Polytope of Type {12,8,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8,10}*1920a
Also Known As : {{12,8|2},{8,10|2}}. if this polytope has another name.
Group : SmallGroup(1920,148891)
Rank : 4
Schlafli Type : {12,8,10}
Number of vertices, edges, etc : 12, 48, 40, 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, {6,8,10}*960
   3-fold quotients : {4,8,10}*640a
   4-fold quotients : {12,2,10}*480, {6,4,10}*480
   5-fold quotients : {12,8,2}*384a
   6-fold quotients : {4,4,10}*320, {2,8,10}*320
   8-fold quotients : {12,2,5}*240, {6,2,10}*240
   10-fold quotients : {12,4,2}*192a, {6,8,2}*192
   12-fold quotients : {2,4,10}*160, {4,2,10}*160
   15-fold quotients : {4,8,2}*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, {2,8,2}*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 := (  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,251)(  7,252)(  8,253)
(  9,254)( 10,255)( 11,246)( 12,247)( 13,248)( 14,249)( 15,250)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)( 24,269)
( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,281)( 37,282)( 38,283)( 39,284)( 40,285)
( 41,276)( 42,277)( 43,278)( 44,279)( 45,280)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)( 56,291)
( 57,292)( 58,293)( 59,294)( 60,295)( 61,301)( 62,302)( 63,303)( 64,304)
( 65,305)( 66,311)( 67,312)( 68,313)( 69,314)( 70,315)( 71,306)( 72,307)
( 73,308)( 74,309)( 75,310)( 76,316)( 77,317)( 78,318)( 79,319)( 80,320)
( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,321)( 87,322)( 88,323)
( 89,324)( 90,325)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)( 96,341)
( 97,342)( 98,343)( 99,344)(100,345)(101,336)(102,337)(103,338)(104,339)
(105,340)(106,346)(107,347)(108,348)(109,349)(110,350)(111,356)(112,357)
(113,358)(114,359)(115,360)(116,351)(117,352)(118,353)(119,354)(120,355)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,371)(127,372)(128,373)
(129,374)(130,375)(131,366)(132,367)(133,368)(134,369)(135,370)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,386)(142,387)(143,388)(144,389)
(145,390)(146,381)(147,382)(148,383)(149,384)(150,385)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,401)(157,402)(158,403)(159,404)(160,405)
(161,396)(162,397)(163,398)(164,399)(165,400)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,416)(172,417)(173,418)(174,419)(175,420)(176,411)
(177,412)(178,413)(179,414)(180,415)(181,421)(182,422)(183,423)(184,424)
(185,425)(186,431)(187,432)(188,433)(189,434)(190,435)(191,426)(192,427)
(193,428)(194,429)(195,430)(196,436)(197,437)(198,438)(199,439)(200,440)
(201,446)(202,447)(203,448)(204,449)(205,450)(206,441)(207,442)(208,443)
(209,444)(210,445)(211,451)(212,452)(213,453)(214,454)(215,455)(216,461)
(217,462)(218,463)(219,464)(220,465)(221,456)(222,457)(223,458)(224,459)
(225,460)(226,466)(227,467)(228,468)(229,469)(230,470)(231,476)(232,477)
(233,478)(234,479)(235,480)(236,471)(237,472)(238,473)(239,474)(240,475)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,731)(487,732)(488,733)
(489,734)(490,735)(491,726)(492,727)(493,728)(494,729)(495,730)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,746)(502,747)(503,748)(504,749)
(505,750)(506,741)(507,742)(508,743)(509,744)(510,745)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,761)(517,762)(518,763)(519,764)(520,765)
(521,756)(522,757)(523,758)(524,759)(525,760)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,776)(532,777)(533,778)(534,779)(535,780)(536,771)
(537,772)(538,773)(539,774)(540,775)(541,781)(542,782)(543,783)(544,784)
(545,785)(546,791)(547,792)(548,793)(549,794)(550,795)(551,786)(552,787)
(553,788)(554,789)(555,790)(556,796)(557,797)(558,798)(559,799)(560,800)
(561,806)(562,807)(563,808)(564,809)(565,810)(566,801)(567,802)(568,803)
(569,804)(570,805)(571,811)(572,812)(573,813)(574,814)(575,815)(576,821)
(577,822)(578,823)(579,824)(580,825)(581,816)(582,817)(583,818)(584,819)
(585,820)(586,826)(587,827)(588,828)(589,829)(590,830)(591,836)(592,837)
(593,838)(594,839)(595,840)(596,831)(597,832)(598,833)(599,834)(600,835)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,851)(607,852)(608,853)
(609,854)(610,855)(611,846)(612,847)(613,848)(614,849)(615,850)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,866)(622,867)(623,868)(624,869)
(625,870)(626,861)(627,862)(628,863)(629,864)(630,865)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,881)(637,882)(638,883)(639,884)(640,885)
(641,876)(642,877)(643,878)(644,879)(645,880)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,896)(652,897)(653,898)(654,899)(655,900)(656,891)
(657,892)(658,893)(659,894)(660,895)(661,901)(662,902)(663,903)(664,904)
(665,905)(666,911)(667,912)(668,913)(669,914)(670,915)(671,906)(672,907)
(673,908)(674,909)(675,910)(676,916)(677,917)(678,918)(679,919)(680,920)
(681,926)(682,927)(683,928)(684,929)(685,930)(686,921)(687,922)(688,923)
(689,924)(690,925)(691,931)(692,932)(693,933)(694,934)(695,935)(696,941)
(697,942)(698,943)(699,944)(700,945)(701,936)(702,937)(703,938)(704,939)
(705,940)(706,946)(707,947)(708,948)(709,949)(710,950)(711,956)(712,957)
(713,958)(714,959)(715,960)(716,951)(717,952)(718,953)(719,954)(720,955);;
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 := (  1,601)(  2,605)(  3,604)(  4,603)(  5,602)(  6,606)(  7,610)(  8,609)
(  9,608)( 10,607)( 11,611)( 12,615)( 13,614)( 14,613)( 15,612)( 16,616)
( 17,620)( 18,619)( 19,618)( 20,617)( 21,621)( 22,625)( 23,624)( 24,623)
( 25,622)( 26,626)( 27,630)( 28,629)( 29,628)( 30,627)( 31,631)( 32,635)
( 33,634)( 34,633)( 35,632)( 36,636)( 37,640)( 38,639)( 39,638)( 40,637)
( 41,641)( 42,645)( 43,644)( 44,643)( 45,642)( 46,646)( 47,650)( 48,649)
( 49,648)( 50,647)( 51,651)( 52,655)( 53,654)( 54,653)( 55,652)( 56,656)
( 57,660)( 58,659)( 59,658)( 60,657)( 61,676)( 62,680)( 63,679)( 64,678)
( 65,677)( 66,681)( 67,685)( 68,684)( 69,683)( 70,682)( 71,686)( 72,690)
( 73,689)( 74,688)( 75,687)( 76,661)( 77,665)( 78,664)( 79,663)( 80,662)
( 81,666)( 82,670)( 83,669)( 84,668)( 85,667)( 86,671)( 87,675)( 88,674)
( 89,673)( 90,672)( 91,706)( 92,710)( 93,709)( 94,708)( 95,707)( 96,711)
( 97,715)( 98,714)( 99,713)(100,712)(101,716)(102,720)(103,719)(104,718)
(105,717)(106,691)(107,695)(108,694)(109,693)(110,692)(111,696)(112,700)
(113,699)(114,698)(115,697)(116,701)(117,705)(118,704)(119,703)(120,702)
(121,481)(122,485)(123,484)(124,483)(125,482)(126,486)(127,490)(128,489)
(129,488)(130,487)(131,491)(132,495)(133,494)(134,493)(135,492)(136,496)
(137,500)(138,499)(139,498)(140,497)(141,501)(142,505)(143,504)(144,503)
(145,502)(146,506)(147,510)(148,509)(149,508)(150,507)(151,511)(152,515)
(153,514)(154,513)(155,512)(156,516)(157,520)(158,519)(159,518)(160,517)
(161,521)(162,525)(163,524)(164,523)(165,522)(166,526)(167,530)(168,529)
(169,528)(170,527)(171,531)(172,535)(173,534)(174,533)(175,532)(176,536)
(177,540)(178,539)(179,538)(180,537)(181,556)(182,560)(183,559)(184,558)
(185,557)(186,561)(187,565)(188,564)(189,563)(190,562)(191,566)(192,570)
(193,569)(194,568)(195,567)(196,541)(197,545)(198,544)(199,543)(200,542)
(201,546)(202,550)(203,549)(204,548)(205,547)(206,551)(207,555)(208,554)
(209,553)(210,552)(211,586)(212,590)(213,589)(214,588)(215,587)(216,591)
(217,595)(218,594)(219,593)(220,592)(221,596)(222,600)(223,599)(224,598)
(225,597)(226,571)(227,575)(228,574)(229,573)(230,572)(231,576)(232,580)
(233,579)(234,578)(235,577)(236,581)(237,585)(238,584)(239,583)(240,582)
(241,841)(242,845)(243,844)(244,843)(245,842)(246,846)(247,850)(248,849)
(249,848)(250,847)(251,851)(252,855)(253,854)(254,853)(255,852)(256,856)
(257,860)(258,859)(259,858)(260,857)(261,861)(262,865)(263,864)(264,863)
(265,862)(266,866)(267,870)(268,869)(269,868)(270,867)(271,871)(272,875)
(273,874)(274,873)(275,872)(276,876)(277,880)(278,879)(279,878)(280,877)
(281,881)(282,885)(283,884)(284,883)(285,882)(286,886)(287,890)(288,889)
(289,888)(290,887)(291,891)(292,895)(293,894)(294,893)(295,892)(296,896)
(297,900)(298,899)(299,898)(300,897)(301,916)(302,920)(303,919)(304,918)
(305,917)(306,921)(307,925)(308,924)(309,923)(310,922)(311,926)(312,930)
(313,929)(314,928)(315,927)(316,901)(317,905)(318,904)(319,903)(320,902)
(321,906)(322,910)(323,909)(324,908)(325,907)(326,911)(327,915)(328,914)
(329,913)(330,912)(331,946)(332,950)(333,949)(334,948)(335,947)(336,951)
(337,955)(338,954)(339,953)(340,952)(341,956)(342,960)(343,959)(344,958)
(345,957)(346,931)(347,935)(348,934)(349,933)(350,932)(351,936)(352,940)
(353,939)(354,938)(355,937)(356,941)(357,945)(358,944)(359,943)(360,942)
(361,721)(362,725)(363,724)(364,723)(365,722)(366,726)(367,730)(368,729)
(369,728)(370,727)(371,731)(372,735)(373,734)(374,733)(375,732)(376,736)
(377,740)(378,739)(379,738)(380,737)(381,741)(382,745)(383,744)(384,743)
(385,742)(386,746)(387,750)(388,749)(389,748)(390,747)(391,751)(392,755)
(393,754)(394,753)(395,752)(396,756)(397,760)(398,759)(399,758)(400,757)
(401,761)(402,765)(403,764)(404,763)(405,762)(406,766)(407,770)(408,769)
(409,768)(410,767)(411,771)(412,775)(413,774)(414,773)(415,772)(416,776)
(417,780)(418,779)(419,778)(420,777)(421,796)(422,800)(423,799)(424,798)
(425,797)(426,801)(427,805)(428,804)(429,803)(430,802)(431,806)(432,810)
(433,809)(434,808)(435,807)(436,781)(437,785)(438,784)(439,783)(440,782)
(441,786)(442,790)(443,789)(444,788)(445,787)(446,791)(447,795)(448,794)
(449,793)(450,792)(451,826)(452,830)(453,829)(454,828)(455,827)(456,831)
(457,835)(458,834)(459,833)(460,832)(461,836)(462,840)(463,839)(464,838)
(465,837)(466,811)(467,815)(468,814)(469,813)(470,812)(471,816)(472,820)
(473,819)(474,818)(475,817)(476,821)(477,825)(478,824)(479,823)(480,822);;
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*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(960)!(  1,241)(  2,242)(  3,243)(  4,244)(  5,245)(  6,251)(  7,252)
(  8,253)(  9,254)( 10,255)( 11,246)( 12,247)( 13,248)( 14,249)( 15,250)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)
( 24,269)( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,281)( 37,282)( 38,283)( 39,284)
( 40,285)( 41,276)( 42,277)( 43,278)( 44,279)( 45,280)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)
( 56,291)( 57,292)( 58,293)( 59,294)( 60,295)( 61,301)( 62,302)( 63,303)
( 64,304)( 65,305)( 66,311)( 67,312)( 68,313)( 69,314)( 70,315)( 71,306)
( 72,307)( 73,308)( 74,309)( 75,310)( 76,316)( 77,317)( 78,318)( 79,319)
( 80,320)( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,321)( 87,322)
( 88,323)( 89,324)( 90,325)( 91,331)( 92,332)( 93,333)( 94,334)( 95,335)
( 96,341)( 97,342)( 98,343)( 99,344)(100,345)(101,336)(102,337)(103,338)
(104,339)(105,340)(106,346)(107,347)(108,348)(109,349)(110,350)(111,356)
(112,357)(113,358)(114,359)(115,360)(116,351)(117,352)(118,353)(119,354)
(120,355)(121,361)(122,362)(123,363)(124,364)(125,365)(126,371)(127,372)
(128,373)(129,374)(130,375)(131,366)(132,367)(133,368)(134,369)(135,370)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,386)(142,387)(143,388)
(144,389)(145,390)(146,381)(147,382)(148,383)(149,384)(150,385)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,401)(157,402)(158,403)(159,404)
(160,405)(161,396)(162,397)(163,398)(164,399)(165,400)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,416)(172,417)(173,418)(174,419)(175,420)
(176,411)(177,412)(178,413)(179,414)(180,415)(181,421)(182,422)(183,423)
(184,424)(185,425)(186,431)(187,432)(188,433)(189,434)(190,435)(191,426)
(192,427)(193,428)(194,429)(195,430)(196,436)(197,437)(198,438)(199,439)
(200,440)(201,446)(202,447)(203,448)(204,449)(205,450)(206,441)(207,442)
(208,443)(209,444)(210,445)(211,451)(212,452)(213,453)(214,454)(215,455)
(216,461)(217,462)(218,463)(219,464)(220,465)(221,456)(222,457)(223,458)
(224,459)(225,460)(226,466)(227,467)(228,468)(229,469)(230,470)(231,476)
(232,477)(233,478)(234,479)(235,480)(236,471)(237,472)(238,473)(239,474)
(240,475)(481,721)(482,722)(483,723)(484,724)(485,725)(486,731)(487,732)
(488,733)(489,734)(490,735)(491,726)(492,727)(493,728)(494,729)(495,730)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,746)(502,747)(503,748)
(504,749)(505,750)(506,741)(507,742)(508,743)(509,744)(510,745)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,761)(517,762)(518,763)(519,764)
(520,765)(521,756)(522,757)(523,758)(524,759)(525,760)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,776)(532,777)(533,778)(534,779)(535,780)
(536,771)(537,772)(538,773)(539,774)(540,775)(541,781)(542,782)(543,783)
(544,784)(545,785)(546,791)(547,792)(548,793)(549,794)(550,795)(551,786)
(552,787)(553,788)(554,789)(555,790)(556,796)(557,797)(558,798)(559,799)
(560,800)(561,806)(562,807)(563,808)(564,809)(565,810)(566,801)(567,802)
(568,803)(569,804)(570,805)(571,811)(572,812)(573,813)(574,814)(575,815)
(576,821)(577,822)(578,823)(579,824)(580,825)(581,816)(582,817)(583,818)
(584,819)(585,820)(586,826)(587,827)(588,828)(589,829)(590,830)(591,836)
(592,837)(593,838)(594,839)(595,840)(596,831)(597,832)(598,833)(599,834)
(600,835)(601,841)(602,842)(603,843)(604,844)(605,845)(606,851)(607,852)
(608,853)(609,854)(610,855)(611,846)(612,847)(613,848)(614,849)(615,850)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,866)(622,867)(623,868)
(624,869)(625,870)(626,861)(627,862)(628,863)(629,864)(630,865)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,881)(637,882)(638,883)(639,884)
(640,885)(641,876)(642,877)(643,878)(644,879)(645,880)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,896)(652,897)(653,898)(654,899)(655,900)
(656,891)(657,892)(658,893)(659,894)(660,895)(661,901)(662,902)(663,903)
(664,904)(665,905)(666,911)(667,912)(668,913)(669,914)(670,915)(671,906)
(672,907)(673,908)(674,909)(675,910)(676,916)(677,917)(678,918)(679,919)
(680,920)(681,926)(682,927)(683,928)(684,929)(685,930)(686,921)(687,922)
(688,923)(689,924)(690,925)(691,931)(692,932)(693,933)(694,934)(695,935)
(696,941)(697,942)(698,943)(699,944)(700,945)(701,936)(702,937)(703,938)
(704,939)(705,940)(706,946)(707,947)(708,948)(709,949)(710,950)(711,956)
(712,957)(713,958)(714,959)(715,960)(716,951)(717,952)(718,953)(719,954)
(720,955);
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)!(  1,601)(  2,605)(  3,604)(  4,603)(  5,602)(  6,606)(  7,610)
(  8,609)(  9,608)( 10,607)( 11,611)( 12,615)( 13,614)( 14,613)( 15,612)
( 16,616)( 17,620)( 18,619)( 19,618)( 20,617)( 21,621)( 22,625)( 23,624)
( 24,623)( 25,622)( 26,626)( 27,630)( 28,629)( 29,628)( 30,627)( 31,631)
( 32,635)( 33,634)( 34,633)( 35,632)( 36,636)( 37,640)( 38,639)( 39,638)
( 40,637)( 41,641)( 42,645)( 43,644)( 44,643)( 45,642)( 46,646)( 47,650)
( 48,649)( 49,648)( 50,647)( 51,651)( 52,655)( 53,654)( 54,653)( 55,652)
( 56,656)( 57,660)( 58,659)( 59,658)( 60,657)( 61,676)( 62,680)( 63,679)
( 64,678)( 65,677)( 66,681)( 67,685)( 68,684)( 69,683)( 70,682)( 71,686)
( 72,690)( 73,689)( 74,688)( 75,687)( 76,661)( 77,665)( 78,664)( 79,663)
( 80,662)( 81,666)( 82,670)( 83,669)( 84,668)( 85,667)( 86,671)( 87,675)
( 88,674)( 89,673)( 90,672)( 91,706)( 92,710)( 93,709)( 94,708)( 95,707)
( 96,711)( 97,715)( 98,714)( 99,713)(100,712)(101,716)(102,720)(103,719)
(104,718)(105,717)(106,691)(107,695)(108,694)(109,693)(110,692)(111,696)
(112,700)(113,699)(114,698)(115,697)(116,701)(117,705)(118,704)(119,703)
(120,702)(121,481)(122,485)(123,484)(124,483)(125,482)(126,486)(127,490)
(128,489)(129,488)(130,487)(131,491)(132,495)(133,494)(134,493)(135,492)
(136,496)(137,500)(138,499)(139,498)(140,497)(141,501)(142,505)(143,504)
(144,503)(145,502)(146,506)(147,510)(148,509)(149,508)(150,507)(151,511)
(152,515)(153,514)(154,513)(155,512)(156,516)(157,520)(158,519)(159,518)
(160,517)(161,521)(162,525)(163,524)(164,523)(165,522)(166,526)(167,530)
(168,529)(169,528)(170,527)(171,531)(172,535)(173,534)(174,533)(175,532)
(176,536)(177,540)(178,539)(179,538)(180,537)(181,556)(182,560)(183,559)
(184,558)(185,557)(186,561)(187,565)(188,564)(189,563)(190,562)(191,566)
(192,570)(193,569)(194,568)(195,567)(196,541)(197,545)(198,544)(199,543)
(200,542)(201,546)(202,550)(203,549)(204,548)(205,547)(206,551)(207,555)
(208,554)(209,553)(210,552)(211,586)(212,590)(213,589)(214,588)(215,587)
(216,591)(217,595)(218,594)(219,593)(220,592)(221,596)(222,600)(223,599)
(224,598)(225,597)(226,571)(227,575)(228,574)(229,573)(230,572)(231,576)
(232,580)(233,579)(234,578)(235,577)(236,581)(237,585)(238,584)(239,583)
(240,582)(241,841)(242,845)(243,844)(244,843)(245,842)(246,846)(247,850)
(248,849)(249,848)(250,847)(251,851)(252,855)(253,854)(254,853)(255,852)
(256,856)(257,860)(258,859)(259,858)(260,857)(261,861)(262,865)(263,864)
(264,863)(265,862)(266,866)(267,870)(268,869)(269,868)(270,867)(271,871)
(272,875)(273,874)(274,873)(275,872)(276,876)(277,880)(278,879)(279,878)
(280,877)(281,881)(282,885)(283,884)(284,883)(285,882)(286,886)(287,890)
(288,889)(289,888)(290,887)(291,891)(292,895)(293,894)(294,893)(295,892)
(296,896)(297,900)(298,899)(299,898)(300,897)(301,916)(302,920)(303,919)
(304,918)(305,917)(306,921)(307,925)(308,924)(309,923)(310,922)(311,926)
(312,930)(313,929)(314,928)(315,927)(316,901)(317,905)(318,904)(319,903)
(320,902)(321,906)(322,910)(323,909)(324,908)(325,907)(326,911)(327,915)
(328,914)(329,913)(330,912)(331,946)(332,950)(333,949)(334,948)(335,947)
(336,951)(337,955)(338,954)(339,953)(340,952)(341,956)(342,960)(343,959)
(344,958)(345,957)(346,931)(347,935)(348,934)(349,933)(350,932)(351,936)
(352,940)(353,939)(354,938)(355,937)(356,941)(357,945)(358,944)(359,943)
(360,942)(361,721)(362,725)(363,724)(364,723)(365,722)(366,726)(367,730)
(368,729)(369,728)(370,727)(371,731)(372,735)(373,734)(374,733)(375,732)
(376,736)(377,740)(378,739)(379,738)(380,737)(381,741)(382,745)(383,744)
(384,743)(385,742)(386,746)(387,750)(388,749)(389,748)(390,747)(391,751)
(392,755)(393,754)(394,753)(395,752)(396,756)(397,760)(398,759)(399,758)
(400,757)(401,761)(402,765)(403,764)(404,763)(405,762)(406,766)(407,770)
(408,769)(409,768)(410,767)(411,771)(412,775)(413,774)(414,773)(415,772)
(416,776)(417,780)(418,779)(419,778)(420,777)(421,796)(422,800)(423,799)
(424,798)(425,797)(426,801)(427,805)(428,804)(429,803)(430,802)(431,806)
(432,810)(433,809)(434,808)(435,807)(436,781)(437,785)(438,784)(439,783)
(440,782)(441,786)(442,790)(443,789)(444,788)(445,787)(446,791)(447,795)
(448,794)(449,793)(450,792)(451,826)(452,830)(453,829)(454,828)(455,827)
(456,831)(457,835)(458,834)(459,833)(460,832)(461,836)(462,840)(463,839)
(464,838)(465,837)(466,811)(467,815)(468,814)(469,813)(470,812)(471,816)
(472,820)(473,819)(474,818)(475,817)(476,821)(477,825)(478,824)(479,823)
(480,822);
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*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 >;
References : None.
to this polytope