Polytope of Type {10,8,12}

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