Polytope of Type {15,4,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,4,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,239472)
Rank : 4
Schlafli Type : {15,4,4}
Number of vertices, edges, etc : 30, 120, 32, 8
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 4
Special Properties :
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 : {15,4,4}*960a
4-fold quotients : {15,4,2}*480
5-fold quotients : {3,4,4}*384b
8-fold quotients : {15,4,2}*240
10-fold quotients : {3,4,4}*192a
16-fold quotients : {15,2,2}*120
20-fold quotients : {3,4,2}*96
40-fold quotients : {3,4,2}*48
48-fold quotients : {5,2,2}*40
80-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 65)( 18, 66)
( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 77)( 26, 78)
( 27, 80)( 28, 79)( 29, 73)( 30, 74)( 31, 76)( 32, 75)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 61)( 42, 62)
( 43, 64)( 44, 63)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 81,161)( 82,162)
( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,173)( 90,174)
( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,225)( 98,226)
( 99,228)(100,227)(101,229)(102,230)(103,232)(104,231)(105,237)(106,238)
(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)(113,209)(114,210)
(115,212)(116,211)(117,213)(118,214)(119,216)(120,215)(121,221)(122,222)
(123,224)(124,223)(125,217)(126,218)(127,220)(128,219)(129,193)(130,194)
(131,196)(132,195)(133,197)(134,198)(135,200)(136,199)(137,205)(138,206)
(139,208)(140,207)(141,201)(142,202)(143,204)(144,203)(145,177)(146,178)
(147,180)(148,179)(149,181)(150,182)(151,184)(152,183)(153,189)(154,190)
(155,192)(156,191)(157,185)(158,186)(159,188)(160,187)(243,244)(247,248)
(249,253)(250,254)(251,256)(252,255)(257,305)(258,306)(259,308)(260,307)
(261,309)(262,310)(263,312)(264,311)(265,317)(266,318)(267,320)(268,319)
(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)(275,292)(276,291)
(277,293)(278,294)(279,296)(280,295)(281,301)(282,302)(283,304)(284,303)
(285,297)(286,298)(287,300)(288,299)(321,401)(322,402)(323,404)(324,403)
(325,405)(326,406)(327,408)(328,407)(329,413)(330,414)(331,416)(332,415)
(333,409)(334,410)(335,412)(336,411)(337,465)(338,466)(339,468)(340,467)
(341,469)(342,470)(343,472)(344,471)(345,477)(346,478)(347,480)(348,479)
(349,473)(350,474)(351,476)(352,475)(353,449)(354,450)(355,452)(356,451)
(357,453)(358,454)(359,456)(360,455)(361,461)(362,462)(363,464)(364,463)
(365,457)(366,458)(367,460)(368,459)(369,433)(370,434)(371,436)(372,435)
(373,437)(374,438)(375,440)(376,439)(377,445)(378,446)(379,448)(380,447)
(381,441)(382,442)(383,444)(384,443)(385,417)(386,418)(387,420)(388,419)
(389,421)(390,422)(391,424)(392,423)(393,429)(394,430)(395,432)(396,431)
(397,425)(398,426)(399,428)(400,427)(483,484)(487,488)(489,493)(490,494)
(491,496)(492,495)(497,545)(498,546)(499,548)(500,547)(501,549)(502,550)
(503,552)(504,551)(505,557)(506,558)(507,560)(508,559)(509,553)(510,554)
(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)(517,533)(518,534)
(519,536)(520,535)(521,541)(522,542)(523,544)(524,543)(525,537)(526,538)
(527,540)(528,539)(561,641)(562,642)(563,644)(564,643)(565,645)(566,646)
(567,648)(568,647)(569,653)(570,654)(571,656)(572,655)(573,649)(574,650)
(575,652)(576,651)(577,705)(578,706)(579,708)(580,707)(581,709)(582,710)
(583,712)(584,711)(585,717)(586,718)(587,720)(588,719)(589,713)(590,714)
(591,716)(592,715)(593,689)(594,690)(595,692)(596,691)(597,693)(598,694)
(599,696)(600,695)(601,701)(602,702)(603,704)(604,703)(605,697)(606,698)
(607,700)(608,699)(609,673)(610,674)(611,676)(612,675)(613,677)(614,678)
(615,680)(616,679)(617,685)(618,686)(619,688)(620,687)(621,681)(622,682)
(623,684)(624,683)(625,657)(626,658)(627,660)(628,659)(629,661)(630,662)
(631,664)(632,663)(633,669)(634,670)(635,672)(636,671)(637,665)(638,666)
(639,668)(640,667)(723,724)(727,728)(729,733)(730,734)(731,736)(732,735)
(737,785)(738,786)(739,788)(740,787)(741,789)(742,790)(743,792)(744,791)
(745,797)(746,798)(747,800)(748,799)(749,793)(750,794)(751,796)(752,795)
(753,769)(754,770)(755,772)(756,771)(757,773)(758,774)(759,776)(760,775)
(761,781)(762,782)(763,784)(764,783)(765,777)(766,778)(767,780)(768,779)
(801,881)(802,882)(803,884)(804,883)(805,885)(806,886)(807,888)(808,887)
(809,893)(810,894)(811,896)(812,895)(813,889)(814,890)(815,892)(816,891)
(817,945)(818,946)(819,948)(820,947)(821,949)(822,950)(823,952)(824,951)
(825,957)(826,958)(827,960)(828,959)(829,953)(830,954)(831,956)(832,955)
(833,929)(834,930)(835,932)(836,931)(837,933)(838,934)(839,936)(840,935)
(841,941)(842,942)(843,944)(844,943)(845,937)(846,938)(847,940)(848,939)
(849,913)(850,914)(851,916)(852,915)(853,917)(854,918)(855,920)(856,919)
(857,925)(858,926)(859,928)(860,927)(861,921)(862,922)(863,924)(864,923)
(865,897)(866,898)(867,900)(868,899)(869,901)(870,902)(871,904)(872,903)
(873,909)(874,910)(875,912)(876,911)(877,905)(878,906)(879,908)(880,907);;
s1 := ( 1, 97)( 2,100)( 3, 99)( 4, 98)( 5,109)( 6,112)( 7,111)( 8,110)
( 9,105)( 10,108)( 11,107)( 12,106)( 13,101)( 14,104)( 15,103)( 16,102)
( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 93)( 22, 96)( 23, 95)( 24, 94)
( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)( 32, 86)
( 33,145)( 34,148)( 35,147)( 36,146)( 37,157)( 38,160)( 39,159)( 40,158)
( 41,153)( 42,156)( 43,155)( 44,154)( 45,149)( 46,152)( 47,151)( 48,150)
( 49,129)( 50,132)( 51,131)( 52,130)( 53,141)( 54,144)( 55,143)( 56,142)
( 57,137)( 58,140)( 59,139)( 60,138)( 61,133)( 62,136)( 63,135)( 64,134)
( 65,113)( 66,116)( 67,115)( 68,114)( 69,125)( 70,128)( 71,127)( 72,126)
( 73,121)( 74,124)( 75,123)( 76,122)( 77,117)( 78,120)( 79,119)( 80,118)
(161,177)(162,180)(163,179)(164,178)(165,189)(166,192)(167,191)(168,190)
(169,185)(170,188)(171,187)(172,186)(173,181)(174,184)(175,183)(176,182)
(193,225)(194,228)(195,227)(196,226)(197,237)(198,240)(199,239)(200,238)
(201,233)(202,236)(203,235)(204,234)(205,229)(206,232)(207,231)(208,230)
(210,212)(213,221)(214,224)(215,223)(216,222)(218,220)(241,337)(242,340)
(243,339)(244,338)(245,349)(246,352)(247,351)(248,350)(249,345)(250,348)
(251,347)(252,346)(253,341)(254,344)(255,343)(256,342)(257,321)(258,324)
(259,323)(260,322)(261,333)(262,336)(263,335)(264,334)(265,329)(266,332)
(267,331)(268,330)(269,325)(270,328)(271,327)(272,326)(273,385)(274,388)
(275,387)(276,386)(277,397)(278,400)(279,399)(280,398)(281,393)(282,396)
(283,395)(284,394)(285,389)(286,392)(287,391)(288,390)(289,369)(290,372)
(291,371)(292,370)(293,381)(294,384)(295,383)(296,382)(297,377)(298,380)
(299,379)(300,378)(301,373)(302,376)(303,375)(304,374)(305,353)(306,356)
(307,355)(308,354)(309,365)(310,368)(311,367)(312,366)(313,361)(314,364)
(315,363)(316,362)(317,357)(318,360)(319,359)(320,358)(401,417)(402,420)
(403,419)(404,418)(405,429)(406,432)(407,431)(408,430)(409,425)(410,428)
(411,427)(412,426)(413,421)(414,424)(415,423)(416,422)(433,465)(434,468)
(435,467)(436,466)(437,477)(438,480)(439,479)(440,478)(441,473)(442,476)
(443,475)(444,474)(445,469)(446,472)(447,471)(448,470)(450,452)(453,461)
(454,464)(455,463)(456,462)(458,460)(481,577)(482,580)(483,579)(484,578)
(485,589)(486,592)(487,591)(488,590)(489,585)(490,588)(491,587)(492,586)
(493,581)(494,584)(495,583)(496,582)(497,561)(498,564)(499,563)(500,562)
(501,573)(502,576)(503,575)(504,574)(505,569)(506,572)(507,571)(508,570)
(509,565)(510,568)(511,567)(512,566)(513,625)(514,628)(515,627)(516,626)
(517,637)(518,640)(519,639)(520,638)(521,633)(522,636)(523,635)(524,634)
(525,629)(526,632)(527,631)(528,630)(529,609)(530,612)(531,611)(532,610)
(533,621)(534,624)(535,623)(536,622)(537,617)(538,620)(539,619)(540,618)
(541,613)(542,616)(543,615)(544,614)(545,593)(546,596)(547,595)(548,594)
(549,605)(550,608)(551,607)(552,606)(553,601)(554,604)(555,603)(556,602)
(557,597)(558,600)(559,599)(560,598)(641,657)(642,660)(643,659)(644,658)
(645,669)(646,672)(647,671)(648,670)(649,665)(650,668)(651,667)(652,666)
(653,661)(654,664)(655,663)(656,662)(673,705)(674,708)(675,707)(676,706)
(677,717)(678,720)(679,719)(680,718)(681,713)(682,716)(683,715)(684,714)
(685,709)(686,712)(687,711)(688,710)(690,692)(693,701)(694,704)(695,703)
(696,702)(698,700)(721,817)(722,820)(723,819)(724,818)(725,829)(726,832)
(727,831)(728,830)(729,825)(730,828)(731,827)(732,826)(733,821)(734,824)
(735,823)(736,822)(737,801)(738,804)(739,803)(740,802)(741,813)(742,816)
(743,815)(744,814)(745,809)(746,812)(747,811)(748,810)(749,805)(750,808)
(751,807)(752,806)(753,865)(754,868)(755,867)(756,866)(757,877)(758,880)
(759,879)(760,878)(761,873)(762,876)(763,875)(764,874)(765,869)(766,872)
(767,871)(768,870)(769,849)(770,852)(771,851)(772,850)(773,861)(774,864)
(775,863)(776,862)(777,857)(778,860)(779,859)(780,858)(781,853)(782,856)
(783,855)(784,854)(785,833)(786,836)(787,835)(788,834)(789,845)(790,848)
(791,847)(792,846)(793,841)(794,844)(795,843)(796,842)(797,837)(798,840)
(799,839)(800,838)(881,897)(882,900)(883,899)(884,898)(885,909)(886,912)
(887,911)(888,910)(889,905)(890,908)(891,907)(892,906)(893,901)(894,904)
(895,903)(896,902)(913,945)(914,948)(915,947)(916,946)(917,957)(918,960)
(919,959)(920,958)(921,953)(922,956)(923,955)(924,954)(925,949)(926,952)
(927,951)(928,950)(930,932)(933,941)(934,944)(935,943)(936,942)(938,940);;
s2 := ( 1,485)( 2,486)( 3,487)( 4,488)( 5,481)( 6,482)( 7,483)( 8,484)
( 9,493)( 10,494)( 11,495)( 12,496)( 13,489)( 14,490)( 15,491)( 16,492)
( 17,501)( 18,502)( 19,503)( 20,504)( 21,497)( 22,498)( 23,499)( 24,500)
( 25,509)( 26,510)( 27,511)( 28,512)( 29,505)( 30,506)( 31,507)( 32,508)
( 33,517)( 34,518)( 35,519)( 36,520)( 37,513)( 38,514)( 39,515)( 40,516)
( 41,525)( 42,526)( 43,527)( 44,528)( 45,521)( 46,522)( 47,523)( 48,524)
( 49,533)( 50,534)( 51,535)( 52,536)( 53,529)( 54,530)( 55,531)( 56,532)
( 57,541)( 58,542)( 59,543)( 60,544)( 61,537)( 62,538)( 63,539)( 64,540)
( 65,549)( 66,550)( 67,551)( 68,552)( 69,545)( 70,546)( 71,547)( 72,548)
( 73,557)( 74,558)( 75,559)( 76,560)( 77,553)( 78,554)( 79,555)( 80,556)
( 81,565)( 82,566)( 83,567)( 84,568)( 85,561)( 86,562)( 87,563)( 88,564)
( 89,573)( 90,574)( 91,575)( 92,576)( 93,569)( 94,570)( 95,571)( 96,572)
( 97,581)( 98,582)( 99,583)(100,584)(101,577)(102,578)(103,579)(104,580)
(105,589)(106,590)(107,591)(108,592)(109,585)(110,586)(111,587)(112,588)
(113,597)(114,598)(115,599)(116,600)(117,593)(118,594)(119,595)(120,596)
(121,605)(122,606)(123,607)(124,608)(125,601)(126,602)(127,603)(128,604)
(129,613)(130,614)(131,615)(132,616)(133,609)(134,610)(135,611)(136,612)
(137,621)(138,622)(139,623)(140,624)(141,617)(142,618)(143,619)(144,620)
(145,629)(146,630)(147,631)(148,632)(149,625)(150,626)(151,627)(152,628)
(153,637)(154,638)(155,639)(156,640)(157,633)(158,634)(159,635)(160,636)
(161,645)(162,646)(163,647)(164,648)(165,641)(166,642)(167,643)(168,644)
(169,653)(170,654)(171,655)(172,656)(173,649)(174,650)(175,651)(176,652)
(177,661)(178,662)(179,663)(180,664)(181,657)(182,658)(183,659)(184,660)
(185,669)(186,670)(187,671)(188,672)(189,665)(190,666)(191,667)(192,668)
(193,677)(194,678)(195,679)(196,680)(197,673)(198,674)(199,675)(200,676)
(201,685)(202,686)(203,687)(204,688)(205,681)(206,682)(207,683)(208,684)
(209,693)(210,694)(211,695)(212,696)(213,689)(214,690)(215,691)(216,692)
(217,701)(218,702)(219,703)(220,704)(221,697)(222,698)(223,699)(224,700)
(225,709)(226,710)(227,711)(228,712)(229,705)(230,706)(231,707)(232,708)
(233,717)(234,718)(235,719)(236,720)(237,713)(238,714)(239,715)(240,716)
(241,725)(242,726)(243,727)(244,728)(245,721)(246,722)(247,723)(248,724)
(249,733)(250,734)(251,735)(252,736)(253,729)(254,730)(255,731)(256,732)
(257,741)(258,742)(259,743)(260,744)(261,737)(262,738)(263,739)(264,740)
(265,749)(266,750)(267,751)(268,752)(269,745)(270,746)(271,747)(272,748)
(273,757)(274,758)(275,759)(276,760)(277,753)(278,754)(279,755)(280,756)
(281,765)(282,766)(283,767)(284,768)(285,761)(286,762)(287,763)(288,764)
(289,773)(290,774)(291,775)(292,776)(293,769)(294,770)(295,771)(296,772)
(297,781)(298,782)(299,783)(300,784)(301,777)(302,778)(303,779)(304,780)
(305,789)(306,790)(307,791)(308,792)(309,785)(310,786)(311,787)(312,788)
(313,797)(314,798)(315,799)(316,800)(317,793)(318,794)(319,795)(320,796)
(321,805)(322,806)(323,807)(324,808)(325,801)(326,802)(327,803)(328,804)
(329,813)(330,814)(331,815)(332,816)(333,809)(334,810)(335,811)(336,812)
(337,821)(338,822)(339,823)(340,824)(341,817)(342,818)(343,819)(344,820)
(345,829)(346,830)(347,831)(348,832)(349,825)(350,826)(351,827)(352,828)
(353,837)(354,838)(355,839)(356,840)(357,833)(358,834)(359,835)(360,836)
(361,845)(362,846)(363,847)(364,848)(365,841)(366,842)(367,843)(368,844)
(369,853)(370,854)(371,855)(372,856)(373,849)(374,850)(375,851)(376,852)
(377,861)(378,862)(379,863)(380,864)(381,857)(382,858)(383,859)(384,860)
(385,869)(386,870)(387,871)(388,872)(389,865)(390,866)(391,867)(392,868)
(393,877)(394,878)(395,879)(396,880)(397,873)(398,874)(399,875)(400,876)
(401,885)(402,886)(403,887)(404,888)(405,881)(406,882)(407,883)(408,884)
(409,893)(410,894)(411,895)(412,896)(413,889)(414,890)(415,891)(416,892)
(417,901)(418,902)(419,903)(420,904)(421,897)(422,898)(423,899)(424,900)
(425,909)(426,910)(427,911)(428,912)(429,905)(430,906)(431,907)(432,908)
(433,917)(434,918)(435,919)(436,920)(437,913)(438,914)(439,915)(440,916)
(441,925)(442,926)(443,927)(444,928)(445,921)(446,922)(447,923)(448,924)
(449,933)(450,934)(451,935)(452,936)(453,929)(454,930)(455,931)(456,932)
(457,941)(458,942)(459,943)(460,944)(461,937)(462,938)(463,939)(464,940)
(465,949)(466,950)(467,951)(468,952)(469,945)(470,946)(471,947)(472,948)
(473,957)(474,958)(475,959)(476,960)(477,953)(478,954)(479,955)(480,956);;
s3 := ( 1,241)( 2,242)( 3,243)( 4,244)( 5,246)( 6,245)( 7,248)( 8,247)
( 9,251)( 10,252)( 11,249)( 12,250)( 13,256)( 14,255)( 15,254)( 16,253)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,262)( 22,261)( 23,264)( 24,263)
( 25,267)( 26,268)( 27,265)( 28,266)( 29,272)( 30,271)( 31,270)( 32,269)
( 33,273)( 34,274)( 35,275)( 36,276)( 37,278)( 38,277)( 39,280)( 40,279)
( 41,283)( 42,284)( 43,281)( 44,282)( 45,288)( 46,287)( 47,286)( 48,285)
( 49,289)( 50,290)( 51,291)( 52,292)( 53,294)( 54,293)( 55,296)( 56,295)
( 57,299)( 58,300)( 59,297)( 60,298)( 61,304)( 62,303)( 63,302)( 64,301)
( 65,305)( 66,306)( 67,307)( 68,308)( 69,310)( 70,309)( 71,312)( 72,311)
( 73,315)( 74,316)( 75,313)( 76,314)( 77,320)( 78,319)( 79,318)( 80,317)
( 81,321)( 82,322)( 83,323)( 84,324)( 85,326)( 86,325)( 87,328)( 88,327)
( 89,331)( 90,332)( 91,329)( 92,330)( 93,336)( 94,335)( 95,334)( 96,333)
( 97,337)( 98,338)( 99,339)(100,340)(101,342)(102,341)(103,344)(104,343)
(105,347)(106,348)(107,345)(108,346)(109,352)(110,351)(111,350)(112,349)
(113,353)(114,354)(115,355)(116,356)(117,358)(118,357)(119,360)(120,359)
(121,363)(122,364)(123,361)(124,362)(125,368)(126,367)(127,366)(128,365)
(129,369)(130,370)(131,371)(132,372)(133,374)(134,373)(135,376)(136,375)
(137,379)(138,380)(139,377)(140,378)(141,384)(142,383)(143,382)(144,381)
(145,385)(146,386)(147,387)(148,388)(149,390)(150,389)(151,392)(152,391)
(153,395)(154,396)(155,393)(156,394)(157,400)(158,399)(159,398)(160,397)
(161,401)(162,402)(163,403)(164,404)(165,406)(166,405)(167,408)(168,407)
(169,411)(170,412)(171,409)(172,410)(173,416)(174,415)(175,414)(176,413)
(177,417)(178,418)(179,419)(180,420)(181,422)(182,421)(183,424)(184,423)
(185,427)(186,428)(187,425)(188,426)(189,432)(190,431)(191,430)(192,429)
(193,433)(194,434)(195,435)(196,436)(197,438)(198,437)(199,440)(200,439)
(201,443)(202,444)(203,441)(204,442)(205,448)(206,447)(207,446)(208,445)
(209,449)(210,450)(211,451)(212,452)(213,454)(214,453)(215,456)(216,455)
(217,459)(218,460)(219,457)(220,458)(221,464)(222,463)(223,462)(224,461)
(225,465)(226,466)(227,467)(228,468)(229,470)(230,469)(231,472)(232,471)
(233,475)(234,476)(235,473)(236,474)(237,480)(238,479)(239,478)(240,477)
(481,721)(482,722)(483,723)(484,724)(485,726)(486,725)(487,728)(488,727)
(489,731)(490,732)(491,729)(492,730)(493,736)(494,735)(495,734)(496,733)
(497,737)(498,738)(499,739)(500,740)(501,742)(502,741)(503,744)(504,743)
(505,747)(506,748)(507,745)(508,746)(509,752)(510,751)(511,750)(512,749)
(513,753)(514,754)(515,755)(516,756)(517,758)(518,757)(519,760)(520,759)
(521,763)(522,764)(523,761)(524,762)(525,768)(526,767)(527,766)(528,765)
(529,769)(530,770)(531,771)(532,772)(533,774)(534,773)(535,776)(536,775)
(537,779)(538,780)(539,777)(540,778)(541,784)(542,783)(543,782)(544,781)
(545,785)(546,786)(547,787)(548,788)(549,790)(550,789)(551,792)(552,791)
(553,795)(554,796)(555,793)(556,794)(557,800)(558,799)(559,798)(560,797)
(561,801)(562,802)(563,803)(564,804)(565,806)(566,805)(567,808)(568,807)
(569,811)(570,812)(571,809)(572,810)(573,816)(574,815)(575,814)(576,813)
(577,817)(578,818)(579,819)(580,820)(581,822)(582,821)(583,824)(584,823)
(585,827)(586,828)(587,825)(588,826)(589,832)(590,831)(591,830)(592,829)
(593,833)(594,834)(595,835)(596,836)(597,838)(598,837)(599,840)(600,839)
(601,843)(602,844)(603,841)(604,842)(605,848)(606,847)(607,846)(608,845)
(609,849)(610,850)(611,851)(612,852)(613,854)(614,853)(615,856)(616,855)
(617,859)(618,860)(619,857)(620,858)(621,864)(622,863)(623,862)(624,861)
(625,865)(626,866)(627,867)(628,868)(629,870)(630,869)(631,872)(632,871)
(633,875)(634,876)(635,873)(636,874)(637,880)(638,879)(639,878)(640,877)
(641,881)(642,882)(643,883)(644,884)(645,886)(646,885)(647,888)(648,887)
(649,891)(650,892)(651,889)(652,890)(653,896)(654,895)(655,894)(656,893)
(657,897)(658,898)(659,899)(660,900)(661,902)(662,901)(663,904)(664,903)
(665,907)(666,908)(667,905)(668,906)(669,912)(670,911)(671,910)(672,909)
(673,913)(674,914)(675,915)(676,916)(677,918)(678,917)(679,920)(680,919)
(681,923)(682,924)(683,921)(684,922)(685,928)(686,927)(687,926)(688,925)
(689,929)(690,930)(691,931)(692,932)(693,934)(694,933)(695,936)(696,935)
(697,939)(698,940)(699,937)(700,938)(701,944)(702,943)(703,942)(704,941)
(705,945)(706,946)(707,947)(708,948)(709,950)(710,949)(711,952)(712,951)
(713,955)(714,956)(715,953)(716,954)(717,960)(718,959)(719,958)(720,957);;
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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s3*s2*s1*s2*s0*s1*s2*s3*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 65)
( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 77)
( 26, 78)( 27, 80)( 28, 79)( 29, 73)( 30, 74)( 31, 76)( 32, 75)( 33, 49)
( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 61)
( 42, 62)( 43, 64)( 44, 63)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 81,161)
( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,173)
( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,225)
( 98,226)( 99,228)(100,227)(101,229)(102,230)(103,232)(104,231)(105,237)
(106,238)(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)(113,209)
(114,210)(115,212)(116,211)(117,213)(118,214)(119,216)(120,215)(121,221)
(122,222)(123,224)(124,223)(125,217)(126,218)(127,220)(128,219)(129,193)
(130,194)(131,196)(132,195)(133,197)(134,198)(135,200)(136,199)(137,205)
(138,206)(139,208)(140,207)(141,201)(142,202)(143,204)(144,203)(145,177)
(146,178)(147,180)(148,179)(149,181)(150,182)(151,184)(152,183)(153,189)
(154,190)(155,192)(156,191)(157,185)(158,186)(159,188)(160,187)(243,244)
(247,248)(249,253)(250,254)(251,256)(252,255)(257,305)(258,306)(259,308)
(260,307)(261,309)(262,310)(263,312)(264,311)(265,317)(266,318)(267,320)
(268,319)(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)(275,292)
(276,291)(277,293)(278,294)(279,296)(280,295)(281,301)(282,302)(283,304)
(284,303)(285,297)(286,298)(287,300)(288,299)(321,401)(322,402)(323,404)
(324,403)(325,405)(326,406)(327,408)(328,407)(329,413)(330,414)(331,416)
(332,415)(333,409)(334,410)(335,412)(336,411)(337,465)(338,466)(339,468)
(340,467)(341,469)(342,470)(343,472)(344,471)(345,477)(346,478)(347,480)
(348,479)(349,473)(350,474)(351,476)(352,475)(353,449)(354,450)(355,452)
(356,451)(357,453)(358,454)(359,456)(360,455)(361,461)(362,462)(363,464)
(364,463)(365,457)(366,458)(367,460)(368,459)(369,433)(370,434)(371,436)
(372,435)(373,437)(374,438)(375,440)(376,439)(377,445)(378,446)(379,448)
(380,447)(381,441)(382,442)(383,444)(384,443)(385,417)(386,418)(387,420)
(388,419)(389,421)(390,422)(391,424)(392,423)(393,429)(394,430)(395,432)
(396,431)(397,425)(398,426)(399,428)(400,427)(483,484)(487,488)(489,493)
(490,494)(491,496)(492,495)(497,545)(498,546)(499,548)(500,547)(501,549)
(502,550)(503,552)(504,551)(505,557)(506,558)(507,560)(508,559)(509,553)
(510,554)(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)(517,533)
(518,534)(519,536)(520,535)(521,541)(522,542)(523,544)(524,543)(525,537)
(526,538)(527,540)(528,539)(561,641)(562,642)(563,644)(564,643)(565,645)
(566,646)(567,648)(568,647)(569,653)(570,654)(571,656)(572,655)(573,649)
(574,650)(575,652)(576,651)(577,705)(578,706)(579,708)(580,707)(581,709)
(582,710)(583,712)(584,711)(585,717)(586,718)(587,720)(588,719)(589,713)
(590,714)(591,716)(592,715)(593,689)(594,690)(595,692)(596,691)(597,693)
(598,694)(599,696)(600,695)(601,701)(602,702)(603,704)(604,703)(605,697)
(606,698)(607,700)(608,699)(609,673)(610,674)(611,676)(612,675)(613,677)
(614,678)(615,680)(616,679)(617,685)(618,686)(619,688)(620,687)(621,681)
(622,682)(623,684)(624,683)(625,657)(626,658)(627,660)(628,659)(629,661)
(630,662)(631,664)(632,663)(633,669)(634,670)(635,672)(636,671)(637,665)
(638,666)(639,668)(640,667)(723,724)(727,728)(729,733)(730,734)(731,736)
(732,735)(737,785)(738,786)(739,788)(740,787)(741,789)(742,790)(743,792)
(744,791)(745,797)(746,798)(747,800)(748,799)(749,793)(750,794)(751,796)
(752,795)(753,769)(754,770)(755,772)(756,771)(757,773)(758,774)(759,776)
(760,775)(761,781)(762,782)(763,784)(764,783)(765,777)(766,778)(767,780)
(768,779)(801,881)(802,882)(803,884)(804,883)(805,885)(806,886)(807,888)
(808,887)(809,893)(810,894)(811,896)(812,895)(813,889)(814,890)(815,892)
(816,891)(817,945)(818,946)(819,948)(820,947)(821,949)(822,950)(823,952)
(824,951)(825,957)(826,958)(827,960)(828,959)(829,953)(830,954)(831,956)
(832,955)(833,929)(834,930)(835,932)(836,931)(837,933)(838,934)(839,936)
(840,935)(841,941)(842,942)(843,944)(844,943)(845,937)(846,938)(847,940)
(848,939)(849,913)(850,914)(851,916)(852,915)(853,917)(854,918)(855,920)
(856,919)(857,925)(858,926)(859,928)(860,927)(861,921)(862,922)(863,924)
(864,923)(865,897)(866,898)(867,900)(868,899)(869,901)(870,902)(871,904)
(872,903)(873,909)(874,910)(875,912)(876,911)(877,905)(878,906)(879,908)
(880,907);
s1 := Sym(960)!( 1, 97)( 2,100)( 3, 99)( 4, 98)( 5,109)( 6,112)( 7,111)
( 8,110)( 9,105)( 10,108)( 11,107)( 12,106)( 13,101)( 14,104)( 15,103)
( 16,102)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 93)( 22, 96)( 23, 95)
( 24, 94)( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)
( 32, 86)( 33,145)( 34,148)( 35,147)( 36,146)( 37,157)( 38,160)( 39,159)
( 40,158)( 41,153)( 42,156)( 43,155)( 44,154)( 45,149)( 46,152)( 47,151)
( 48,150)( 49,129)( 50,132)( 51,131)( 52,130)( 53,141)( 54,144)( 55,143)
( 56,142)( 57,137)( 58,140)( 59,139)( 60,138)( 61,133)( 62,136)( 63,135)
( 64,134)( 65,113)( 66,116)( 67,115)( 68,114)( 69,125)( 70,128)( 71,127)
( 72,126)( 73,121)( 74,124)( 75,123)( 76,122)( 77,117)( 78,120)( 79,119)
( 80,118)(161,177)(162,180)(163,179)(164,178)(165,189)(166,192)(167,191)
(168,190)(169,185)(170,188)(171,187)(172,186)(173,181)(174,184)(175,183)
(176,182)(193,225)(194,228)(195,227)(196,226)(197,237)(198,240)(199,239)
(200,238)(201,233)(202,236)(203,235)(204,234)(205,229)(206,232)(207,231)
(208,230)(210,212)(213,221)(214,224)(215,223)(216,222)(218,220)(241,337)
(242,340)(243,339)(244,338)(245,349)(246,352)(247,351)(248,350)(249,345)
(250,348)(251,347)(252,346)(253,341)(254,344)(255,343)(256,342)(257,321)
(258,324)(259,323)(260,322)(261,333)(262,336)(263,335)(264,334)(265,329)
(266,332)(267,331)(268,330)(269,325)(270,328)(271,327)(272,326)(273,385)
(274,388)(275,387)(276,386)(277,397)(278,400)(279,399)(280,398)(281,393)
(282,396)(283,395)(284,394)(285,389)(286,392)(287,391)(288,390)(289,369)
(290,372)(291,371)(292,370)(293,381)(294,384)(295,383)(296,382)(297,377)
(298,380)(299,379)(300,378)(301,373)(302,376)(303,375)(304,374)(305,353)
(306,356)(307,355)(308,354)(309,365)(310,368)(311,367)(312,366)(313,361)
(314,364)(315,363)(316,362)(317,357)(318,360)(319,359)(320,358)(401,417)
(402,420)(403,419)(404,418)(405,429)(406,432)(407,431)(408,430)(409,425)
(410,428)(411,427)(412,426)(413,421)(414,424)(415,423)(416,422)(433,465)
(434,468)(435,467)(436,466)(437,477)(438,480)(439,479)(440,478)(441,473)
(442,476)(443,475)(444,474)(445,469)(446,472)(447,471)(448,470)(450,452)
(453,461)(454,464)(455,463)(456,462)(458,460)(481,577)(482,580)(483,579)
(484,578)(485,589)(486,592)(487,591)(488,590)(489,585)(490,588)(491,587)
(492,586)(493,581)(494,584)(495,583)(496,582)(497,561)(498,564)(499,563)
(500,562)(501,573)(502,576)(503,575)(504,574)(505,569)(506,572)(507,571)
(508,570)(509,565)(510,568)(511,567)(512,566)(513,625)(514,628)(515,627)
(516,626)(517,637)(518,640)(519,639)(520,638)(521,633)(522,636)(523,635)
(524,634)(525,629)(526,632)(527,631)(528,630)(529,609)(530,612)(531,611)
(532,610)(533,621)(534,624)(535,623)(536,622)(537,617)(538,620)(539,619)
(540,618)(541,613)(542,616)(543,615)(544,614)(545,593)(546,596)(547,595)
(548,594)(549,605)(550,608)(551,607)(552,606)(553,601)(554,604)(555,603)
(556,602)(557,597)(558,600)(559,599)(560,598)(641,657)(642,660)(643,659)
(644,658)(645,669)(646,672)(647,671)(648,670)(649,665)(650,668)(651,667)
(652,666)(653,661)(654,664)(655,663)(656,662)(673,705)(674,708)(675,707)
(676,706)(677,717)(678,720)(679,719)(680,718)(681,713)(682,716)(683,715)
(684,714)(685,709)(686,712)(687,711)(688,710)(690,692)(693,701)(694,704)
(695,703)(696,702)(698,700)(721,817)(722,820)(723,819)(724,818)(725,829)
(726,832)(727,831)(728,830)(729,825)(730,828)(731,827)(732,826)(733,821)
(734,824)(735,823)(736,822)(737,801)(738,804)(739,803)(740,802)(741,813)
(742,816)(743,815)(744,814)(745,809)(746,812)(747,811)(748,810)(749,805)
(750,808)(751,807)(752,806)(753,865)(754,868)(755,867)(756,866)(757,877)
(758,880)(759,879)(760,878)(761,873)(762,876)(763,875)(764,874)(765,869)
(766,872)(767,871)(768,870)(769,849)(770,852)(771,851)(772,850)(773,861)
(774,864)(775,863)(776,862)(777,857)(778,860)(779,859)(780,858)(781,853)
(782,856)(783,855)(784,854)(785,833)(786,836)(787,835)(788,834)(789,845)
(790,848)(791,847)(792,846)(793,841)(794,844)(795,843)(796,842)(797,837)
(798,840)(799,839)(800,838)(881,897)(882,900)(883,899)(884,898)(885,909)
(886,912)(887,911)(888,910)(889,905)(890,908)(891,907)(892,906)(893,901)
(894,904)(895,903)(896,902)(913,945)(914,948)(915,947)(916,946)(917,957)
(918,960)(919,959)(920,958)(921,953)(922,956)(923,955)(924,954)(925,949)
(926,952)(927,951)(928,950)(930,932)(933,941)(934,944)(935,943)(936,942)
(938,940);
s2 := Sym(960)!( 1,485)( 2,486)( 3,487)( 4,488)( 5,481)( 6,482)( 7,483)
( 8,484)( 9,493)( 10,494)( 11,495)( 12,496)( 13,489)( 14,490)( 15,491)
( 16,492)( 17,501)( 18,502)( 19,503)( 20,504)( 21,497)( 22,498)( 23,499)
( 24,500)( 25,509)( 26,510)( 27,511)( 28,512)( 29,505)( 30,506)( 31,507)
( 32,508)( 33,517)( 34,518)( 35,519)( 36,520)( 37,513)( 38,514)( 39,515)
( 40,516)( 41,525)( 42,526)( 43,527)( 44,528)( 45,521)( 46,522)( 47,523)
( 48,524)( 49,533)( 50,534)( 51,535)( 52,536)( 53,529)( 54,530)( 55,531)
( 56,532)( 57,541)( 58,542)( 59,543)( 60,544)( 61,537)( 62,538)( 63,539)
( 64,540)( 65,549)( 66,550)( 67,551)( 68,552)( 69,545)( 70,546)( 71,547)
( 72,548)( 73,557)( 74,558)( 75,559)( 76,560)( 77,553)( 78,554)( 79,555)
( 80,556)( 81,565)( 82,566)( 83,567)( 84,568)( 85,561)( 86,562)( 87,563)
( 88,564)( 89,573)( 90,574)( 91,575)( 92,576)( 93,569)( 94,570)( 95,571)
( 96,572)( 97,581)( 98,582)( 99,583)(100,584)(101,577)(102,578)(103,579)
(104,580)(105,589)(106,590)(107,591)(108,592)(109,585)(110,586)(111,587)
(112,588)(113,597)(114,598)(115,599)(116,600)(117,593)(118,594)(119,595)
(120,596)(121,605)(122,606)(123,607)(124,608)(125,601)(126,602)(127,603)
(128,604)(129,613)(130,614)(131,615)(132,616)(133,609)(134,610)(135,611)
(136,612)(137,621)(138,622)(139,623)(140,624)(141,617)(142,618)(143,619)
(144,620)(145,629)(146,630)(147,631)(148,632)(149,625)(150,626)(151,627)
(152,628)(153,637)(154,638)(155,639)(156,640)(157,633)(158,634)(159,635)
(160,636)(161,645)(162,646)(163,647)(164,648)(165,641)(166,642)(167,643)
(168,644)(169,653)(170,654)(171,655)(172,656)(173,649)(174,650)(175,651)
(176,652)(177,661)(178,662)(179,663)(180,664)(181,657)(182,658)(183,659)
(184,660)(185,669)(186,670)(187,671)(188,672)(189,665)(190,666)(191,667)
(192,668)(193,677)(194,678)(195,679)(196,680)(197,673)(198,674)(199,675)
(200,676)(201,685)(202,686)(203,687)(204,688)(205,681)(206,682)(207,683)
(208,684)(209,693)(210,694)(211,695)(212,696)(213,689)(214,690)(215,691)
(216,692)(217,701)(218,702)(219,703)(220,704)(221,697)(222,698)(223,699)
(224,700)(225,709)(226,710)(227,711)(228,712)(229,705)(230,706)(231,707)
(232,708)(233,717)(234,718)(235,719)(236,720)(237,713)(238,714)(239,715)
(240,716)(241,725)(242,726)(243,727)(244,728)(245,721)(246,722)(247,723)
(248,724)(249,733)(250,734)(251,735)(252,736)(253,729)(254,730)(255,731)
(256,732)(257,741)(258,742)(259,743)(260,744)(261,737)(262,738)(263,739)
(264,740)(265,749)(266,750)(267,751)(268,752)(269,745)(270,746)(271,747)
(272,748)(273,757)(274,758)(275,759)(276,760)(277,753)(278,754)(279,755)
(280,756)(281,765)(282,766)(283,767)(284,768)(285,761)(286,762)(287,763)
(288,764)(289,773)(290,774)(291,775)(292,776)(293,769)(294,770)(295,771)
(296,772)(297,781)(298,782)(299,783)(300,784)(301,777)(302,778)(303,779)
(304,780)(305,789)(306,790)(307,791)(308,792)(309,785)(310,786)(311,787)
(312,788)(313,797)(314,798)(315,799)(316,800)(317,793)(318,794)(319,795)
(320,796)(321,805)(322,806)(323,807)(324,808)(325,801)(326,802)(327,803)
(328,804)(329,813)(330,814)(331,815)(332,816)(333,809)(334,810)(335,811)
(336,812)(337,821)(338,822)(339,823)(340,824)(341,817)(342,818)(343,819)
(344,820)(345,829)(346,830)(347,831)(348,832)(349,825)(350,826)(351,827)
(352,828)(353,837)(354,838)(355,839)(356,840)(357,833)(358,834)(359,835)
(360,836)(361,845)(362,846)(363,847)(364,848)(365,841)(366,842)(367,843)
(368,844)(369,853)(370,854)(371,855)(372,856)(373,849)(374,850)(375,851)
(376,852)(377,861)(378,862)(379,863)(380,864)(381,857)(382,858)(383,859)
(384,860)(385,869)(386,870)(387,871)(388,872)(389,865)(390,866)(391,867)
(392,868)(393,877)(394,878)(395,879)(396,880)(397,873)(398,874)(399,875)
(400,876)(401,885)(402,886)(403,887)(404,888)(405,881)(406,882)(407,883)
(408,884)(409,893)(410,894)(411,895)(412,896)(413,889)(414,890)(415,891)
(416,892)(417,901)(418,902)(419,903)(420,904)(421,897)(422,898)(423,899)
(424,900)(425,909)(426,910)(427,911)(428,912)(429,905)(430,906)(431,907)
(432,908)(433,917)(434,918)(435,919)(436,920)(437,913)(438,914)(439,915)
(440,916)(441,925)(442,926)(443,927)(444,928)(445,921)(446,922)(447,923)
(448,924)(449,933)(450,934)(451,935)(452,936)(453,929)(454,930)(455,931)
(456,932)(457,941)(458,942)(459,943)(460,944)(461,937)(462,938)(463,939)
(464,940)(465,949)(466,950)(467,951)(468,952)(469,945)(470,946)(471,947)
(472,948)(473,957)(474,958)(475,959)(476,960)(477,953)(478,954)(479,955)
(480,956);
s3 := Sym(960)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,246)( 6,245)( 7,248)
( 8,247)( 9,251)( 10,252)( 11,249)( 12,250)( 13,256)( 14,255)( 15,254)
( 16,253)( 17,257)( 18,258)( 19,259)( 20,260)( 21,262)( 22,261)( 23,264)
( 24,263)( 25,267)( 26,268)( 27,265)( 28,266)( 29,272)( 30,271)( 31,270)
( 32,269)( 33,273)( 34,274)( 35,275)( 36,276)( 37,278)( 38,277)( 39,280)
( 40,279)( 41,283)( 42,284)( 43,281)( 44,282)( 45,288)( 46,287)( 47,286)
( 48,285)( 49,289)( 50,290)( 51,291)( 52,292)( 53,294)( 54,293)( 55,296)
( 56,295)( 57,299)( 58,300)( 59,297)( 60,298)( 61,304)( 62,303)( 63,302)
( 64,301)( 65,305)( 66,306)( 67,307)( 68,308)( 69,310)( 70,309)( 71,312)
( 72,311)( 73,315)( 74,316)( 75,313)( 76,314)( 77,320)( 78,319)( 79,318)
( 80,317)( 81,321)( 82,322)( 83,323)( 84,324)( 85,326)( 86,325)( 87,328)
( 88,327)( 89,331)( 90,332)( 91,329)( 92,330)( 93,336)( 94,335)( 95,334)
( 96,333)( 97,337)( 98,338)( 99,339)(100,340)(101,342)(102,341)(103,344)
(104,343)(105,347)(106,348)(107,345)(108,346)(109,352)(110,351)(111,350)
(112,349)(113,353)(114,354)(115,355)(116,356)(117,358)(118,357)(119,360)
(120,359)(121,363)(122,364)(123,361)(124,362)(125,368)(126,367)(127,366)
(128,365)(129,369)(130,370)(131,371)(132,372)(133,374)(134,373)(135,376)
(136,375)(137,379)(138,380)(139,377)(140,378)(141,384)(142,383)(143,382)
(144,381)(145,385)(146,386)(147,387)(148,388)(149,390)(150,389)(151,392)
(152,391)(153,395)(154,396)(155,393)(156,394)(157,400)(158,399)(159,398)
(160,397)(161,401)(162,402)(163,403)(164,404)(165,406)(166,405)(167,408)
(168,407)(169,411)(170,412)(171,409)(172,410)(173,416)(174,415)(175,414)
(176,413)(177,417)(178,418)(179,419)(180,420)(181,422)(182,421)(183,424)
(184,423)(185,427)(186,428)(187,425)(188,426)(189,432)(190,431)(191,430)
(192,429)(193,433)(194,434)(195,435)(196,436)(197,438)(198,437)(199,440)
(200,439)(201,443)(202,444)(203,441)(204,442)(205,448)(206,447)(207,446)
(208,445)(209,449)(210,450)(211,451)(212,452)(213,454)(214,453)(215,456)
(216,455)(217,459)(218,460)(219,457)(220,458)(221,464)(222,463)(223,462)
(224,461)(225,465)(226,466)(227,467)(228,468)(229,470)(230,469)(231,472)
(232,471)(233,475)(234,476)(235,473)(236,474)(237,480)(238,479)(239,478)
(240,477)(481,721)(482,722)(483,723)(484,724)(485,726)(486,725)(487,728)
(488,727)(489,731)(490,732)(491,729)(492,730)(493,736)(494,735)(495,734)
(496,733)(497,737)(498,738)(499,739)(500,740)(501,742)(502,741)(503,744)
(504,743)(505,747)(506,748)(507,745)(508,746)(509,752)(510,751)(511,750)
(512,749)(513,753)(514,754)(515,755)(516,756)(517,758)(518,757)(519,760)
(520,759)(521,763)(522,764)(523,761)(524,762)(525,768)(526,767)(527,766)
(528,765)(529,769)(530,770)(531,771)(532,772)(533,774)(534,773)(535,776)
(536,775)(537,779)(538,780)(539,777)(540,778)(541,784)(542,783)(543,782)
(544,781)(545,785)(546,786)(547,787)(548,788)(549,790)(550,789)(551,792)
(552,791)(553,795)(554,796)(555,793)(556,794)(557,800)(558,799)(559,798)
(560,797)(561,801)(562,802)(563,803)(564,804)(565,806)(566,805)(567,808)
(568,807)(569,811)(570,812)(571,809)(572,810)(573,816)(574,815)(575,814)
(576,813)(577,817)(578,818)(579,819)(580,820)(581,822)(582,821)(583,824)
(584,823)(585,827)(586,828)(587,825)(588,826)(589,832)(590,831)(591,830)
(592,829)(593,833)(594,834)(595,835)(596,836)(597,838)(598,837)(599,840)
(600,839)(601,843)(602,844)(603,841)(604,842)(605,848)(606,847)(607,846)
(608,845)(609,849)(610,850)(611,851)(612,852)(613,854)(614,853)(615,856)
(616,855)(617,859)(618,860)(619,857)(620,858)(621,864)(622,863)(623,862)
(624,861)(625,865)(626,866)(627,867)(628,868)(629,870)(630,869)(631,872)
(632,871)(633,875)(634,876)(635,873)(636,874)(637,880)(638,879)(639,878)
(640,877)(641,881)(642,882)(643,883)(644,884)(645,886)(646,885)(647,888)
(648,887)(649,891)(650,892)(651,889)(652,890)(653,896)(654,895)(655,894)
(656,893)(657,897)(658,898)(659,899)(660,900)(661,902)(662,901)(663,904)
(664,903)(665,907)(666,908)(667,905)(668,906)(669,912)(670,911)(671,910)
(672,909)(673,913)(674,914)(675,915)(676,916)(677,918)(678,917)(679,920)
(680,919)(681,923)(682,924)(683,921)(684,922)(685,928)(686,927)(687,926)
(688,925)(689,929)(690,930)(691,931)(692,932)(693,934)(694,933)(695,936)
(696,935)(697,939)(698,940)(699,937)(700,938)(701,944)(702,943)(703,942)
(704,941)(705,945)(706,946)(707,947)(708,948)(709,950)(710,949)(711,952)
(712,951)(713,955)(714,956)(715,953)(716,954)(717,960)(718,959)(719,958)
(720,957);
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,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s3*s2*s1*s2*s0*s1*s2*s3*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope