Polytope of Type {12,8,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8,10}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150673)
Rank : 4
Schlafli Type : {12,8,10}
Number of vertices, edges, etc : 12, 48, 40, 10
Order of s0s1s2s3 : 120
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {12,4,10}*960
3-fold quotients : {4,8,10}*640b
4-fold quotients : {12,2,10}*480, {6,4,10}*480
5-fold quotients : {12,8,2}*384b
6-fold quotients : {4,4,10}*320
8-fold quotients : {12,2,5}*240, {6,2,10}*240
10-fold quotients : {12,4,2}*192a
12-fold quotients : {2,4,10}*160, {4,2,10}*160
15-fold quotients : {4,8,2}*128b
16-fold quotients : {3,2,10}*120, {6,2,5}*120
20-fold quotients : {12,2,2}*96, {6,4,2}*96a
24-fold quotients : {4,2,5}*80, {2,2,10}*80
30-fold quotients : {4,4,2}*64
32-fold quotients : {3,2,5}*60
40-fold quotients : {6,2,2}*48
48-fold quotients : {2,2,5}*40
60-fold quotients : {2,4,2}*32, {4,2,2}*32
80-fold quotients : {3,2,2}*24
120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,251)( 7,252)( 8,253)
( 9,254)( 10,255)( 11,246)( 12,247)( 13,248)( 14,249)( 15,250)( 16,256)
( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)( 24,269)
( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,271)( 32,272)
( 33,273)( 34,274)( 35,275)( 36,281)( 37,282)( 38,283)( 39,284)( 40,285)
( 41,276)( 42,277)( 43,278)( 44,279)( 45,280)( 46,286)( 47,287)( 48,288)
( 49,289)( 50,290)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)( 56,291)
( 57,292)( 58,293)( 59,294)( 60,295)( 61,316)( 62,317)( 63,318)( 64,319)
( 65,320)( 66,326)( 67,327)( 68,328)( 69,329)( 70,330)( 71,321)( 72,322)
( 73,323)( 74,324)( 75,325)( 76,301)( 77,302)( 78,303)( 79,304)( 80,305)
( 81,311)( 82,312)( 83,313)( 84,314)( 85,315)( 86,306)( 87,307)( 88,308)
( 89,309)( 90,310)( 91,346)( 92,347)( 93,348)( 94,349)( 95,350)( 96,356)
( 97,357)( 98,358)( 99,359)(100,360)(101,351)(102,352)(103,353)(104,354)
(105,355)(106,331)(107,332)(108,333)(109,334)(110,335)(111,341)(112,342)
(113,343)(114,344)(115,345)(116,336)(117,337)(118,338)(119,339)(120,340)
(121,361)(122,362)(123,363)(124,364)(125,365)(126,371)(127,372)(128,373)
(129,374)(130,375)(131,366)(132,367)(133,368)(134,369)(135,370)(136,376)
(137,377)(138,378)(139,379)(140,380)(141,386)(142,387)(143,388)(144,389)
(145,390)(146,381)(147,382)(148,383)(149,384)(150,385)(151,391)(152,392)
(153,393)(154,394)(155,395)(156,401)(157,402)(158,403)(159,404)(160,405)
(161,396)(162,397)(163,398)(164,399)(165,400)(166,406)(167,407)(168,408)
(169,409)(170,410)(171,416)(172,417)(173,418)(174,419)(175,420)(176,411)
(177,412)(178,413)(179,414)(180,415)(181,436)(182,437)(183,438)(184,439)
(185,440)(186,446)(187,447)(188,448)(189,449)(190,450)(191,441)(192,442)
(193,443)(194,444)(195,445)(196,421)(197,422)(198,423)(199,424)(200,425)
(201,431)(202,432)(203,433)(204,434)(205,435)(206,426)(207,427)(208,428)
(209,429)(210,430)(211,466)(212,467)(213,468)(214,469)(215,470)(216,476)
(217,477)(218,478)(219,479)(220,480)(221,471)(222,472)(223,473)(224,474)
(225,475)(226,451)(227,452)(228,453)(229,454)(230,455)(231,461)(232,462)
(233,463)(234,464)(235,465)(236,456)(237,457)(238,458)(239,459)(240,460)
(481,721)(482,722)(483,723)(484,724)(485,725)(486,731)(487,732)(488,733)
(489,734)(490,735)(491,726)(492,727)(493,728)(494,729)(495,730)(496,736)
(497,737)(498,738)(499,739)(500,740)(501,746)(502,747)(503,748)(504,749)
(505,750)(506,741)(507,742)(508,743)(509,744)(510,745)(511,751)(512,752)
(513,753)(514,754)(515,755)(516,761)(517,762)(518,763)(519,764)(520,765)
(521,756)(522,757)(523,758)(524,759)(525,760)(526,766)(527,767)(528,768)
(529,769)(530,770)(531,776)(532,777)(533,778)(534,779)(535,780)(536,771)
(537,772)(538,773)(539,774)(540,775)(541,796)(542,797)(543,798)(544,799)
(545,800)(546,806)(547,807)(548,808)(549,809)(550,810)(551,801)(552,802)
(553,803)(554,804)(555,805)(556,781)(557,782)(558,783)(559,784)(560,785)
(561,791)(562,792)(563,793)(564,794)(565,795)(566,786)(567,787)(568,788)
(569,789)(570,790)(571,826)(572,827)(573,828)(574,829)(575,830)(576,836)
(577,837)(578,838)(579,839)(580,840)(581,831)(582,832)(583,833)(584,834)
(585,835)(586,811)(587,812)(588,813)(589,814)(590,815)(591,821)(592,822)
(593,823)(594,824)(595,825)(596,816)(597,817)(598,818)(599,819)(600,820)
(601,841)(602,842)(603,843)(604,844)(605,845)(606,851)(607,852)(608,853)
(609,854)(610,855)(611,846)(612,847)(613,848)(614,849)(615,850)(616,856)
(617,857)(618,858)(619,859)(620,860)(621,866)(622,867)(623,868)(624,869)
(625,870)(626,861)(627,862)(628,863)(629,864)(630,865)(631,871)(632,872)
(633,873)(634,874)(635,875)(636,881)(637,882)(638,883)(639,884)(640,885)
(641,876)(642,877)(643,878)(644,879)(645,880)(646,886)(647,887)(648,888)
(649,889)(650,890)(651,896)(652,897)(653,898)(654,899)(655,900)(656,891)
(657,892)(658,893)(659,894)(660,895)(661,916)(662,917)(663,918)(664,919)
(665,920)(666,926)(667,927)(668,928)(669,929)(670,930)(671,921)(672,922)
(673,923)(674,924)(675,925)(676,901)(677,902)(678,903)(679,904)(680,905)
(681,911)(682,912)(683,913)(684,914)(685,915)(686,906)(687,907)(688,908)
(689,909)(690,910)(691,946)(692,947)(693,948)(694,949)(695,950)(696,956)
(697,957)(698,958)(699,959)(700,960)(701,951)(702,952)(703,953)(704,954)
(705,955)(706,931)(707,932)(708,933)(709,934)(710,935)(711,941)(712,942)
(713,943)(714,944)(715,945)(716,936)(717,937)(718,938)(719,939)(720,940);;
s1 := ( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)( 18, 23)
( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 46, 51)
( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 81)( 62, 82)( 63, 83)( 64, 84)
( 65, 85)( 66, 76)( 67, 77)( 68, 78)( 69, 79)( 70, 80)( 71, 86)( 72, 87)
( 73, 88)( 74, 89)( 75, 90)( 91,111)( 92,112)( 93,113)( 94,114)( 95,115)
( 96,106)( 97,107)( 98,108)( 99,109)(100,110)(101,116)(102,117)(103,118)
(104,119)(105,120)(121,126)(122,127)(123,128)(124,129)(125,130)(136,141)
(137,142)(138,143)(139,144)(140,145)(151,156)(152,157)(153,158)(154,159)
(155,160)(166,171)(167,172)(168,173)(169,174)(170,175)(181,201)(182,202)
(183,203)(184,204)(185,205)(186,196)(187,197)(188,198)(189,199)(190,200)
(191,206)(192,207)(193,208)(194,209)(195,210)(211,231)(212,232)(213,233)
(214,234)(215,235)(216,226)(217,227)(218,228)(219,229)(220,230)(221,236)
(222,237)(223,238)(224,239)(225,240)(241,276)(242,277)(243,278)(244,279)
(245,280)(246,271)(247,272)(248,273)(249,274)(250,275)(251,281)(252,282)
(253,283)(254,284)(255,285)(256,291)(257,292)(258,293)(259,294)(260,295)
(261,286)(262,287)(263,288)(264,289)(265,290)(266,296)(267,297)(268,298)
(269,299)(270,300)(301,351)(302,352)(303,353)(304,354)(305,355)(306,346)
(307,347)(308,348)(309,349)(310,350)(311,356)(312,357)(313,358)(314,359)
(315,360)(316,336)(317,337)(318,338)(319,339)(320,340)(321,331)(322,332)
(323,333)(324,334)(325,335)(326,341)(327,342)(328,343)(329,344)(330,345)
(361,396)(362,397)(363,398)(364,399)(365,400)(366,391)(367,392)(368,393)
(369,394)(370,395)(371,401)(372,402)(373,403)(374,404)(375,405)(376,411)
(377,412)(378,413)(379,414)(380,415)(381,406)(382,407)(383,408)(384,409)
(385,410)(386,416)(387,417)(388,418)(389,419)(390,420)(421,471)(422,472)
(423,473)(424,474)(425,475)(426,466)(427,467)(428,468)(429,469)(430,470)
(431,476)(432,477)(433,478)(434,479)(435,480)(436,456)(437,457)(438,458)
(439,459)(440,460)(441,451)(442,452)(443,453)(444,454)(445,455)(446,461)
(447,462)(448,463)(449,464)(450,465)(481,546)(482,547)(483,548)(484,549)
(485,550)(486,541)(487,542)(488,543)(489,544)(490,545)(491,551)(492,552)
(493,553)(494,554)(495,555)(496,561)(497,562)(498,563)(499,564)(500,565)
(501,556)(502,557)(503,558)(504,559)(505,560)(506,566)(507,567)(508,568)
(509,569)(510,570)(511,576)(512,577)(513,578)(514,579)(515,580)(516,571)
(517,572)(518,573)(519,574)(520,575)(521,581)(522,582)(523,583)(524,584)
(525,585)(526,591)(527,592)(528,593)(529,594)(530,595)(531,586)(532,587)
(533,588)(534,589)(535,590)(536,596)(537,597)(538,598)(539,599)(540,600)
(601,666)(602,667)(603,668)(604,669)(605,670)(606,661)(607,662)(608,663)
(609,664)(610,665)(611,671)(612,672)(613,673)(614,674)(615,675)(616,681)
(617,682)(618,683)(619,684)(620,685)(621,676)(622,677)(623,678)(624,679)
(625,680)(626,686)(627,687)(628,688)(629,689)(630,690)(631,696)(632,697)
(633,698)(634,699)(635,700)(636,691)(637,692)(638,693)(639,694)(640,695)
(641,701)(642,702)(643,703)(644,704)(645,705)(646,711)(647,712)(648,713)
(649,714)(650,715)(651,706)(652,707)(653,708)(654,709)(655,710)(656,716)
(657,717)(658,718)(659,719)(660,720)(721,831)(722,832)(723,833)(724,834)
(725,835)(726,826)(727,827)(728,828)(729,829)(730,830)(731,836)(732,837)
(733,838)(734,839)(735,840)(736,816)(737,817)(738,818)(739,819)(740,820)
(741,811)(742,812)(743,813)(744,814)(745,815)(746,821)(747,822)(748,823)
(749,824)(750,825)(751,801)(752,802)(753,803)(754,804)(755,805)(756,796)
(757,797)(758,798)(759,799)(760,800)(761,806)(762,807)(763,808)(764,809)
(765,810)(766,786)(767,787)(768,788)(769,789)(770,790)(771,781)(772,782)
(773,783)(774,784)(775,785)(776,791)(777,792)(778,793)(779,794)(780,795)
(841,951)(842,952)(843,953)(844,954)(845,955)(846,946)(847,947)(848,948)
(849,949)(850,950)(851,956)(852,957)(853,958)(854,959)(855,960)(856,936)
(857,937)(858,938)(859,939)(860,940)(861,931)(862,932)(863,933)(864,934)
(865,935)(866,941)(867,942)(868,943)(869,944)(870,945)(871,921)(872,922)
(873,923)(874,924)(875,925)(876,916)(877,917)(878,918)(879,919)(880,920)
(881,926)(882,927)(883,928)(884,929)(885,930)(886,906)(887,907)(888,908)
(889,909)(890,910)(891,901)(892,902)(893,903)(894,904)(895,905)(896,911)
(897,912)(898,913)(899,914)(900,915);;
s2 := ( 1,601)( 2,605)( 3,604)( 4,603)( 5,602)( 6,606)( 7,610)( 8,609)
( 9,608)( 10,607)( 11,611)( 12,615)( 13,614)( 14,613)( 15,612)( 16,616)
( 17,620)( 18,619)( 19,618)( 20,617)( 21,621)( 22,625)( 23,624)( 24,623)
( 25,622)( 26,626)( 27,630)( 28,629)( 29,628)( 30,627)( 31,646)( 32,650)
( 33,649)( 34,648)( 35,647)( 36,651)( 37,655)( 38,654)( 39,653)( 40,652)
( 41,656)( 42,660)( 43,659)( 44,658)( 45,657)( 46,631)( 47,635)( 48,634)
( 49,633)( 50,632)( 51,636)( 52,640)( 53,639)( 54,638)( 55,637)( 56,641)
( 57,645)( 58,644)( 59,643)( 60,642)( 61,676)( 62,680)( 63,679)( 64,678)
( 65,677)( 66,681)( 67,685)( 68,684)( 69,683)( 70,682)( 71,686)( 72,690)
( 73,689)( 74,688)( 75,687)( 76,661)( 77,665)( 78,664)( 79,663)( 80,662)
( 81,666)( 82,670)( 83,669)( 84,668)( 85,667)( 86,671)( 87,675)( 88,674)
( 89,673)( 90,672)( 91,691)( 92,695)( 93,694)( 94,693)( 95,692)( 96,696)
( 97,700)( 98,699)( 99,698)(100,697)(101,701)(102,705)(103,704)(104,703)
(105,702)(106,706)(107,710)(108,709)(109,708)(110,707)(111,711)(112,715)
(113,714)(114,713)(115,712)(116,716)(117,720)(118,719)(119,718)(120,717)
(121,481)(122,485)(123,484)(124,483)(125,482)(126,486)(127,490)(128,489)
(129,488)(130,487)(131,491)(132,495)(133,494)(134,493)(135,492)(136,496)
(137,500)(138,499)(139,498)(140,497)(141,501)(142,505)(143,504)(144,503)
(145,502)(146,506)(147,510)(148,509)(149,508)(150,507)(151,526)(152,530)
(153,529)(154,528)(155,527)(156,531)(157,535)(158,534)(159,533)(160,532)
(161,536)(162,540)(163,539)(164,538)(165,537)(166,511)(167,515)(168,514)
(169,513)(170,512)(171,516)(172,520)(173,519)(174,518)(175,517)(176,521)
(177,525)(178,524)(179,523)(180,522)(181,556)(182,560)(183,559)(184,558)
(185,557)(186,561)(187,565)(188,564)(189,563)(190,562)(191,566)(192,570)
(193,569)(194,568)(195,567)(196,541)(197,545)(198,544)(199,543)(200,542)
(201,546)(202,550)(203,549)(204,548)(205,547)(206,551)(207,555)(208,554)
(209,553)(210,552)(211,571)(212,575)(213,574)(214,573)(215,572)(216,576)
(217,580)(218,579)(219,578)(220,577)(221,581)(222,585)(223,584)(224,583)
(225,582)(226,586)(227,590)(228,589)(229,588)(230,587)(231,591)(232,595)
(233,594)(234,593)(235,592)(236,596)(237,600)(238,599)(239,598)(240,597)
(241,841)(242,845)(243,844)(244,843)(245,842)(246,846)(247,850)(248,849)
(249,848)(250,847)(251,851)(252,855)(253,854)(254,853)(255,852)(256,856)
(257,860)(258,859)(259,858)(260,857)(261,861)(262,865)(263,864)(264,863)
(265,862)(266,866)(267,870)(268,869)(269,868)(270,867)(271,886)(272,890)
(273,889)(274,888)(275,887)(276,891)(277,895)(278,894)(279,893)(280,892)
(281,896)(282,900)(283,899)(284,898)(285,897)(286,871)(287,875)(288,874)
(289,873)(290,872)(291,876)(292,880)(293,879)(294,878)(295,877)(296,881)
(297,885)(298,884)(299,883)(300,882)(301,916)(302,920)(303,919)(304,918)
(305,917)(306,921)(307,925)(308,924)(309,923)(310,922)(311,926)(312,930)
(313,929)(314,928)(315,927)(316,901)(317,905)(318,904)(319,903)(320,902)
(321,906)(322,910)(323,909)(324,908)(325,907)(326,911)(327,915)(328,914)
(329,913)(330,912)(331,931)(332,935)(333,934)(334,933)(335,932)(336,936)
(337,940)(338,939)(339,938)(340,937)(341,941)(342,945)(343,944)(344,943)
(345,942)(346,946)(347,950)(348,949)(349,948)(350,947)(351,951)(352,955)
(353,954)(354,953)(355,952)(356,956)(357,960)(358,959)(359,958)(360,957)
(361,721)(362,725)(363,724)(364,723)(365,722)(366,726)(367,730)(368,729)
(369,728)(370,727)(371,731)(372,735)(373,734)(374,733)(375,732)(376,736)
(377,740)(378,739)(379,738)(380,737)(381,741)(382,745)(383,744)(384,743)
(385,742)(386,746)(387,750)(388,749)(389,748)(390,747)(391,766)(392,770)
(393,769)(394,768)(395,767)(396,771)(397,775)(398,774)(399,773)(400,772)
(401,776)(402,780)(403,779)(404,778)(405,777)(406,751)(407,755)(408,754)
(409,753)(410,752)(411,756)(412,760)(413,759)(414,758)(415,757)(416,761)
(417,765)(418,764)(419,763)(420,762)(421,796)(422,800)(423,799)(424,798)
(425,797)(426,801)(427,805)(428,804)(429,803)(430,802)(431,806)(432,810)
(433,809)(434,808)(435,807)(436,781)(437,785)(438,784)(439,783)(440,782)
(441,786)(442,790)(443,789)(444,788)(445,787)(446,791)(447,795)(448,794)
(449,793)(450,792)(451,811)(452,815)(453,814)(454,813)(455,812)(456,816)
(457,820)(458,819)(459,818)(460,817)(461,821)(462,825)(463,824)(464,823)
(465,822)(466,826)(467,830)(468,829)(469,828)(470,827)(471,831)(472,835)
(473,834)(474,833)(475,832)(476,836)(477,840)(478,839)(479,838)(480,837);;
s3 := ( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,127)( 7,126)( 8,130)
( 9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)( 16,137)
( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)( 24,144)
( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)( 32,151)
( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)( 40,158)
( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)( 48,170)
( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)( 56,177)
( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)( 64,184)
( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)( 72,191)
( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)( 80,198)
( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)( 88,210)
( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)( 96,217)
( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)(104,224)
(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)(112,231)
(113,235)(114,234)(115,233)(116,237)(117,236)(118,240)(119,239)(120,238)
(241,362)(242,361)(243,365)(244,364)(245,363)(246,367)(247,366)(248,370)
(249,369)(250,368)(251,372)(252,371)(253,375)(254,374)(255,373)(256,377)
(257,376)(258,380)(259,379)(260,378)(261,382)(262,381)(263,385)(264,384)
(265,383)(266,387)(267,386)(268,390)(269,389)(270,388)(271,392)(272,391)
(273,395)(274,394)(275,393)(276,397)(277,396)(278,400)(279,399)(280,398)
(281,402)(282,401)(283,405)(284,404)(285,403)(286,407)(287,406)(288,410)
(289,409)(290,408)(291,412)(292,411)(293,415)(294,414)(295,413)(296,417)
(297,416)(298,420)(299,419)(300,418)(301,422)(302,421)(303,425)(304,424)
(305,423)(306,427)(307,426)(308,430)(309,429)(310,428)(311,432)(312,431)
(313,435)(314,434)(315,433)(316,437)(317,436)(318,440)(319,439)(320,438)
(321,442)(322,441)(323,445)(324,444)(325,443)(326,447)(327,446)(328,450)
(329,449)(330,448)(331,452)(332,451)(333,455)(334,454)(335,453)(336,457)
(337,456)(338,460)(339,459)(340,458)(341,462)(342,461)(343,465)(344,464)
(345,463)(346,467)(347,466)(348,470)(349,469)(350,468)(351,472)(352,471)
(353,475)(354,474)(355,473)(356,477)(357,476)(358,480)(359,479)(360,478)
(481,602)(482,601)(483,605)(484,604)(485,603)(486,607)(487,606)(488,610)
(489,609)(490,608)(491,612)(492,611)(493,615)(494,614)(495,613)(496,617)
(497,616)(498,620)(499,619)(500,618)(501,622)(502,621)(503,625)(504,624)
(505,623)(506,627)(507,626)(508,630)(509,629)(510,628)(511,632)(512,631)
(513,635)(514,634)(515,633)(516,637)(517,636)(518,640)(519,639)(520,638)
(521,642)(522,641)(523,645)(524,644)(525,643)(526,647)(527,646)(528,650)
(529,649)(530,648)(531,652)(532,651)(533,655)(534,654)(535,653)(536,657)
(537,656)(538,660)(539,659)(540,658)(541,662)(542,661)(543,665)(544,664)
(545,663)(546,667)(547,666)(548,670)(549,669)(550,668)(551,672)(552,671)
(553,675)(554,674)(555,673)(556,677)(557,676)(558,680)(559,679)(560,678)
(561,682)(562,681)(563,685)(564,684)(565,683)(566,687)(567,686)(568,690)
(569,689)(570,688)(571,692)(572,691)(573,695)(574,694)(575,693)(576,697)
(577,696)(578,700)(579,699)(580,698)(581,702)(582,701)(583,705)(584,704)
(585,703)(586,707)(587,706)(588,710)(589,709)(590,708)(591,712)(592,711)
(593,715)(594,714)(595,713)(596,717)(597,716)(598,720)(599,719)(600,718)
(721,842)(722,841)(723,845)(724,844)(725,843)(726,847)(727,846)(728,850)
(729,849)(730,848)(731,852)(732,851)(733,855)(734,854)(735,853)(736,857)
(737,856)(738,860)(739,859)(740,858)(741,862)(742,861)(743,865)(744,864)
(745,863)(746,867)(747,866)(748,870)(749,869)(750,868)(751,872)(752,871)
(753,875)(754,874)(755,873)(756,877)(757,876)(758,880)(759,879)(760,878)
(761,882)(762,881)(763,885)(764,884)(765,883)(766,887)(767,886)(768,890)
(769,889)(770,888)(771,892)(772,891)(773,895)(774,894)(775,893)(776,897)
(777,896)(778,900)(779,899)(780,898)(781,902)(782,901)(783,905)(784,904)
(785,903)(786,907)(787,906)(788,910)(789,909)(790,908)(791,912)(792,911)
(793,915)(794,914)(795,913)(796,917)(797,916)(798,920)(799,919)(800,918)
(801,922)(802,921)(803,925)(804,924)(805,923)(806,927)(807,926)(808,930)
(809,929)(810,928)(811,932)(812,931)(813,935)(814,934)(815,933)(816,937)
(817,936)(818,940)(819,939)(820,938)(821,942)(822,941)(823,945)(824,944)
(825,943)(826,947)(827,946)(828,950)(829,949)(830,948)(831,952)(832,951)
(833,955)(834,954)(835,953)(836,957)(837,956)(838,960)(839,959)(840,958);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,241)( 2,242)( 3,243)( 4,244)( 5,245)( 6,251)( 7,252)
( 8,253)( 9,254)( 10,255)( 11,246)( 12,247)( 13,248)( 14,249)( 15,250)
( 16,256)( 17,257)( 18,258)( 19,259)( 20,260)( 21,266)( 22,267)( 23,268)
( 24,269)( 25,270)( 26,261)( 27,262)( 28,263)( 29,264)( 30,265)( 31,271)
( 32,272)( 33,273)( 34,274)( 35,275)( 36,281)( 37,282)( 38,283)( 39,284)
( 40,285)( 41,276)( 42,277)( 43,278)( 44,279)( 45,280)( 46,286)( 47,287)
( 48,288)( 49,289)( 50,290)( 51,296)( 52,297)( 53,298)( 54,299)( 55,300)
( 56,291)( 57,292)( 58,293)( 59,294)( 60,295)( 61,316)( 62,317)( 63,318)
( 64,319)( 65,320)( 66,326)( 67,327)( 68,328)( 69,329)( 70,330)( 71,321)
( 72,322)( 73,323)( 74,324)( 75,325)( 76,301)( 77,302)( 78,303)( 79,304)
( 80,305)( 81,311)( 82,312)( 83,313)( 84,314)( 85,315)( 86,306)( 87,307)
( 88,308)( 89,309)( 90,310)( 91,346)( 92,347)( 93,348)( 94,349)( 95,350)
( 96,356)( 97,357)( 98,358)( 99,359)(100,360)(101,351)(102,352)(103,353)
(104,354)(105,355)(106,331)(107,332)(108,333)(109,334)(110,335)(111,341)
(112,342)(113,343)(114,344)(115,345)(116,336)(117,337)(118,338)(119,339)
(120,340)(121,361)(122,362)(123,363)(124,364)(125,365)(126,371)(127,372)
(128,373)(129,374)(130,375)(131,366)(132,367)(133,368)(134,369)(135,370)
(136,376)(137,377)(138,378)(139,379)(140,380)(141,386)(142,387)(143,388)
(144,389)(145,390)(146,381)(147,382)(148,383)(149,384)(150,385)(151,391)
(152,392)(153,393)(154,394)(155,395)(156,401)(157,402)(158,403)(159,404)
(160,405)(161,396)(162,397)(163,398)(164,399)(165,400)(166,406)(167,407)
(168,408)(169,409)(170,410)(171,416)(172,417)(173,418)(174,419)(175,420)
(176,411)(177,412)(178,413)(179,414)(180,415)(181,436)(182,437)(183,438)
(184,439)(185,440)(186,446)(187,447)(188,448)(189,449)(190,450)(191,441)
(192,442)(193,443)(194,444)(195,445)(196,421)(197,422)(198,423)(199,424)
(200,425)(201,431)(202,432)(203,433)(204,434)(205,435)(206,426)(207,427)
(208,428)(209,429)(210,430)(211,466)(212,467)(213,468)(214,469)(215,470)
(216,476)(217,477)(218,478)(219,479)(220,480)(221,471)(222,472)(223,473)
(224,474)(225,475)(226,451)(227,452)(228,453)(229,454)(230,455)(231,461)
(232,462)(233,463)(234,464)(235,465)(236,456)(237,457)(238,458)(239,459)
(240,460)(481,721)(482,722)(483,723)(484,724)(485,725)(486,731)(487,732)
(488,733)(489,734)(490,735)(491,726)(492,727)(493,728)(494,729)(495,730)
(496,736)(497,737)(498,738)(499,739)(500,740)(501,746)(502,747)(503,748)
(504,749)(505,750)(506,741)(507,742)(508,743)(509,744)(510,745)(511,751)
(512,752)(513,753)(514,754)(515,755)(516,761)(517,762)(518,763)(519,764)
(520,765)(521,756)(522,757)(523,758)(524,759)(525,760)(526,766)(527,767)
(528,768)(529,769)(530,770)(531,776)(532,777)(533,778)(534,779)(535,780)
(536,771)(537,772)(538,773)(539,774)(540,775)(541,796)(542,797)(543,798)
(544,799)(545,800)(546,806)(547,807)(548,808)(549,809)(550,810)(551,801)
(552,802)(553,803)(554,804)(555,805)(556,781)(557,782)(558,783)(559,784)
(560,785)(561,791)(562,792)(563,793)(564,794)(565,795)(566,786)(567,787)
(568,788)(569,789)(570,790)(571,826)(572,827)(573,828)(574,829)(575,830)
(576,836)(577,837)(578,838)(579,839)(580,840)(581,831)(582,832)(583,833)
(584,834)(585,835)(586,811)(587,812)(588,813)(589,814)(590,815)(591,821)
(592,822)(593,823)(594,824)(595,825)(596,816)(597,817)(598,818)(599,819)
(600,820)(601,841)(602,842)(603,843)(604,844)(605,845)(606,851)(607,852)
(608,853)(609,854)(610,855)(611,846)(612,847)(613,848)(614,849)(615,850)
(616,856)(617,857)(618,858)(619,859)(620,860)(621,866)(622,867)(623,868)
(624,869)(625,870)(626,861)(627,862)(628,863)(629,864)(630,865)(631,871)
(632,872)(633,873)(634,874)(635,875)(636,881)(637,882)(638,883)(639,884)
(640,885)(641,876)(642,877)(643,878)(644,879)(645,880)(646,886)(647,887)
(648,888)(649,889)(650,890)(651,896)(652,897)(653,898)(654,899)(655,900)
(656,891)(657,892)(658,893)(659,894)(660,895)(661,916)(662,917)(663,918)
(664,919)(665,920)(666,926)(667,927)(668,928)(669,929)(670,930)(671,921)
(672,922)(673,923)(674,924)(675,925)(676,901)(677,902)(678,903)(679,904)
(680,905)(681,911)(682,912)(683,913)(684,914)(685,915)(686,906)(687,907)
(688,908)(689,909)(690,910)(691,946)(692,947)(693,948)(694,949)(695,950)
(696,956)(697,957)(698,958)(699,959)(700,960)(701,951)(702,952)(703,953)
(704,954)(705,955)(706,931)(707,932)(708,933)(709,934)(710,935)(711,941)
(712,942)(713,943)(714,944)(715,945)(716,936)(717,937)(718,938)(719,939)
(720,940);
s1 := Sym(960)!( 1, 6)( 2, 7)( 3, 8)( 4, 9)( 5, 10)( 16, 21)( 17, 22)
( 18, 23)( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)
( 46, 51)( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 81)( 62, 82)( 63, 83)
( 64, 84)( 65, 85)( 66, 76)( 67, 77)( 68, 78)( 69, 79)( 70, 80)( 71, 86)
( 72, 87)( 73, 88)( 74, 89)( 75, 90)( 91,111)( 92,112)( 93,113)( 94,114)
( 95,115)( 96,106)( 97,107)( 98,108)( 99,109)(100,110)(101,116)(102,117)
(103,118)(104,119)(105,120)(121,126)(122,127)(123,128)(124,129)(125,130)
(136,141)(137,142)(138,143)(139,144)(140,145)(151,156)(152,157)(153,158)
(154,159)(155,160)(166,171)(167,172)(168,173)(169,174)(170,175)(181,201)
(182,202)(183,203)(184,204)(185,205)(186,196)(187,197)(188,198)(189,199)
(190,200)(191,206)(192,207)(193,208)(194,209)(195,210)(211,231)(212,232)
(213,233)(214,234)(215,235)(216,226)(217,227)(218,228)(219,229)(220,230)
(221,236)(222,237)(223,238)(224,239)(225,240)(241,276)(242,277)(243,278)
(244,279)(245,280)(246,271)(247,272)(248,273)(249,274)(250,275)(251,281)
(252,282)(253,283)(254,284)(255,285)(256,291)(257,292)(258,293)(259,294)
(260,295)(261,286)(262,287)(263,288)(264,289)(265,290)(266,296)(267,297)
(268,298)(269,299)(270,300)(301,351)(302,352)(303,353)(304,354)(305,355)
(306,346)(307,347)(308,348)(309,349)(310,350)(311,356)(312,357)(313,358)
(314,359)(315,360)(316,336)(317,337)(318,338)(319,339)(320,340)(321,331)
(322,332)(323,333)(324,334)(325,335)(326,341)(327,342)(328,343)(329,344)
(330,345)(361,396)(362,397)(363,398)(364,399)(365,400)(366,391)(367,392)
(368,393)(369,394)(370,395)(371,401)(372,402)(373,403)(374,404)(375,405)
(376,411)(377,412)(378,413)(379,414)(380,415)(381,406)(382,407)(383,408)
(384,409)(385,410)(386,416)(387,417)(388,418)(389,419)(390,420)(421,471)
(422,472)(423,473)(424,474)(425,475)(426,466)(427,467)(428,468)(429,469)
(430,470)(431,476)(432,477)(433,478)(434,479)(435,480)(436,456)(437,457)
(438,458)(439,459)(440,460)(441,451)(442,452)(443,453)(444,454)(445,455)
(446,461)(447,462)(448,463)(449,464)(450,465)(481,546)(482,547)(483,548)
(484,549)(485,550)(486,541)(487,542)(488,543)(489,544)(490,545)(491,551)
(492,552)(493,553)(494,554)(495,555)(496,561)(497,562)(498,563)(499,564)
(500,565)(501,556)(502,557)(503,558)(504,559)(505,560)(506,566)(507,567)
(508,568)(509,569)(510,570)(511,576)(512,577)(513,578)(514,579)(515,580)
(516,571)(517,572)(518,573)(519,574)(520,575)(521,581)(522,582)(523,583)
(524,584)(525,585)(526,591)(527,592)(528,593)(529,594)(530,595)(531,586)
(532,587)(533,588)(534,589)(535,590)(536,596)(537,597)(538,598)(539,599)
(540,600)(601,666)(602,667)(603,668)(604,669)(605,670)(606,661)(607,662)
(608,663)(609,664)(610,665)(611,671)(612,672)(613,673)(614,674)(615,675)
(616,681)(617,682)(618,683)(619,684)(620,685)(621,676)(622,677)(623,678)
(624,679)(625,680)(626,686)(627,687)(628,688)(629,689)(630,690)(631,696)
(632,697)(633,698)(634,699)(635,700)(636,691)(637,692)(638,693)(639,694)
(640,695)(641,701)(642,702)(643,703)(644,704)(645,705)(646,711)(647,712)
(648,713)(649,714)(650,715)(651,706)(652,707)(653,708)(654,709)(655,710)
(656,716)(657,717)(658,718)(659,719)(660,720)(721,831)(722,832)(723,833)
(724,834)(725,835)(726,826)(727,827)(728,828)(729,829)(730,830)(731,836)
(732,837)(733,838)(734,839)(735,840)(736,816)(737,817)(738,818)(739,819)
(740,820)(741,811)(742,812)(743,813)(744,814)(745,815)(746,821)(747,822)
(748,823)(749,824)(750,825)(751,801)(752,802)(753,803)(754,804)(755,805)
(756,796)(757,797)(758,798)(759,799)(760,800)(761,806)(762,807)(763,808)
(764,809)(765,810)(766,786)(767,787)(768,788)(769,789)(770,790)(771,781)
(772,782)(773,783)(774,784)(775,785)(776,791)(777,792)(778,793)(779,794)
(780,795)(841,951)(842,952)(843,953)(844,954)(845,955)(846,946)(847,947)
(848,948)(849,949)(850,950)(851,956)(852,957)(853,958)(854,959)(855,960)
(856,936)(857,937)(858,938)(859,939)(860,940)(861,931)(862,932)(863,933)
(864,934)(865,935)(866,941)(867,942)(868,943)(869,944)(870,945)(871,921)
(872,922)(873,923)(874,924)(875,925)(876,916)(877,917)(878,918)(879,919)
(880,920)(881,926)(882,927)(883,928)(884,929)(885,930)(886,906)(887,907)
(888,908)(889,909)(890,910)(891,901)(892,902)(893,903)(894,904)(895,905)
(896,911)(897,912)(898,913)(899,914)(900,915);
s2 := Sym(960)!( 1,601)( 2,605)( 3,604)( 4,603)( 5,602)( 6,606)( 7,610)
( 8,609)( 9,608)( 10,607)( 11,611)( 12,615)( 13,614)( 14,613)( 15,612)
( 16,616)( 17,620)( 18,619)( 19,618)( 20,617)( 21,621)( 22,625)( 23,624)
( 24,623)( 25,622)( 26,626)( 27,630)( 28,629)( 29,628)( 30,627)( 31,646)
( 32,650)( 33,649)( 34,648)( 35,647)( 36,651)( 37,655)( 38,654)( 39,653)
( 40,652)( 41,656)( 42,660)( 43,659)( 44,658)( 45,657)( 46,631)( 47,635)
( 48,634)( 49,633)( 50,632)( 51,636)( 52,640)( 53,639)( 54,638)( 55,637)
( 56,641)( 57,645)( 58,644)( 59,643)( 60,642)( 61,676)( 62,680)( 63,679)
( 64,678)( 65,677)( 66,681)( 67,685)( 68,684)( 69,683)( 70,682)( 71,686)
( 72,690)( 73,689)( 74,688)( 75,687)( 76,661)( 77,665)( 78,664)( 79,663)
( 80,662)( 81,666)( 82,670)( 83,669)( 84,668)( 85,667)( 86,671)( 87,675)
( 88,674)( 89,673)( 90,672)( 91,691)( 92,695)( 93,694)( 94,693)( 95,692)
( 96,696)( 97,700)( 98,699)( 99,698)(100,697)(101,701)(102,705)(103,704)
(104,703)(105,702)(106,706)(107,710)(108,709)(109,708)(110,707)(111,711)
(112,715)(113,714)(114,713)(115,712)(116,716)(117,720)(118,719)(119,718)
(120,717)(121,481)(122,485)(123,484)(124,483)(125,482)(126,486)(127,490)
(128,489)(129,488)(130,487)(131,491)(132,495)(133,494)(134,493)(135,492)
(136,496)(137,500)(138,499)(139,498)(140,497)(141,501)(142,505)(143,504)
(144,503)(145,502)(146,506)(147,510)(148,509)(149,508)(150,507)(151,526)
(152,530)(153,529)(154,528)(155,527)(156,531)(157,535)(158,534)(159,533)
(160,532)(161,536)(162,540)(163,539)(164,538)(165,537)(166,511)(167,515)
(168,514)(169,513)(170,512)(171,516)(172,520)(173,519)(174,518)(175,517)
(176,521)(177,525)(178,524)(179,523)(180,522)(181,556)(182,560)(183,559)
(184,558)(185,557)(186,561)(187,565)(188,564)(189,563)(190,562)(191,566)
(192,570)(193,569)(194,568)(195,567)(196,541)(197,545)(198,544)(199,543)
(200,542)(201,546)(202,550)(203,549)(204,548)(205,547)(206,551)(207,555)
(208,554)(209,553)(210,552)(211,571)(212,575)(213,574)(214,573)(215,572)
(216,576)(217,580)(218,579)(219,578)(220,577)(221,581)(222,585)(223,584)
(224,583)(225,582)(226,586)(227,590)(228,589)(229,588)(230,587)(231,591)
(232,595)(233,594)(234,593)(235,592)(236,596)(237,600)(238,599)(239,598)
(240,597)(241,841)(242,845)(243,844)(244,843)(245,842)(246,846)(247,850)
(248,849)(249,848)(250,847)(251,851)(252,855)(253,854)(254,853)(255,852)
(256,856)(257,860)(258,859)(259,858)(260,857)(261,861)(262,865)(263,864)
(264,863)(265,862)(266,866)(267,870)(268,869)(269,868)(270,867)(271,886)
(272,890)(273,889)(274,888)(275,887)(276,891)(277,895)(278,894)(279,893)
(280,892)(281,896)(282,900)(283,899)(284,898)(285,897)(286,871)(287,875)
(288,874)(289,873)(290,872)(291,876)(292,880)(293,879)(294,878)(295,877)
(296,881)(297,885)(298,884)(299,883)(300,882)(301,916)(302,920)(303,919)
(304,918)(305,917)(306,921)(307,925)(308,924)(309,923)(310,922)(311,926)
(312,930)(313,929)(314,928)(315,927)(316,901)(317,905)(318,904)(319,903)
(320,902)(321,906)(322,910)(323,909)(324,908)(325,907)(326,911)(327,915)
(328,914)(329,913)(330,912)(331,931)(332,935)(333,934)(334,933)(335,932)
(336,936)(337,940)(338,939)(339,938)(340,937)(341,941)(342,945)(343,944)
(344,943)(345,942)(346,946)(347,950)(348,949)(349,948)(350,947)(351,951)
(352,955)(353,954)(354,953)(355,952)(356,956)(357,960)(358,959)(359,958)
(360,957)(361,721)(362,725)(363,724)(364,723)(365,722)(366,726)(367,730)
(368,729)(369,728)(370,727)(371,731)(372,735)(373,734)(374,733)(375,732)
(376,736)(377,740)(378,739)(379,738)(380,737)(381,741)(382,745)(383,744)
(384,743)(385,742)(386,746)(387,750)(388,749)(389,748)(390,747)(391,766)
(392,770)(393,769)(394,768)(395,767)(396,771)(397,775)(398,774)(399,773)
(400,772)(401,776)(402,780)(403,779)(404,778)(405,777)(406,751)(407,755)
(408,754)(409,753)(410,752)(411,756)(412,760)(413,759)(414,758)(415,757)
(416,761)(417,765)(418,764)(419,763)(420,762)(421,796)(422,800)(423,799)
(424,798)(425,797)(426,801)(427,805)(428,804)(429,803)(430,802)(431,806)
(432,810)(433,809)(434,808)(435,807)(436,781)(437,785)(438,784)(439,783)
(440,782)(441,786)(442,790)(443,789)(444,788)(445,787)(446,791)(447,795)
(448,794)(449,793)(450,792)(451,811)(452,815)(453,814)(454,813)(455,812)
(456,816)(457,820)(458,819)(459,818)(460,817)(461,821)(462,825)(463,824)
(464,823)(465,822)(466,826)(467,830)(468,829)(469,828)(470,827)(471,831)
(472,835)(473,834)(474,833)(475,832)(476,836)(477,840)(478,839)(479,838)
(480,837);
s3 := Sym(960)!( 1,122)( 2,121)( 3,125)( 4,124)( 5,123)( 6,127)( 7,126)
( 8,130)( 9,129)( 10,128)( 11,132)( 12,131)( 13,135)( 14,134)( 15,133)
( 16,137)( 17,136)( 18,140)( 19,139)( 20,138)( 21,142)( 22,141)( 23,145)
( 24,144)( 25,143)( 26,147)( 27,146)( 28,150)( 29,149)( 30,148)( 31,152)
( 32,151)( 33,155)( 34,154)( 35,153)( 36,157)( 37,156)( 38,160)( 39,159)
( 40,158)( 41,162)( 42,161)( 43,165)( 44,164)( 45,163)( 46,167)( 47,166)
( 48,170)( 49,169)( 50,168)( 51,172)( 52,171)( 53,175)( 54,174)( 55,173)
( 56,177)( 57,176)( 58,180)( 59,179)( 60,178)( 61,182)( 62,181)( 63,185)
( 64,184)( 65,183)( 66,187)( 67,186)( 68,190)( 69,189)( 70,188)( 71,192)
( 72,191)( 73,195)( 74,194)( 75,193)( 76,197)( 77,196)( 78,200)( 79,199)
( 80,198)( 81,202)( 82,201)( 83,205)( 84,204)( 85,203)( 86,207)( 87,206)
( 88,210)( 89,209)( 90,208)( 91,212)( 92,211)( 93,215)( 94,214)( 95,213)
( 96,217)( 97,216)( 98,220)( 99,219)(100,218)(101,222)(102,221)(103,225)
(104,224)(105,223)(106,227)(107,226)(108,230)(109,229)(110,228)(111,232)
(112,231)(113,235)(114,234)(115,233)(116,237)(117,236)(118,240)(119,239)
(120,238)(241,362)(242,361)(243,365)(244,364)(245,363)(246,367)(247,366)
(248,370)(249,369)(250,368)(251,372)(252,371)(253,375)(254,374)(255,373)
(256,377)(257,376)(258,380)(259,379)(260,378)(261,382)(262,381)(263,385)
(264,384)(265,383)(266,387)(267,386)(268,390)(269,389)(270,388)(271,392)
(272,391)(273,395)(274,394)(275,393)(276,397)(277,396)(278,400)(279,399)
(280,398)(281,402)(282,401)(283,405)(284,404)(285,403)(286,407)(287,406)
(288,410)(289,409)(290,408)(291,412)(292,411)(293,415)(294,414)(295,413)
(296,417)(297,416)(298,420)(299,419)(300,418)(301,422)(302,421)(303,425)
(304,424)(305,423)(306,427)(307,426)(308,430)(309,429)(310,428)(311,432)
(312,431)(313,435)(314,434)(315,433)(316,437)(317,436)(318,440)(319,439)
(320,438)(321,442)(322,441)(323,445)(324,444)(325,443)(326,447)(327,446)
(328,450)(329,449)(330,448)(331,452)(332,451)(333,455)(334,454)(335,453)
(336,457)(337,456)(338,460)(339,459)(340,458)(341,462)(342,461)(343,465)
(344,464)(345,463)(346,467)(347,466)(348,470)(349,469)(350,468)(351,472)
(352,471)(353,475)(354,474)(355,473)(356,477)(357,476)(358,480)(359,479)
(360,478)(481,602)(482,601)(483,605)(484,604)(485,603)(486,607)(487,606)
(488,610)(489,609)(490,608)(491,612)(492,611)(493,615)(494,614)(495,613)
(496,617)(497,616)(498,620)(499,619)(500,618)(501,622)(502,621)(503,625)
(504,624)(505,623)(506,627)(507,626)(508,630)(509,629)(510,628)(511,632)
(512,631)(513,635)(514,634)(515,633)(516,637)(517,636)(518,640)(519,639)
(520,638)(521,642)(522,641)(523,645)(524,644)(525,643)(526,647)(527,646)
(528,650)(529,649)(530,648)(531,652)(532,651)(533,655)(534,654)(535,653)
(536,657)(537,656)(538,660)(539,659)(540,658)(541,662)(542,661)(543,665)
(544,664)(545,663)(546,667)(547,666)(548,670)(549,669)(550,668)(551,672)
(552,671)(553,675)(554,674)(555,673)(556,677)(557,676)(558,680)(559,679)
(560,678)(561,682)(562,681)(563,685)(564,684)(565,683)(566,687)(567,686)
(568,690)(569,689)(570,688)(571,692)(572,691)(573,695)(574,694)(575,693)
(576,697)(577,696)(578,700)(579,699)(580,698)(581,702)(582,701)(583,705)
(584,704)(585,703)(586,707)(587,706)(588,710)(589,709)(590,708)(591,712)
(592,711)(593,715)(594,714)(595,713)(596,717)(597,716)(598,720)(599,719)
(600,718)(721,842)(722,841)(723,845)(724,844)(725,843)(726,847)(727,846)
(728,850)(729,849)(730,848)(731,852)(732,851)(733,855)(734,854)(735,853)
(736,857)(737,856)(738,860)(739,859)(740,858)(741,862)(742,861)(743,865)
(744,864)(745,863)(746,867)(747,866)(748,870)(749,869)(750,868)(751,872)
(752,871)(753,875)(754,874)(755,873)(756,877)(757,876)(758,880)(759,879)
(760,878)(761,882)(762,881)(763,885)(764,884)(765,883)(766,887)(767,886)
(768,890)(769,889)(770,888)(771,892)(772,891)(773,895)(774,894)(775,893)
(776,897)(777,896)(778,900)(779,899)(780,898)(781,902)(782,901)(783,905)
(784,904)(785,903)(786,907)(787,906)(788,910)(789,909)(790,908)(791,912)
(792,911)(793,915)(794,914)(795,913)(796,917)(797,916)(798,920)(799,919)
(800,918)(801,922)(802,921)(803,925)(804,924)(805,923)(806,927)(807,926)
(808,930)(809,929)(810,928)(811,932)(812,931)(813,935)(814,934)(815,933)
(816,937)(817,936)(818,940)(819,939)(820,938)(821,942)(822,941)(823,945)
(824,944)(825,943)(826,947)(827,946)(828,950)(829,949)(830,948)(831,952)
(832,951)(833,955)(834,954)(835,953)(836,957)(837,956)(838,960)(839,959)
(840,958);
poly := sub<Sym(960)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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