Polytope of Type {4,40,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,40,6}*1920a
Also Known As : {{4,40|2},{40,6|2}}. if this polytope has another name.
Group : SmallGroup(1920,148902)
Rank : 4
Schlafli Type : {4,40,6}
Number of vertices, edges, etc : 4, 80, 120, 6
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,20,6}*960, {2,40,6}*960
3-fold quotients : {4,40,2}*640a
4-fold quotients : {2,20,6}*480a, {4,10,6}*480
5-fold quotients : {4,8,6}*384a
6-fold quotients : {4,20,2}*320, {2,40,2}*320
8-fold quotients : {2,10,6}*240
10-fold quotients : {4,4,6}*192, {2,8,6}*192
12-fold quotients : {2,20,2}*160, {4,10,2}*160
15-fold quotients : {4,8,2}*128a
20-fold quotients : {2,4,6}*96a, {4,2,6}*96
24-fold quotients : {2,10,2}*80
30-fold quotients : {4,4,2}*64, {2,8,2}*64
40-fold quotients : {4,2,3}*48, {2,2,6}*48
48-fold quotients : {2,5,2}*40
60-fold quotients : {2,4,2}*32, {4,2,2}*32
80-fold quotients : {2,2,3}*24
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,241)( 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);;
s1 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)( 38, 39)
( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)
( 61, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 81)( 67, 85)( 68, 84)
( 69, 83)( 70, 82)( 71, 86)( 72, 90)( 73, 89)( 74, 88)( 75, 87)( 91,106)
( 92,110)( 93,109)( 94,108)( 95,107)( 96,111)( 97,115)( 98,114)( 99,113)
(100,112)(101,116)(102,120)(103,119)(104,118)(105,117)(122,125)(123,124)
(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(142,145)(143,144)
(147,150)(148,149)(152,155)(153,154)(157,160)(158,159)(162,165)(163,164)
(167,170)(168,169)(172,175)(173,174)(177,180)(178,179)(181,196)(182,200)
(183,199)(184,198)(185,197)(186,201)(187,205)(188,204)(189,203)(190,202)
(191,206)(192,210)(193,209)(194,208)(195,207)(211,226)(212,230)(213,229)
(214,228)(215,227)(216,231)(217,235)(218,234)(219,233)(220,232)(221,236)
(222,240)(223,239)(224,238)(225,237)(241,271)(242,275)(243,274)(244,273)
(245,272)(246,276)(247,280)(248,279)(249,278)(250,277)(251,281)(252,285)
(253,284)(254,283)(255,282)(256,286)(257,290)(258,289)(259,288)(260,287)
(261,291)(262,295)(263,294)(264,293)(265,292)(266,296)(267,300)(268,299)
(269,298)(270,297)(301,346)(302,350)(303,349)(304,348)(305,347)(306,351)
(307,355)(308,354)(309,353)(310,352)(311,356)(312,360)(313,359)(314,358)
(315,357)(316,331)(317,335)(318,334)(319,333)(320,332)(321,336)(322,340)
(323,339)(324,338)(325,337)(326,341)(327,345)(328,344)(329,343)(330,342)
(361,391)(362,395)(363,394)(364,393)(365,392)(366,396)(367,400)(368,399)
(369,398)(370,397)(371,401)(372,405)(373,404)(374,403)(375,402)(376,406)
(377,410)(378,409)(379,408)(380,407)(381,411)(382,415)(383,414)(384,413)
(385,412)(386,416)(387,420)(388,419)(389,418)(390,417)(421,466)(422,470)
(423,469)(424,468)(425,467)(426,471)(427,475)(428,474)(429,473)(430,472)
(431,476)(432,480)(433,479)(434,478)(435,477)(436,451)(437,455)(438,454)
(439,453)(440,452)(441,456)(442,460)(443,459)(444,458)(445,457)(446,461)
(447,465)(448,464)(449,463)(450,462)(481,541)(482,545)(483,544)(484,543)
(485,542)(486,546)(487,550)(488,549)(489,548)(490,547)(491,551)(492,555)
(493,554)(494,553)(495,552)(496,556)(497,560)(498,559)(499,558)(500,557)
(501,561)(502,565)(503,564)(504,563)(505,562)(506,566)(507,570)(508,569)
(509,568)(510,567)(511,571)(512,575)(513,574)(514,573)(515,572)(516,576)
(517,580)(518,579)(519,578)(520,577)(521,581)(522,585)(523,584)(524,583)
(525,582)(526,586)(527,590)(528,589)(529,588)(530,587)(531,591)(532,595)
(533,594)(534,593)(535,592)(536,596)(537,600)(538,599)(539,598)(540,597)
(601,661)(602,665)(603,664)(604,663)(605,662)(606,666)(607,670)(608,669)
(609,668)(610,667)(611,671)(612,675)(613,674)(614,673)(615,672)(616,676)
(617,680)(618,679)(619,678)(620,677)(621,681)(622,685)(623,684)(624,683)
(625,682)(626,686)(627,690)(628,689)(629,688)(630,687)(631,691)(632,695)
(633,694)(634,693)(635,692)(636,696)(637,700)(638,699)(639,698)(640,697)
(641,701)(642,705)(643,704)(644,703)(645,702)(646,706)(647,710)(648,709)
(649,708)(650,707)(651,711)(652,715)(653,714)(654,713)(655,712)(656,716)
(657,720)(658,719)(659,718)(660,717)(721,811)(722,815)(723,814)(724,813)
(725,812)(726,816)(727,820)(728,819)(729,818)(730,817)(731,821)(732,825)
(733,824)(734,823)(735,822)(736,826)(737,830)(738,829)(739,828)(740,827)
(741,831)(742,835)(743,834)(744,833)(745,832)(746,836)(747,840)(748,839)
(749,838)(750,837)(751,781)(752,785)(753,784)(754,783)(755,782)(756,786)
(757,790)(758,789)(759,788)(760,787)(761,791)(762,795)(763,794)(764,793)
(765,792)(766,796)(767,800)(768,799)(769,798)(770,797)(771,801)(772,805)
(773,804)(774,803)(775,802)(776,806)(777,810)(778,809)(779,808)(780,807)
(841,931)(842,935)(843,934)(844,933)(845,932)(846,936)(847,940)(848,939)
(849,938)(850,937)(851,941)(852,945)(853,944)(854,943)(855,942)(856,946)
(857,950)(858,949)(859,948)(860,947)(861,951)(862,955)(863,954)(864,953)
(865,952)(866,956)(867,960)(868,959)(869,958)(870,957)(871,901)(872,905)
(873,904)(874,903)(875,902)(876,906)(877,910)(878,909)(879,908)(880,907)
(881,911)(882,915)(883,914)(884,913)(885,912)(886,916)(887,920)(888,919)
(889,918)(890,917)(891,921)(892,925)(893,924)(894,923)(895,922)(896,926)
(897,930)(898,929)(899,928)(900,927);;
s2 := ( 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);;
s3 := ( 1,126)( 2,127)( 3,128)( 4,129)( 5,130)( 6,121)( 7,122)( 8,123)
( 9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,141)
( 17,142)( 18,143)( 19,144)( 20,145)( 21,136)( 22,137)( 23,138)( 24,139)
( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,156)( 32,157)
( 33,158)( 34,159)( 35,160)( 36,151)( 37,152)( 38,153)( 39,154)( 40,155)
( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,171)( 47,172)( 48,173)
( 49,174)( 50,175)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)( 56,176)
( 57,177)( 58,178)( 59,179)( 60,180)( 61,186)( 62,187)( 63,188)( 64,189)
( 65,190)( 66,181)( 67,182)( 68,183)( 69,184)( 70,185)( 71,191)( 72,192)
( 73,193)( 74,194)( 75,195)( 76,201)( 77,202)( 78,203)( 79,204)( 80,205)
( 81,196)( 82,197)( 83,198)( 84,199)( 85,200)( 86,206)( 87,207)( 88,208)
( 89,209)( 90,210)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)( 96,211)
( 97,212)( 98,213)( 99,214)(100,215)(101,221)(102,222)(103,223)(104,224)
(105,225)(106,231)(107,232)(108,233)(109,234)(110,235)(111,226)(112,227)
(113,228)(114,229)(115,230)(116,236)(117,237)(118,238)(119,239)(120,240)
(241,366)(242,367)(243,368)(244,369)(245,370)(246,361)(247,362)(248,363)
(249,364)(250,365)(251,371)(252,372)(253,373)(254,374)(255,375)(256,381)
(257,382)(258,383)(259,384)(260,385)(261,376)(262,377)(263,378)(264,379)
(265,380)(266,386)(267,387)(268,388)(269,389)(270,390)(271,396)(272,397)
(273,398)(274,399)(275,400)(276,391)(277,392)(278,393)(279,394)(280,395)
(281,401)(282,402)(283,403)(284,404)(285,405)(286,411)(287,412)(288,413)
(289,414)(290,415)(291,406)(292,407)(293,408)(294,409)(295,410)(296,416)
(297,417)(298,418)(299,419)(300,420)(301,426)(302,427)(303,428)(304,429)
(305,430)(306,421)(307,422)(308,423)(309,424)(310,425)(311,431)(312,432)
(313,433)(314,434)(315,435)(316,441)(317,442)(318,443)(319,444)(320,445)
(321,436)(322,437)(323,438)(324,439)(325,440)(326,446)(327,447)(328,448)
(329,449)(330,450)(331,456)(332,457)(333,458)(334,459)(335,460)(336,451)
(337,452)(338,453)(339,454)(340,455)(341,461)(342,462)(343,463)(344,464)
(345,465)(346,471)(347,472)(348,473)(349,474)(350,475)(351,466)(352,467)
(353,468)(354,469)(355,470)(356,476)(357,477)(358,478)(359,479)(360,480)
(481,606)(482,607)(483,608)(484,609)(485,610)(486,601)(487,602)(488,603)
(489,604)(490,605)(491,611)(492,612)(493,613)(494,614)(495,615)(496,621)
(497,622)(498,623)(499,624)(500,625)(501,616)(502,617)(503,618)(504,619)
(505,620)(506,626)(507,627)(508,628)(509,629)(510,630)(511,636)(512,637)
(513,638)(514,639)(515,640)(516,631)(517,632)(518,633)(519,634)(520,635)
(521,641)(522,642)(523,643)(524,644)(525,645)(526,651)(527,652)(528,653)
(529,654)(530,655)(531,646)(532,647)(533,648)(534,649)(535,650)(536,656)
(537,657)(538,658)(539,659)(540,660)(541,666)(542,667)(543,668)(544,669)
(545,670)(546,661)(547,662)(548,663)(549,664)(550,665)(551,671)(552,672)
(553,673)(554,674)(555,675)(556,681)(557,682)(558,683)(559,684)(560,685)
(561,676)(562,677)(563,678)(564,679)(565,680)(566,686)(567,687)(568,688)
(569,689)(570,690)(571,696)(572,697)(573,698)(574,699)(575,700)(576,691)
(577,692)(578,693)(579,694)(580,695)(581,701)(582,702)(583,703)(584,704)
(585,705)(586,711)(587,712)(588,713)(589,714)(590,715)(591,706)(592,707)
(593,708)(594,709)(595,710)(596,716)(597,717)(598,718)(599,719)(600,720)
(721,846)(722,847)(723,848)(724,849)(725,850)(726,841)(727,842)(728,843)
(729,844)(730,845)(731,851)(732,852)(733,853)(734,854)(735,855)(736,861)
(737,862)(738,863)(739,864)(740,865)(741,856)(742,857)(743,858)(744,859)
(745,860)(746,866)(747,867)(748,868)(749,869)(750,870)(751,876)(752,877)
(753,878)(754,879)(755,880)(756,871)(757,872)(758,873)(759,874)(760,875)
(761,881)(762,882)(763,883)(764,884)(765,885)(766,891)(767,892)(768,893)
(769,894)(770,895)(771,886)(772,887)(773,888)(774,889)(775,890)(776,896)
(777,897)(778,898)(779,899)(780,900)(781,906)(782,907)(783,908)(784,909)
(785,910)(786,901)(787,902)(788,903)(789,904)(790,905)(791,911)(792,912)
(793,913)(794,914)(795,915)(796,921)(797,922)(798,923)(799,924)(800,925)
(801,916)(802,917)(803,918)(804,919)(805,920)(806,926)(807,927)(808,928)
(809,929)(810,930)(811,936)(812,937)(813,938)(814,939)(815,940)(816,931)
(817,932)(818,933)(819,934)(820,935)(821,941)(822,942)(823,943)(824,944)
(825,945)(826,951)(827,952)(828,953)(829,954)(830,955)(831,946)(832,947)
(833,948)(834,949)(835,950)(836,956)(837,957)(838,958)(839,959)(840,960);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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*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)!( 1,241)( 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);
s1 := Sym(960)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 37, 40)
( 38, 39)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)
( 58, 59)( 61, 76)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 81)( 67, 85)
( 68, 84)( 69, 83)( 70, 82)( 71, 86)( 72, 90)( 73, 89)( 74, 88)( 75, 87)
( 91,106)( 92,110)( 93,109)( 94,108)( 95,107)( 96,111)( 97,115)( 98,114)
( 99,113)(100,112)(101,116)(102,120)(103,119)(104,118)(105,117)(122,125)
(123,124)(127,130)(128,129)(132,135)(133,134)(137,140)(138,139)(142,145)
(143,144)(147,150)(148,149)(152,155)(153,154)(157,160)(158,159)(162,165)
(163,164)(167,170)(168,169)(172,175)(173,174)(177,180)(178,179)(181,196)
(182,200)(183,199)(184,198)(185,197)(186,201)(187,205)(188,204)(189,203)
(190,202)(191,206)(192,210)(193,209)(194,208)(195,207)(211,226)(212,230)
(213,229)(214,228)(215,227)(216,231)(217,235)(218,234)(219,233)(220,232)
(221,236)(222,240)(223,239)(224,238)(225,237)(241,271)(242,275)(243,274)
(244,273)(245,272)(246,276)(247,280)(248,279)(249,278)(250,277)(251,281)
(252,285)(253,284)(254,283)(255,282)(256,286)(257,290)(258,289)(259,288)
(260,287)(261,291)(262,295)(263,294)(264,293)(265,292)(266,296)(267,300)
(268,299)(269,298)(270,297)(301,346)(302,350)(303,349)(304,348)(305,347)
(306,351)(307,355)(308,354)(309,353)(310,352)(311,356)(312,360)(313,359)
(314,358)(315,357)(316,331)(317,335)(318,334)(319,333)(320,332)(321,336)
(322,340)(323,339)(324,338)(325,337)(326,341)(327,345)(328,344)(329,343)
(330,342)(361,391)(362,395)(363,394)(364,393)(365,392)(366,396)(367,400)
(368,399)(369,398)(370,397)(371,401)(372,405)(373,404)(374,403)(375,402)
(376,406)(377,410)(378,409)(379,408)(380,407)(381,411)(382,415)(383,414)
(384,413)(385,412)(386,416)(387,420)(388,419)(389,418)(390,417)(421,466)
(422,470)(423,469)(424,468)(425,467)(426,471)(427,475)(428,474)(429,473)
(430,472)(431,476)(432,480)(433,479)(434,478)(435,477)(436,451)(437,455)
(438,454)(439,453)(440,452)(441,456)(442,460)(443,459)(444,458)(445,457)
(446,461)(447,465)(448,464)(449,463)(450,462)(481,541)(482,545)(483,544)
(484,543)(485,542)(486,546)(487,550)(488,549)(489,548)(490,547)(491,551)
(492,555)(493,554)(494,553)(495,552)(496,556)(497,560)(498,559)(499,558)
(500,557)(501,561)(502,565)(503,564)(504,563)(505,562)(506,566)(507,570)
(508,569)(509,568)(510,567)(511,571)(512,575)(513,574)(514,573)(515,572)
(516,576)(517,580)(518,579)(519,578)(520,577)(521,581)(522,585)(523,584)
(524,583)(525,582)(526,586)(527,590)(528,589)(529,588)(530,587)(531,591)
(532,595)(533,594)(534,593)(535,592)(536,596)(537,600)(538,599)(539,598)
(540,597)(601,661)(602,665)(603,664)(604,663)(605,662)(606,666)(607,670)
(608,669)(609,668)(610,667)(611,671)(612,675)(613,674)(614,673)(615,672)
(616,676)(617,680)(618,679)(619,678)(620,677)(621,681)(622,685)(623,684)
(624,683)(625,682)(626,686)(627,690)(628,689)(629,688)(630,687)(631,691)
(632,695)(633,694)(634,693)(635,692)(636,696)(637,700)(638,699)(639,698)
(640,697)(641,701)(642,705)(643,704)(644,703)(645,702)(646,706)(647,710)
(648,709)(649,708)(650,707)(651,711)(652,715)(653,714)(654,713)(655,712)
(656,716)(657,720)(658,719)(659,718)(660,717)(721,811)(722,815)(723,814)
(724,813)(725,812)(726,816)(727,820)(728,819)(729,818)(730,817)(731,821)
(732,825)(733,824)(734,823)(735,822)(736,826)(737,830)(738,829)(739,828)
(740,827)(741,831)(742,835)(743,834)(744,833)(745,832)(746,836)(747,840)
(748,839)(749,838)(750,837)(751,781)(752,785)(753,784)(754,783)(755,782)
(756,786)(757,790)(758,789)(759,788)(760,787)(761,791)(762,795)(763,794)
(764,793)(765,792)(766,796)(767,800)(768,799)(769,798)(770,797)(771,801)
(772,805)(773,804)(774,803)(775,802)(776,806)(777,810)(778,809)(779,808)
(780,807)(841,931)(842,935)(843,934)(844,933)(845,932)(846,936)(847,940)
(848,939)(849,938)(850,937)(851,941)(852,945)(853,944)(854,943)(855,942)
(856,946)(857,950)(858,949)(859,948)(860,947)(861,951)(862,955)(863,954)
(864,953)(865,952)(866,956)(867,960)(868,959)(869,958)(870,957)(871,901)
(872,905)(873,904)(874,903)(875,902)(876,906)(877,910)(878,909)(879,908)
(880,907)(881,911)(882,915)(883,914)(884,913)(885,912)(886,916)(887,920)
(888,919)(889,918)(890,917)(891,921)(892,925)(893,924)(894,923)(895,922)
(896,926)(897,930)(898,929)(899,928)(900,927);
s2 := 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);
s3 := Sym(960)!( 1,126)( 2,127)( 3,128)( 4,129)( 5,130)( 6,121)( 7,122)
( 8,123)( 9,124)( 10,125)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)
( 16,141)( 17,142)( 18,143)( 19,144)( 20,145)( 21,136)( 22,137)( 23,138)
( 24,139)( 25,140)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,156)
( 32,157)( 33,158)( 34,159)( 35,160)( 36,151)( 37,152)( 38,153)( 39,154)
( 40,155)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,171)( 47,172)
( 48,173)( 49,174)( 50,175)( 51,166)( 52,167)( 53,168)( 54,169)( 55,170)
( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,186)( 62,187)( 63,188)
( 64,189)( 65,190)( 66,181)( 67,182)( 68,183)( 69,184)( 70,185)( 71,191)
( 72,192)( 73,193)( 74,194)( 75,195)( 76,201)( 77,202)( 78,203)( 79,204)
( 80,205)( 81,196)( 82,197)( 83,198)( 84,199)( 85,200)( 86,206)( 87,207)
( 88,208)( 89,209)( 90,210)( 91,216)( 92,217)( 93,218)( 94,219)( 95,220)
( 96,211)( 97,212)( 98,213)( 99,214)(100,215)(101,221)(102,222)(103,223)
(104,224)(105,225)(106,231)(107,232)(108,233)(109,234)(110,235)(111,226)
(112,227)(113,228)(114,229)(115,230)(116,236)(117,237)(118,238)(119,239)
(120,240)(241,366)(242,367)(243,368)(244,369)(245,370)(246,361)(247,362)
(248,363)(249,364)(250,365)(251,371)(252,372)(253,373)(254,374)(255,375)
(256,381)(257,382)(258,383)(259,384)(260,385)(261,376)(262,377)(263,378)
(264,379)(265,380)(266,386)(267,387)(268,388)(269,389)(270,390)(271,396)
(272,397)(273,398)(274,399)(275,400)(276,391)(277,392)(278,393)(279,394)
(280,395)(281,401)(282,402)(283,403)(284,404)(285,405)(286,411)(287,412)
(288,413)(289,414)(290,415)(291,406)(292,407)(293,408)(294,409)(295,410)
(296,416)(297,417)(298,418)(299,419)(300,420)(301,426)(302,427)(303,428)
(304,429)(305,430)(306,421)(307,422)(308,423)(309,424)(310,425)(311,431)
(312,432)(313,433)(314,434)(315,435)(316,441)(317,442)(318,443)(319,444)
(320,445)(321,436)(322,437)(323,438)(324,439)(325,440)(326,446)(327,447)
(328,448)(329,449)(330,450)(331,456)(332,457)(333,458)(334,459)(335,460)
(336,451)(337,452)(338,453)(339,454)(340,455)(341,461)(342,462)(343,463)
(344,464)(345,465)(346,471)(347,472)(348,473)(349,474)(350,475)(351,466)
(352,467)(353,468)(354,469)(355,470)(356,476)(357,477)(358,478)(359,479)
(360,480)(481,606)(482,607)(483,608)(484,609)(485,610)(486,601)(487,602)
(488,603)(489,604)(490,605)(491,611)(492,612)(493,613)(494,614)(495,615)
(496,621)(497,622)(498,623)(499,624)(500,625)(501,616)(502,617)(503,618)
(504,619)(505,620)(506,626)(507,627)(508,628)(509,629)(510,630)(511,636)
(512,637)(513,638)(514,639)(515,640)(516,631)(517,632)(518,633)(519,634)
(520,635)(521,641)(522,642)(523,643)(524,644)(525,645)(526,651)(527,652)
(528,653)(529,654)(530,655)(531,646)(532,647)(533,648)(534,649)(535,650)
(536,656)(537,657)(538,658)(539,659)(540,660)(541,666)(542,667)(543,668)
(544,669)(545,670)(546,661)(547,662)(548,663)(549,664)(550,665)(551,671)
(552,672)(553,673)(554,674)(555,675)(556,681)(557,682)(558,683)(559,684)
(560,685)(561,676)(562,677)(563,678)(564,679)(565,680)(566,686)(567,687)
(568,688)(569,689)(570,690)(571,696)(572,697)(573,698)(574,699)(575,700)
(576,691)(577,692)(578,693)(579,694)(580,695)(581,701)(582,702)(583,703)
(584,704)(585,705)(586,711)(587,712)(588,713)(589,714)(590,715)(591,706)
(592,707)(593,708)(594,709)(595,710)(596,716)(597,717)(598,718)(599,719)
(600,720)(721,846)(722,847)(723,848)(724,849)(725,850)(726,841)(727,842)
(728,843)(729,844)(730,845)(731,851)(732,852)(733,853)(734,854)(735,855)
(736,861)(737,862)(738,863)(739,864)(740,865)(741,856)(742,857)(743,858)
(744,859)(745,860)(746,866)(747,867)(748,868)(749,869)(750,870)(751,876)
(752,877)(753,878)(754,879)(755,880)(756,871)(757,872)(758,873)(759,874)
(760,875)(761,881)(762,882)(763,883)(764,884)(765,885)(766,891)(767,892)
(768,893)(769,894)(770,895)(771,886)(772,887)(773,888)(774,889)(775,890)
(776,896)(777,897)(778,898)(779,899)(780,900)(781,906)(782,907)(783,908)
(784,909)(785,910)(786,901)(787,902)(788,903)(789,904)(790,905)(791,911)
(792,912)(793,913)(794,914)(795,915)(796,921)(797,922)(798,923)(799,924)
(800,925)(801,916)(802,917)(803,918)(804,919)(805,920)(806,926)(807,927)
(808,928)(809,929)(810,930)(811,936)(812,937)(813,938)(814,939)(815,940)
(816,931)(817,932)(818,933)(819,934)(820,935)(821,941)(822,942)(823,943)
(824,944)(825,945)(826,951)(827,952)(828,953)(829,954)(830,955)(831,946)
(832,947)(833,948)(834,949)(835,950)(836,956)(837,957)(838,958)(839,959)
(840,960);
poly := sub<Sym(960)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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*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