Polytope of Type {4,40,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,40,6}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150684)
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
3-fold quotients : {4,40,2}*640b
4-fold quotients : {2,20,6}*480a, {4,10,6}*480
5-fold quotients : {4,8,6}*384b
6-fold quotients : {4,20,2}*320
8-fold quotients : {2,10,6}*240
10-fold quotients : {4,4,6}*192
12-fold quotients : {2,20,2}*160, {4,10,2}*160
15-fold quotients : {4,8,2}*128b
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
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)( 61,316)( 62,317)( 63,318)( 64,319)
( 65,320)( 66,321)( 67,322)( 68,323)( 69,324)( 70,325)( 71,326)( 72,327)
( 73,328)( 74,329)( 75,330)( 76,301)( 77,302)( 78,303)( 79,304)( 80,305)
( 81,306)( 82,307)( 83,308)( 84,309)( 85,310)( 86,311)( 87,312)( 88,313)
( 89,314)( 90,315)( 91,346)( 92,347)( 93,348)( 94,349)( 95,350)( 96,351)
( 97,352)( 98,353)( 99,354)(100,355)(101,356)(102,357)(103,358)(104,359)
(105,360)(106,331)(107,332)(108,333)(109,334)(110,335)(111,336)(112,337)
(113,338)(114,339)(115,340)(116,341)(117,342)(118,343)(119,344)(120,345)
(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)(181,436)(182,437)(183,438)(184,439)
(185,440)(186,441)(187,442)(188,443)(189,444)(190,445)(191,446)(192,447)
(193,448)(194,449)(195,450)(196,421)(197,422)(198,423)(199,424)(200,425)
(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)(208,433)
(209,434)(210,435)(211,466)(212,467)(213,468)(214,469)(215,470)(216,471)
(217,472)(218,473)(219,474)(220,475)(221,476)(222,477)(223,478)(224,479)
(225,480)(226,451)(227,452)(228,453)(229,454)(230,455)(231,456)(232,457)
(233,458)(234,459)(235,460)(236,461)(237,462)(238,463)(239,464)(240,465)
(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)(541,796)(542,797)(543,798)(544,799)
(545,800)(546,801)(547,802)(548,803)(549,804)(550,805)(551,806)(552,807)
(553,808)(554,809)(555,810)(556,781)(557,782)(558,783)(559,784)(560,785)
(561,786)(562,787)(563,788)(564,789)(565,790)(566,791)(567,792)(568,793)
(569,794)(570,795)(571,826)(572,827)(573,828)(574,829)(575,830)(576,831)
(577,832)(578,833)(579,834)(580,835)(581,836)(582,837)(583,838)(584,839)
(585,840)(586,811)(587,812)(588,813)(589,814)(590,815)(591,816)(592,817)
(593,818)(594,819)(595,820)(596,821)(597,822)(598,823)(599,824)(600,825)
(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)(661,916)(662,917)(663,918)(664,919)
(665,920)(666,921)(667,922)(668,923)(669,924)(670,925)(671,926)(672,927)
(673,928)(674,929)(675,930)(676,901)(677,902)(678,903)(679,904)(680,905)
(681,906)(682,907)(683,908)(684,909)(685,910)(686,911)(687,912)(688,913)
(689,914)(690,915)(691,946)(692,947)(693,948)(694,949)(695,950)(696,951)
(697,952)(698,953)(699,954)(700,955)(701,956)(702,957)(703,958)(704,959)
(705,960)(706,931)(707,932)(708,933)(709,934)(710,935)(711,936)(712,937)
(713,938)(714,939)(715,940)(716,941)(717,942)(718,943)(719,944)(720,945);;
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)(721,826)(722,830)(723,829)(724,828)
(725,827)(726,831)(727,835)(728,834)(729,833)(730,832)(731,836)(732,840)
(733,839)(734,838)(735,837)(736,811)(737,815)(738,814)(739,813)(740,812)
(741,816)(742,820)(743,819)(744,818)(745,817)(746,821)(747,825)(748,824)
(749,823)(750,822)(751,796)(752,800)(753,799)(754,798)(755,797)(756,801)
(757,805)(758,804)(759,803)(760,802)(761,806)(762,810)(763,809)(764,808)
(765,807)(766,781)(767,785)(768,784)(769,783)(770,782)(771,786)(772,790)
(773,789)(774,788)(775,787)(776,791)(777,795)(778,794)(779,793)(780,792)
(841,946)(842,950)(843,949)(844,948)(845,947)(846,951)(847,955)(848,954)
(849,953)(850,952)(851,956)(852,960)(853,959)(854,958)(855,957)(856,931)
(857,935)(858,934)(859,933)(860,932)(861,936)(862,940)(863,939)(864,938)
(865,937)(866,941)(867,945)(868,944)(869,943)(870,942)(871,916)(872,920)
(873,919)(874,918)(875,917)(876,921)(877,925)(878,924)(879,923)(880,922)
(881,926)(882,930)(883,929)(884,928)(885,927)(886,901)(887,905)(888,904)
(889,903)(890,902)(891,906)(892,910)(893,909)(894,908)(895,907)(896,911)
(897,915)(898,914)(899,913)(900,912);;
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)( 31,647)( 32,646)
( 33,650)( 34,649)( 35,648)( 36,657)( 37,656)( 38,660)( 39,659)( 40,658)
( 41,652)( 42,651)( 43,655)( 44,654)( 45,653)( 46,632)( 47,631)( 48,635)
( 49,634)( 50,633)( 51,642)( 52,641)( 53,645)( 54,644)( 55,643)( 56,637)
( 57,636)( 58,640)( 59,639)( 60,638)( 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)( 91,692)( 92,691)( 93,695)( 94,694)( 95,693)( 96,702)
( 97,701)( 98,705)( 99,704)(100,703)(101,697)(102,696)(103,700)(104,699)
(105,698)(106,707)(107,706)(108,710)(109,709)(110,708)(111,717)(112,716)
(113,720)(114,719)(115,718)(116,712)(117,711)(118,715)(119,714)(120,713)
(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)(151,527)(152,526)
(153,530)(154,529)(155,528)(156,537)(157,536)(158,540)(159,539)(160,538)
(161,532)(162,531)(163,535)(164,534)(165,533)(166,512)(167,511)(168,515)
(169,514)(170,513)(171,522)(172,521)(173,525)(174,524)(175,523)(176,517)
(177,516)(178,520)(179,519)(180,518)(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)(211,572)(212,571)(213,575)(214,574)(215,573)(216,582)
(217,581)(218,585)(219,584)(220,583)(221,577)(222,576)(223,580)(224,579)
(225,578)(226,587)(227,586)(228,590)(229,589)(230,588)(231,597)(232,596)
(233,600)(234,599)(235,598)(236,592)(237,591)(238,595)(239,594)(240,593)
(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)(271,887)(272,886)
(273,890)(274,889)(275,888)(276,897)(277,896)(278,900)(279,899)(280,898)
(281,892)(282,891)(283,895)(284,894)(285,893)(286,872)(287,871)(288,875)
(289,874)(290,873)(291,882)(292,881)(293,885)(294,884)(295,883)(296,877)
(297,876)(298,880)(299,879)(300,878)(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)(331,932)(332,931)(333,935)(334,934)(335,933)(336,942)
(337,941)(338,945)(339,944)(340,943)(341,937)(342,936)(343,940)(344,939)
(345,938)(346,947)(347,946)(348,950)(349,949)(350,948)(351,957)(352,956)
(353,960)(354,959)(355,958)(356,952)(357,951)(358,955)(359,954)(360,953)
(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)(391,767)(392,766)
(393,770)(394,769)(395,768)(396,777)(397,776)(398,780)(399,779)(400,778)
(401,772)(402,771)(403,775)(404,774)(405,773)(406,752)(407,751)(408,755)
(409,754)(410,753)(411,762)(412,761)(413,765)(414,764)(415,763)(416,757)
(417,756)(418,760)(419,759)(420,758)(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)(451,812)(452,811)(453,815)(454,814)(455,813)(456,822)
(457,821)(458,825)(459,824)(460,823)(461,817)(462,816)(463,820)(464,819)
(465,818)(466,827)(467,826)(468,830)(469,829)(470,828)(471,837)(472,836)
(473,840)(474,839)(475,838)(476,832)(477,831)(478,835)(479,834)(480,833);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*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*s0*s1*s2*s1 ];;
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)( 61,316)( 62,317)( 63,318)
( 64,319)( 65,320)( 66,321)( 67,322)( 68,323)( 69,324)( 70,325)( 71,326)
( 72,327)( 73,328)( 74,329)( 75,330)( 76,301)( 77,302)( 78,303)( 79,304)
( 80,305)( 81,306)( 82,307)( 83,308)( 84,309)( 85,310)( 86,311)( 87,312)
( 88,313)( 89,314)( 90,315)( 91,346)( 92,347)( 93,348)( 94,349)( 95,350)
( 96,351)( 97,352)( 98,353)( 99,354)(100,355)(101,356)(102,357)(103,358)
(104,359)(105,360)(106,331)(107,332)(108,333)(109,334)(110,335)(111,336)
(112,337)(113,338)(114,339)(115,340)(116,341)(117,342)(118,343)(119,344)
(120,345)(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)(181,436)(182,437)(183,438)
(184,439)(185,440)(186,441)(187,442)(188,443)(189,444)(190,445)(191,446)
(192,447)(193,448)(194,449)(195,450)(196,421)(197,422)(198,423)(199,424)
(200,425)(201,426)(202,427)(203,428)(204,429)(205,430)(206,431)(207,432)
(208,433)(209,434)(210,435)(211,466)(212,467)(213,468)(214,469)(215,470)
(216,471)(217,472)(218,473)(219,474)(220,475)(221,476)(222,477)(223,478)
(224,479)(225,480)(226,451)(227,452)(228,453)(229,454)(230,455)(231,456)
(232,457)(233,458)(234,459)(235,460)(236,461)(237,462)(238,463)(239,464)
(240,465)(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)(541,796)(542,797)(543,798)
(544,799)(545,800)(546,801)(547,802)(548,803)(549,804)(550,805)(551,806)
(552,807)(553,808)(554,809)(555,810)(556,781)(557,782)(558,783)(559,784)
(560,785)(561,786)(562,787)(563,788)(564,789)(565,790)(566,791)(567,792)
(568,793)(569,794)(570,795)(571,826)(572,827)(573,828)(574,829)(575,830)
(576,831)(577,832)(578,833)(579,834)(580,835)(581,836)(582,837)(583,838)
(584,839)(585,840)(586,811)(587,812)(588,813)(589,814)(590,815)(591,816)
(592,817)(593,818)(594,819)(595,820)(596,821)(597,822)(598,823)(599,824)
(600,825)(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)(661,916)(662,917)(663,918)
(664,919)(665,920)(666,921)(667,922)(668,923)(669,924)(670,925)(671,926)
(672,927)(673,928)(674,929)(675,930)(676,901)(677,902)(678,903)(679,904)
(680,905)(681,906)(682,907)(683,908)(684,909)(685,910)(686,911)(687,912)
(688,913)(689,914)(690,915)(691,946)(692,947)(693,948)(694,949)(695,950)
(696,951)(697,952)(698,953)(699,954)(700,955)(701,956)(702,957)(703,958)
(704,959)(705,960)(706,931)(707,932)(708,933)(709,934)(710,935)(711,936)
(712,937)(713,938)(714,939)(715,940)(716,941)(717,942)(718,943)(719,944)
(720,945);
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)(721,826)(722,830)(723,829)
(724,828)(725,827)(726,831)(727,835)(728,834)(729,833)(730,832)(731,836)
(732,840)(733,839)(734,838)(735,837)(736,811)(737,815)(738,814)(739,813)
(740,812)(741,816)(742,820)(743,819)(744,818)(745,817)(746,821)(747,825)
(748,824)(749,823)(750,822)(751,796)(752,800)(753,799)(754,798)(755,797)
(756,801)(757,805)(758,804)(759,803)(760,802)(761,806)(762,810)(763,809)
(764,808)(765,807)(766,781)(767,785)(768,784)(769,783)(770,782)(771,786)
(772,790)(773,789)(774,788)(775,787)(776,791)(777,795)(778,794)(779,793)
(780,792)(841,946)(842,950)(843,949)(844,948)(845,947)(846,951)(847,955)
(848,954)(849,953)(850,952)(851,956)(852,960)(853,959)(854,958)(855,957)
(856,931)(857,935)(858,934)(859,933)(860,932)(861,936)(862,940)(863,939)
(864,938)(865,937)(866,941)(867,945)(868,944)(869,943)(870,942)(871,916)
(872,920)(873,919)(874,918)(875,917)(876,921)(877,925)(878,924)(879,923)
(880,922)(881,926)(882,930)(883,929)(884,928)(885,927)(886,901)(887,905)
(888,904)(889,903)(890,902)(891,906)(892,910)(893,909)(894,908)(895,907)
(896,911)(897,915)(898,914)(899,913)(900,912);
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)( 31,647)
( 32,646)( 33,650)( 34,649)( 35,648)( 36,657)( 37,656)( 38,660)( 39,659)
( 40,658)( 41,652)( 42,651)( 43,655)( 44,654)( 45,653)( 46,632)( 47,631)
( 48,635)( 49,634)( 50,633)( 51,642)( 52,641)( 53,645)( 54,644)( 55,643)
( 56,637)( 57,636)( 58,640)( 59,639)( 60,638)( 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)( 91,692)( 92,691)( 93,695)( 94,694)( 95,693)
( 96,702)( 97,701)( 98,705)( 99,704)(100,703)(101,697)(102,696)(103,700)
(104,699)(105,698)(106,707)(107,706)(108,710)(109,709)(110,708)(111,717)
(112,716)(113,720)(114,719)(115,718)(116,712)(117,711)(118,715)(119,714)
(120,713)(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)(151,527)
(152,526)(153,530)(154,529)(155,528)(156,537)(157,536)(158,540)(159,539)
(160,538)(161,532)(162,531)(163,535)(164,534)(165,533)(166,512)(167,511)
(168,515)(169,514)(170,513)(171,522)(172,521)(173,525)(174,524)(175,523)
(176,517)(177,516)(178,520)(179,519)(180,518)(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)(211,572)(212,571)(213,575)(214,574)(215,573)
(216,582)(217,581)(218,585)(219,584)(220,583)(221,577)(222,576)(223,580)
(224,579)(225,578)(226,587)(227,586)(228,590)(229,589)(230,588)(231,597)
(232,596)(233,600)(234,599)(235,598)(236,592)(237,591)(238,595)(239,594)
(240,593)(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)(271,887)
(272,886)(273,890)(274,889)(275,888)(276,897)(277,896)(278,900)(279,899)
(280,898)(281,892)(282,891)(283,895)(284,894)(285,893)(286,872)(287,871)
(288,875)(289,874)(290,873)(291,882)(292,881)(293,885)(294,884)(295,883)
(296,877)(297,876)(298,880)(299,879)(300,878)(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)(331,932)(332,931)(333,935)(334,934)(335,933)
(336,942)(337,941)(338,945)(339,944)(340,943)(341,937)(342,936)(343,940)
(344,939)(345,938)(346,947)(347,946)(348,950)(349,949)(350,948)(351,957)
(352,956)(353,960)(354,959)(355,958)(356,952)(357,951)(358,955)(359,954)
(360,953)(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)(391,767)
(392,766)(393,770)(394,769)(395,768)(396,777)(397,776)(398,780)(399,779)
(400,778)(401,772)(402,771)(403,775)(404,774)(405,773)(406,752)(407,751)
(408,755)(409,754)(410,753)(411,762)(412,761)(413,765)(414,764)(415,763)
(416,757)(417,756)(418,760)(419,759)(420,758)(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)(451,812)(452,811)(453,815)(454,814)(455,813)
(456,822)(457,821)(458,825)(459,824)(460,823)(461,817)(462,816)(463,820)
(464,819)(465,818)(466,827)(467,826)(468,830)(469,829)(470,828)(471,837)
(472,836)(473,840)(474,839)(475,838)(476,832)(477,831)(478,835)(479,834)
(480,833);
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*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*s0*s1*s2*s1 >;
References : None.
to this polytope