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