Polytope of Type {10,12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,12,8}*1920a
Also Known As : {{10,12|2},{12,8|2}}. if this polytope has another name.
Group : SmallGroup(1920,148891)
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, {10,6,8}*960
3-fold quotients : {10,4,8}*640a
4-fold quotients : {10,12,2}*480, {10,6,4}*480a
5-fold quotients : {2,12,8}*384a
6-fold quotients : {10,4,4}*320, {10,2,8}*320
8-fold quotients : {10,6,2}*240
10-fold quotients : {2,12,4}*192a, {2,6,8}*192
12-fold quotients : {5,2,8}*160, {10,2,4}*160, {10,4,2}*160
15-fold quotients : {2,4,8}*128a
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, {2,2,8}*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)( 61,422)( 62,421)( 63,425)( 64,424)
( 65,423)( 66,432)( 67,431)( 68,435)( 69,434)( 70,433)( 71,427)( 72,426)
( 73,430)( 74,429)( 75,428)( 76,437)( 77,436)( 78,440)( 79,439)( 80,438)
( 81,447)( 82,446)( 83,450)( 84,449)( 85,448)( 86,442)( 87,441)( 88,445)
( 89,444)( 90,443)( 91,452)( 92,451)( 93,455)( 94,454)( 95,453)( 96,462)
( 97,461)( 98,465)( 99,464)(100,463)(101,457)(102,456)(103,460)(104,459)
(105,458)(106,467)(107,466)(108,470)(109,469)(110,468)(111,477)(112,476)
(113,480)(114,479)(115,478)(116,472)(117,471)(118,475)(119,474)(120,473)
(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)(181,302)(182,301)(183,305)(184,304)
(185,303)(186,312)(187,311)(188,315)(189,314)(190,313)(191,307)(192,306)
(193,310)(194,309)(195,308)(196,317)(197,316)(198,320)(199,319)(200,318)
(201,327)(202,326)(203,330)(204,329)(205,328)(206,322)(207,321)(208,325)
(209,324)(210,323)(211,332)(212,331)(213,335)(214,334)(215,333)(216,342)
(217,341)(218,345)(219,344)(220,343)(221,337)(222,336)(223,340)(224,339)
(225,338)(226,347)(227,346)(228,350)(229,349)(230,348)(231,357)(232,356)
(233,360)(234,359)(235,358)(236,352)(237,351)(238,355)(239,354)(240,353)
(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)(541,902)(542,901)(543,905)(544,904)
(545,903)(546,912)(547,911)(548,915)(549,914)(550,913)(551,907)(552,906)
(553,910)(554,909)(555,908)(556,917)(557,916)(558,920)(559,919)(560,918)
(561,927)(562,926)(563,930)(564,929)(565,928)(566,922)(567,921)(568,925)
(569,924)(570,923)(571,932)(572,931)(573,935)(574,934)(575,933)(576,942)
(577,941)(578,945)(579,944)(580,943)(581,937)(582,936)(583,940)(584,939)
(585,938)(586,947)(587,946)(588,950)(589,949)(590,948)(591,957)(592,956)
(593,960)(594,959)(595,958)(596,952)(597,951)(598,955)(599,954)(600,953)
(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)(661,782)(662,781)(663,785)(664,784)
(665,783)(666,792)(667,791)(668,795)(669,794)(670,793)(671,787)(672,786)
(673,790)(674,789)(675,788)(676,797)(677,796)(678,800)(679,799)(680,798)
(681,807)(682,806)(683,810)(684,809)(685,808)(686,802)(687,801)(688,805)
(689,804)(690,803)(691,812)(692,811)(693,815)(694,814)(695,813)(696,822)
(697,821)(698,825)(699,824)(700,823)(701,817)(702,816)(703,820)(704,819)
(705,818)(706,827)(707,826)(708,830)(709,829)(710,828)(711,837)(712,836)
(713,840)(714,839)(715,838)(716,832)(717,831)(718,835)(719,834)(720,833);;
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)(721,816)(722,817)(723,818)(724,819)
(725,820)(726,811)(727,812)(728,813)(729,814)(730,815)(731,821)(732,822)
(733,823)(734,824)(735,825)(736,831)(737,832)(738,833)(739,834)(740,835)
(741,826)(742,827)(743,828)(744,829)(745,830)(746,836)(747,837)(748,838)
(749,839)(750,840)(751,786)(752,787)(753,788)(754,789)(755,790)(756,781)
(757,782)(758,783)(759,784)(760,785)(761,791)(762,792)(763,793)(764,794)
(765,795)(766,801)(767,802)(768,803)(769,804)(770,805)(771,796)(772,797)
(773,798)(774,799)(775,800)(776,806)(777,807)(778,808)(779,809)(780,810)
(841,936)(842,937)(843,938)(844,939)(845,940)(846,931)(847,932)(848,933)
(849,934)(850,935)(851,941)(852,942)(853,943)(854,944)(855,945)(856,951)
(857,952)(858,953)(859,954)(860,955)(861,946)(862,947)(863,948)(864,949)
(865,950)(866,956)(867,957)(868,958)(869,959)(870,960)(871,906)(872,907)
(873,908)(874,909)(875,910)(876,901)(877,902)(878,903)(879,904)(880,905)
(881,911)(882,912)(883,913)(884,914)(885,915)(886,921)(887,922)(888,923)
(889,924)(890,925)(891,916)(892,917)(893,918)(894,919)(895,920)(896,926)
(897,927)(898,928)(899,929)(900,930);;
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)( 31,511)( 32,512)
( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)( 40,520)
( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)( 48,528)
( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)( 56,536)
( 57,537)( 58,538)( 59,539)( 60,540)( 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)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)( 96,591)
( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)(104,599)
(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)(112,577)
(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)(120,585)
(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)(151,631)(152,632)
(153,633)(154,634)(155,635)(156,636)(157,637)(158,638)(159,639)(160,640)
(161,641)(162,642)(163,643)(164,644)(165,645)(166,646)(167,647)(168,648)
(169,649)(170,650)(171,651)(172,652)(173,653)(174,654)(175,655)(176,656)
(177,657)(178,658)(179,659)(180,660)(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)(211,706)(212,707)(213,708)(214,709)(215,710)(216,711)
(217,712)(218,713)(219,714)(220,715)(221,716)(222,717)(223,718)(224,719)
(225,720)(226,691)(227,692)(228,693)(229,694)(230,695)(231,696)(232,697)
(233,698)(234,699)(235,700)(236,701)(237,702)(238,703)(239,704)(240,705)
(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)(271,751)(272,752)
(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)(280,760)
(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)(288,768)
(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)(296,776)
(297,777)(298,778)(299,779)(300,780)(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)(331,826)(332,827)(333,828)(334,829)(335,830)(336,831)
(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)(344,839)
(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)(352,817)
(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)(360,825)
(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)(391,871)(392,872)
(393,873)(394,874)(395,875)(396,876)(397,877)(398,878)(399,879)(400,880)
(401,881)(402,882)(403,883)(404,884)(405,885)(406,886)(407,887)(408,888)
(409,889)(410,890)(411,891)(412,892)(413,893)(414,894)(415,895)(416,896)
(417,897)(418,898)(419,899)(420,900)(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)(451,946)(452,947)(453,948)(454,949)(455,950)(456,951)
(457,952)(458,953)(459,954)(460,955)(461,956)(462,957)(463,958)(464,959)
(465,960)(466,931)(467,932)(468,933)(469,934)(470,935)(471,936)(472,937)
(473,938)(474,939)(475,940)(476,941)(477,942)(478,943)(479,944)(480,945);;
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,
s1*s2*s3*s2*s1*s2*s3*s2, 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,
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)( 61,422)( 62,421)( 63,425)
( 64,424)( 65,423)( 66,432)( 67,431)( 68,435)( 69,434)( 70,433)( 71,427)
( 72,426)( 73,430)( 74,429)( 75,428)( 76,437)( 77,436)( 78,440)( 79,439)
( 80,438)( 81,447)( 82,446)( 83,450)( 84,449)( 85,448)( 86,442)( 87,441)
( 88,445)( 89,444)( 90,443)( 91,452)( 92,451)( 93,455)( 94,454)( 95,453)
( 96,462)( 97,461)( 98,465)( 99,464)(100,463)(101,457)(102,456)(103,460)
(104,459)(105,458)(106,467)(107,466)(108,470)(109,469)(110,468)(111,477)
(112,476)(113,480)(114,479)(115,478)(116,472)(117,471)(118,475)(119,474)
(120,473)(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)(181,302)(182,301)(183,305)
(184,304)(185,303)(186,312)(187,311)(188,315)(189,314)(190,313)(191,307)
(192,306)(193,310)(194,309)(195,308)(196,317)(197,316)(198,320)(199,319)
(200,318)(201,327)(202,326)(203,330)(204,329)(205,328)(206,322)(207,321)
(208,325)(209,324)(210,323)(211,332)(212,331)(213,335)(214,334)(215,333)
(216,342)(217,341)(218,345)(219,344)(220,343)(221,337)(222,336)(223,340)
(224,339)(225,338)(226,347)(227,346)(228,350)(229,349)(230,348)(231,357)
(232,356)(233,360)(234,359)(235,358)(236,352)(237,351)(238,355)(239,354)
(240,353)(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)(541,902)(542,901)(543,905)
(544,904)(545,903)(546,912)(547,911)(548,915)(549,914)(550,913)(551,907)
(552,906)(553,910)(554,909)(555,908)(556,917)(557,916)(558,920)(559,919)
(560,918)(561,927)(562,926)(563,930)(564,929)(565,928)(566,922)(567,921)
(568,925)(569,924)(570,923)(571,932)(572,931)(573,935)(574,934)(575,933)
(576,942)(577,941)(578,945)(579,944)(580,943)(581,937)(582,936)(583,940)
(584,939)(585,938)(586,947)(587,946)(588,950)(589,949)(590,948)(591,957)
(592,956)(593,960)(594,959)(595,958)(596,952)(597,951)(598,955)(599,954)
(600,953)(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)(661,782)(662,781)(663,785)
(664,784)(665,783)(666,792)(667,791)(668,795)(669,794)(670,793)(671,787)
(672,786)(673,790)(674,789)(675,788)(676,797)(677,796)(678,800)(679,799)
(680,798)(681,807)(682,806)(683,810)(684,809)(685,808)(686,802)(687,801)
(688,805)(689,804)(690,803)(691,812)(692,811)(693,815)(694,814)(695,813)
(696,822)(697,821)(698,825)(699,824)(700,823)(701,817)(702,816)(703,820)
(704,819)(705,818)(706,827)(707,826)(708,830)(709,829)(710,828)(711,837)
(712,836)(713,840)(714,839)(715,838)(716,832)(717,831)(718,835)(719,834)
(720,833);
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)(721,816)(722,817)(723,818)
(724,819)(725,820)(726,811)(727,812)(728,813)(729,814)(730,815)(731,821)
(732,822)(733,823)(734,824)(735,825)(736,831)(737,832)(738,833)(739,834)
(740,835)(741,826)(742,827)(743,828)(744,829)(745,830)(746,836)(747,837)
(748,838)(749,839)(750,840)(751,786)(752,787)(753,788)(754,789)(755,790)
(756,781)(757,782)(758,783)(759,784)(760,785)(761,791)(762,792)(763,793)
(764,794)(765,795)(766,801)(767,802)(768,803)(769,804)(770,805)(771,796)
(772,797)(773,798)(774,799)(775,800)(776,806)(777,807)(778,808)(779,809)
(780,810)(841,936)(842,937)(843,938)(844,939)(845,940)(846,931)(847,932)
(848,933)(849,934)(850,935)(851,941)(852,942)(853,943)(854,944)(855,945)
(856,951)(857,952)(858,953)(859,954)(860,955)(861,946)(862,947)(863,948)
(864,949)(865,950)(866,956)(867,957)(868,958)(869,959)(870,960)(871,906)
(872,907)(873,908)(874,909)(875,910)(876,901)(877,902)(878,903)(879,904)
(880,905)(881,911)(882,912)(883,913)(884,914)(885,915)(886,921)(887,922)
(888,923)(889,924)(890,925)(891,916)(892,917)(893,918)(894,919)(895,920)
(896,926)(897,927)(898,928)(899,929)(900,930);
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)( 31,511)
( 32,512)( 33,513)( 34,514)( 35,515)( 36,516)( 37,517)( 38,518)( 39,519)
( 40,520)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)
( 48,528)( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)
( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 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)( 91,586)( 92,587)( 93,588)( 94,589)( 95,590)
( 96,591)( 97,592)( 98,593)( 99,594)(100,595)(101,596)(102,597)(103,598)
(104,599)(105,600)(106,571)(107,572)(108,573)(109,574)(110,575)(111,576)
(112,577)(113,578)(114,579)(115,580)(116,581)(117,582)(118,583)(119,584)
(120,585)(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)(151,631)
(152,632)(153,633)(154,634)(155,635)(156,636)(157,637)(158,638)(159,639)
(160,640)(161,641)(162,642)(163,643)(164,644)(165,645)(166,646)(167,647)
(168,648)(169,649)(170,650)(171,651)(172,652)(173,653)(174,654)(175,655)
(176,656)(177,657)(178,658)(179,659)(180,660)(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)(211,706)(212,707)(213,708)(214,709)(215,710)
(216,711)(217,712)(218,713)(219,714)(220,715)(221,716)(222,717)(223,718)
(224,719)(225,720)(226,691)(227,692)(228,693)(229,694)(230,695)(231,696)
(232,697)(233,698)(234,699)(235,700)(236,701)(237,702)(238,703)(239,704)
(240,705)(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)(271,751)
(272,752)(273,753)(274,754)(275,755)(276,756)(277,757)(278,758)(279,759)
(280,760)(281,761)(282,762)(283,763)(284,764)(285,765)(286,766)(287,767)
(288,768)(289,769)(290,770)(291,771)(292,772)(293,773)(294,774)(295,775)
(296,776)(297,777)(298,778)(299,779)(300,780)(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)(331,826)(332,827)(333,828)(334,829)(335,830)
(336,831)(337,832)(338,833)(339,834)(340,835)(341,836)(342,837)(343,838)
(344,839)(345,840)(346,811)(347,812)(348,813)(349,814)(350,815)(351,816)
(352,817)(353,818)(354,819)(355,820)(356,821)(357,822)(358,823)(359,824)
(360,825)(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)(391,871)
(392,872)(393,873)(394,874)(395,875)(396,876)(397,877)(398,878)(399,879)
(400,880)(401,881)(402,882)(403,883)(404,884)(405,885)(406,886)(407,887)
(408,888)(409,889)(410,890)(411,891)(412,892)(413,893)(414,894)(415,895)
(416,896)(417,897)(418,898)(419,899)(420,900)(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)(451,946)(452,947)(453,948)(454,949)(455,950)
(456,951)(457,952)(458,953)(459,954)(460,955)(461,956)(462,957)(463,958)
(464,959)(465,960)(466,931)(467,932)(468,933)(469,934)(470,935)(471,936)
(472,937)(473,938)(474,939)(475,940)(476,941)(477,942)(478,943)(479,944)
(480,945);
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, s1*s2*s3*s2*s1*s2*s3*s2,
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,
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