,950)(828,949)(829,948)(830,947)(831,951)
(832,955)(833,954)(834,953)(835,952)(836,956)(837,960)(838,959)(839,958)
(840,957);
s1 := Sym(960)!(  1,602)(  2,601)(  3,605)(  4,604)(  5,603)(  6,612)(  7,611)
(  8,615)(  9,614)( 10,613)( 11,607)( 12,606)( 13,610)( 14,609)( 15,608)
( 16,617)( 17,616)( 18,620)( 19,619)( 20,618)( 21,627)( 22,626)( 23,630)
( 24,629)( 25,628)( 26,622)( 27,621)( 28,625)( 29,624)( 30,623)( 31,632)
( 32,631)( 33,635)( 34,634)( 35,633)( 36,642)( 37,641)( 38,645)( 39,644)
( 40,643)( 41,637)( 42,636)( 43,640)( 44,639)( 45,638)( 46,647)( 47,646)
( 48,650)( 49,649)( 50,648)( 51,657)( 52,656)( 53,660)( 54,659)( 55,658)
( 56,652)( 57,651)( 58,655)( 59,654)( 60,653)( 61,677)( 62,676)( 63,680)
( 64,679)( 65,678)( 66,687)( 67,686)( 68,690)( 69,689)( 70,688)( 71,682)
( 72,681)( 73,685)( 74,684)( 75,683)( 76,662)( 77,661)( 78,665)( 79,664)
( 80,663)( 81,672)( 82,671)( 83,675)( 84,674)( 85,673)( 86,667)( 87,666)
( 88,670)( 89,669)( 90,668)( 91,707)( 92,706)( 93,710)( 94,709)( 95,708)
( 96,717)( 97,716)( 98,720)( 99,719)(100,718)(101,712)(102,711)(103,715)
(104,714)(105,713)(106,692)(107,691)(108,695)(109,694)(110,693)(111,702)
(112,701)(113,705)(114,704)(115,703)(116,697)(117,696)(118,700)(119,699)
(120,698)(121,482)(122,481)(123,485)(124,484)(125,483)(126,492)(127,491)
(128,495)(129,494)(130,493)(131,487)(132,486)(133,490)(134,489)(135,488)
(136,497)(137,496)(138,500)(139,499)(140,498)(141,507)(142,506)(143,510)
(144,509)(145,508)(146,502)(147,501)(148,505)(149,504)(150,503)(151,512)
(152,511)(153,515)(154,514)(155,513)(156,522)(157,521)(158,525)(159,524)
(160,523)(161,517)(162,516)(163,520)(164,519)(165,518)(166,527)(167,526)
(168,530)(169,529)(170,528)(171,537)(172,536)(173,540)(174,539)(175,538)
(176,532)(177,531)(178,535)(179,534)(180,533)(181,557)(182,556)(183,560)
(184,559)(185,558)(186,567)(187,566)(188,570)(189,569)(190,568)(191,562)
(192,561)(193,565)(194,564)(195,563)(196,542)(197,541)(198,545)(199,544)
(200,543)(201,552)(202,551)(203,555)(204,554)(205,553)(206,547)(207,546)
(208,550)(209,549)(210,548)(211,587)(212,586)(213,590)(214,589)(215,588)
(216,597)(217,596)(218,600)(219,599)(220,598)(221,592)(222,591)(223,595)
(224,594)(225,593)(226,572)(227,571)(228,575)(229,574)(230,573)(231,582)
(232,581)(233,585)(234,584)(235,583)(236,577)(237,576)(238,580)(239,579)
(240,578)(241,842)(242,841)(243,845)(244,844)(245,843)(246,852)(247,851)
(248,855)(249,854)(250,853)(251,847)(252,846)(253,850)(254,849)(255,848)
(256,857)(257,856)(258,860)(259,859)(260,858)(261,867)(262,866)(263,870)
(264,869)(265,868)(266,862)(267,861)(268,865)(269,864)(270,863)(271,872)
(272,871)(273,875)(274,874)(275,873)(276,882)(277,881)(278,885)(279,884)
(280,883)(281,877)(282,876)(283,880)(284,879)(285,878)(286,887)(287,886)
(288,890)(289,889)(290,888)(291,897)(292,896)(293,900)(294,899)(295,898)
(296,892)(297,891)(298,895)(299,894)(300,893)(301,917)(302,916)(303,920)
(304,919)(305,918)(306,927)(307,926)(308,930)(309,929)(310,928)(311,922)
(312,921)(313,925)(314,924)(315,923)(316,902)(317,901)(318,905)(319,904)
(320,903)(321,912)(322,911)(323,915)(324,914)(325,913)(326,907)(327,906)
(328,910)(329,909)(330,908)(331,947)(332,946)(333,950)(334,949)(335,948)
(336,957)(337,956)(338,960)(339,959)(340,958)(341,952)(342,951)(343,955)
(344,954)(345,953)(346,932)(347,931)(348,935)(349,934)(350,933)(351,942)
(352,941)(353,945)(354,944)(355,943)(356,937)(357,936)(358,940)(359,939)
(360,938)(361,722)(362,721)(363,725)(364,724)(365,723)(366,732)(367,731)
(368,735)(369,734)(370,733)(371,727)(372,726)(373,730)(374,729)(375,728)
(376,737)(377,736)(378,740)(379,739)(380,738)(381,747)(382,746)(383,750)
(384,749)(385,748)(386,742)(387,741)(388,745)(389,744)(390,743)(391,752)
(392,751)(393,755)(394,754)(395,753)(396,762)(397,761)(398,765)(399,764)
(400,763)(401,757)(402,756)(403,760)(404,759)(405,758)(406,767)(407,766)
(408,770)(409,769)(410,768)(411,777)(412,776)(413,780)(414,779)(415,778)
(416,772)(417,771)(418,775)(419,774)(420,773)(421,797)(422,796)(423,800)
(424,799)(425,798)(426,807)(427,806)(428,810)(429,809)(430,808)(431,802)
(432,801)(433,805)(434,804)(435,803)(436,782)(437,781)(438,785)(439,784)
(440,783)(441,792)(442,791)(443,795)(444,794)(445,793)(446,787)(447,786)
(448,790)(449,789)(450,788)(451,827)(452,826)(453,830)(454,829)(455,828)
(456,837)(457,836)(458,840)(459,839)(460,838)(461,832)(462,831)(463,835)
(464,834)(465,833)(466,812)(467,811)(468,815)(469,814)(470,813)(471,822)
(472,821)(473,825)(474,824)(475,823)(476,817)(477,816)(478,820)(479,819)
(480,818);
s2 := 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);
s3 := Sym(960)!(  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,246)(  7,247)
(  8,248)(  9,249)( 10,250)( 11,251)( 12,252)( 13,253)( 14,254)( 15,255)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,261)( 22,262)( 23,263)
( 24,264)( 25,265)( 26,266)( 27,267)( 28,268)( 29,269)( 30,270)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,276)( 37,277)( 38,278)( 39,279)
( 40,280)( 41,281)( 42,282)( 43,283)( 44,284)( 45,285)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,291)( 52,292)( 53,293)( 54,294)( 55,295)
( 56,296)( 57,297)( 58,298)( 59,299)( 60,300)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,306)( 67,307)( 68,308)( 69,309)( 70,310)( 71,311)
( 72,312)( 73,313)( 74,314)( 75,315)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,321)( 82,322)( 83,323)( 84,324)( 85,325)( 86,326)( 87,327)
( 88,328)( 89,329)( 90,330)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,336)( 97,337)( 98,338)( 99,339)(100,340)(101,341)(102,342)(103,343)
(104,344)(105,345)(106,346)(107,347)(108,348)(109,349)(110,350)(111,351)
(112,352)(113,353)(114,354)(115,355)(116,356)(117,357)(118,358)(119,359)
(120,360)(121,361)(122,362)(123,363)(124,364)(125,365)(126,366)(127,367)
(128,368)(129,369)(130,370)(131,371)(132,372)(133,373)(134,374)(135,375)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,381)(142,382)(143,383)
(144,384)(145,385)(146,386)(147,387)(148,388)(149,389)(150,390)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,396)(157,397)(158,398)(159,399)
(160,400)(161,401)(162,402)(163,403)(164,404)(165,405)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,411)(172,412)(173,413)(174,414)(175,415)
(176,416)(177,417)(178,418)(179,419)(180,420)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,426)(187,427)(188,428)(189,429)(190,430)(191,431)
(192,432)(193,433)(194,434)(195,435)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,441)(202,442)(203,443)(204,444)(205,445)(206,446)(207,447)
(208,448)(209,449)(210,450)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,456)(217,457)(218,458)(219,459)(220,460)(221,461)(222,462)(223,463)
(224,464)(225,465)(226,466)(227,467)(228,468)(229,469)(230,470)(231,471)
(232,472)(233,473)(234,474)(235,475)(236,476)(237,477)(238,478)(239,479)
(240,480)(481,721)(482,722)(483,723)(484,724)(485,725)(486,726)(487,727)
(488,728)(489,729)(490,730)(491,731)(492,732)(493,733)(494,734)(495,735)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,741)(502,742)(503,743)
(504,744)(505,745)(506,746)(507,747)(508,748)(509,749)(510,750)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,756)(517,757)(518,758)(519,759)
(520,760)(521,761)(522,762)(523,763)(524,764)(525,765)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,771)(532,772)(533,773)(534,774)(535,775)
(536,776)(537,777)(538,778)(539,779)(540,780)(541,781)(542,782)(543,783)
(544,784)(545,785)(546,786)(547,787)(548,788)(549,789)(550,790)(551,791)
(552,792)(553,793)(554,794)(555,795)(556,796)(557,797)(558,798)(559,799)
(560,800)(561,801)(562,802)(563,803)(564,804)(565,805)(566,806)(567,807)
(568,808)(569,809)(570,810)(571,811)(572,812)(573,813)(574,814)(575,815)
(576,816)(577,817)(578,818)(579,819)(580,820)(581,821)(582,822)(583,823)
(584,824)(585,825)(586,826)(587,827)(588,828)(589,829)(590,830)(591,831)
(592,832)(593,833)(594,834)(595,835)(596,836)(597,837)(598,838)(599,839)
(600,840)(601,841)(602,842)(603,843)(604,844)(605,845)(606,846)(607,847)
(608,848)(609,849)(610,850)(611,851)(612,852)(613,853)(614,854)(615,855)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,861)(622,862)(623,863)
(624,864)(625,865)(626,866)(627,867)(628,868)(629,869)(630,870)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,876)(637,877)(638,878)(639,879)
(640,880)(641,881)(642,882)(643,883)(644,884)(645,885)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,891)(652,892)(653,893)(654,894)(655,895)
(656,896)(657,897)(658,898)(659,899)(660,900)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,906)(667,907)(668,908)(669,909)(670,910)(671,911)
(672,912)(673,913)(674,914)(675,915)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,921)(682,922)(683,923)(684,924)(685,925)(686,926)(687,927)
(688,928)(689,929)(690,930)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,936)(697,937)(698,938)(699,939)(700,940)(701,941)(702,942)(703,943)
(704,944)(705,945)(706,946)(707,947)(708,948)(709,949)(710,950)(711,951)
(712,952)(713,953)(714,954)(715,955)(716,956)(717,957)(718,958)(719,959)
(720,960);
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*s3*s2*s1*s2*s3*s2, 
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope