Polytope of Type {30,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,4}*1920a
if this polytope has a name.
Group : SmallGroup(1920,239472)
Rank : 3
Schlafli Type : {30,4}
Number of vertices, edges, etc : 240, 480, 32
Order of s0s1s2 : 30
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {30,4}*960a
4-fold quotients : {30,4}*480
5-fold quotients : {6,4}*384a
8-fold quotients : {15,4}*240, {30,4}*240b, {30,4}*240c
10-fold quotients : {6,4}*192a
16-fold quotients : {15,4}*120, {30,2}*120
20-fold quotients : {6,4}*96
32-fold quotients : {15,2}*60
40-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
48-fold quotients : {10,2}*40
80-fold quotients : {3,4}*24, {6,2}*24
96-fold quotients : {5,2}*20
160-fold quotients : {3,2}*12
240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 65)( 18, 66)
( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 77)( 26, 78)
( 27, 80)( 28, 79)( 29, 73)( 30, 74)( 31, 76)( 32, 75)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 61)( 42, 62)
( 43, 64)( 44, 63)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 81,161)( 82,162)
( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,173)( 90,174)
( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,225)( 98,226)
( 99,228)(100,227)(101,229)(102,230)(103,232)(104,231)(105,237)(106,238)
(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)(113,209)(114,210)
(115,212)(116,211)(117,213)(118,214)(119,216)(120,215)(121,221)(122,222)
(123,224)(124,223)(125,217)(126,218)(127,220)(128,219)(129,193)(130,194)
(131,196)(132,195)(133,197)(134,198)(135,200)(136,199)(137,205)(138,206)
(139,208)(140,207)(141,201)(142,202)(143,204)(144,203)(145,177)(146,178)
(147,180)(148,179)(149,181)(150,182)(151,184)(152,183)(153,189)(154,190)
(155,192)(156,191)(157,185)(158,186)(159,188)(160,187)(243,244)(247,248)
(249,253)(250,254)(251,256)(252,255)(257,305)(258,306)(259,308)(260,307)
(261,309)(262,310)(263,312)(264,311)(265,317)(266,318)(267,320)(268,319)
(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)(275,292)(276,291)
(277,293)(278,294)(279,296)(280,295)(281,301)(282,302)(283,304)(284,303)
(285,297)(286,298)(287,300)(288,299)(321,401)(322,402)(323,404)(324,403)
(325,405)(326,406)(327,408)(328,407)(329,413)(330,414)(331,416)(332,415)
(333,409)(334,410)(335,412)(336,411)(337,465)(338,466)(339,468)(340,467)
(341,469)(342,470)(343,472)(344,471)(345,477)(346,478)(347,480)(348,479)
(349,473)(350,474)(351,476)(352,475)(353,449)(354,450)(355,452)(356,451)
(357,453)(358,454)(359,456)(360,455)(361,461)(362,462)(363,464)(364,463)
(365,457)(366,458)(367,460)(368,459)(369,433)(370,434)(371,436)(372,435)
(373,437)(374,438)(375,440)(376,439)(377,445)(378,446)(379,448)(380,447)
(381,441)(382,442)(383,444)(384,443)(385,417)(386,418)(387,420)(388,419)
(389,421)(390,422)(391,424)(392,423)(393,429)(394,430)(395,432)(396,431)
(397,425)(398,426)(399,428)(400,427)(483,484)(487,488)(489,493)(490,494)
(491,496)(492,495)(497,545)(498,546)(499,548)(500,547)(501,549)(502,550)
(503,552)(504,551)(505,557)(506,558)(507,560)(508,559)(509,553)(510,554)
(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)(517,533)(518,534)
(519,536)(520,535)(521,541)(522,542)(523,544)(524,543)(525,537)(526,538)
(527,540)(528,539)(561,641)(562,642)(563,644)(564,643)(565,645)(566,646)
(567,648)(568,647)(569,653)(570,654)(571,656)(572,655)(573,649)(574,650)
(575,652)(576,651)(577,705)(578,706)(579,708)(580,707)(581,709)(582,710)
(583,712)(584,711)(585,717)(586,718)(587,720)(588,719)(589,713)(590,714)
(591,716)(592,715)(593,689)(594,690)(595,692)(596,691)(597,693)(598,694)
(599,696)(600,695)(601,701)(602,702)(603,704)(604,703)(605,697)(606,698)
(607,700)(608,699)(609,673)(610,674)(611,676)(612,675)(613,677)(614,678)
(615,680)(616,679)(617,685)(618,686)(619,688)(620,687)(621,681)(622,682)
(623,684)(624,683)(625,657)(626,658)(627,660)(628,659)(629,661)(630,662)
(631,664)(632,663)(633,669)(634,670)(635,672)(636,671)(637,665)(638,666)
(639,668)(640,667)(723,724)(727,728)(729,733)(730,734)(731,736)(732,735)
(737,785)(738,786)(739,788)(740,787)(741,789)(742,790)(743,792)(744,791)
(745,797)(746,798)(747,800)(748,799)(749,793)(750,794)(751,796)(752,795)
(753,769)(754,770)(755,772)(756,771)(757,773)(758,774)(759,776)(760,775)
(761,781)(762,782)(763,784)(764,783)(765,777)(766,778)(767,780)(768,779)
(801,881)(802,882)(803,884)(804,883)(805,885)(806,886)(807,888)(808,887)
(809,893)(810,894)(811,896)(812,895)(813,889)(814,890)(815,892)(816,891)
(817,945)(818,946)(819,948)(820,947)(821,949)(822,950)(823,952)(824,951)
(825,957)(826,958)(827,960)(828,959)(829,953)(830,954)(831,956)(832,955)
(833,929)(834,930)(835,932)(836,931)(837,933)(838,934)(839,936)(840,935)
(841,941)(842,942)(843,944)(844,943)(845,937)(846,938)(847,940)(848,939)
(849,913)(850,914)(851,916)(852,915)(853,917)(854,918)(855,920)(856,919)
(857,925)(858,926)(859,928)(860,927)(861,921)(862,922)(863,924)(864,923)
(865,897)(866,898)(867,900)(868,899)(869,901)(870,902)(871,904)(872,903)
(873,909)(874,910)(875,912)(876,911)(877,905)(878,906)(879,908)(880,907);;
s1 := ( 1,337)( 2,340)( 3,339)( 4,338)( 5,352)( 6,349)( 7,350)( 8,351)
( 9,347)( 10,346)( 11,345)( 12,348)( 13,342)( 14,343)( 15,344)( 16,341)
( 17,321)( 18,324)( 19,323)( 20,322)( 21,336)( 22,333)( 23,334)( 24,335)
( 25,331)( 26,330)( 27,329)( 28,332)( 29,326)( 30,327)( 31,328)( 32,325)
( 33,385)( 34,388)( 35,387)( 36,386)( 37,400)( 38,397)( 39,398)( 40,399)
( 41,395)( 42,394)( 43,393)( 44,396)( 45,390)( 46,391)( 47,392)( 48,389)
( 49,369)( 50,372)( 51,371)( 52,370)( 53,384)( 54,381)( 55,382)( 56,383)
( 57,379)( 58,378)( 59,377)( 60,380)( 61,374)( 62,375)( 63,376)( 64,373)
( 65,353)( 66,356)( 67,355)( 68,354)( 69,368)( 70,365)( 71,366)( 72,367)
( 73,363)( 74,362)( 75,361)( 76,364)( 77,358)( 78,359)( 79,360)( 80,357)
( 81,257)( 82,260)( 83,259)( 84,258)( 85,272)( 86,269)( 87,270)( 88,271)
( 89,267)( 90,266)( 91,265)( 92,268)( 93,262)( 94,263)( 95,264)( 96,261)
( 97,241)( 98,244)( 99,243)(100,242)(101,256)(102,253)(103,254)(104,255)
(105,251)(106,250)(107,249)(108,252)(109,246)(110,247)(111,248)(112,245)
(113,305)(114,308)(115,307)(116,306)(117,320)(118,317)(119,318)(120,319)
(121,315)(122,314)(123,313)(124,316)(125,310)(126,311)(127,312)(128,309)
(129,289)(130,292)(131,291)(132,290)(133,304)(134,301)(135,302)(136,303)
(137,299)(138,298)(139,297)(140,300)(141,294)(142,295)(143,296)(144,293)
(145,273)(146,276)(147,275)(148,274)(149,288)(150,285)(151,286)(152,287)
(153,283)(154,282)(155,281)(156,284)(157,278)(158,279)(159,280)(160,277)
(161,417)(162,420)(163,419)(164,418)(165,432)(166,429)(167,430)(168,431)
(169,427)(170,426)(171,425)(172,428)(173,422)(174,423)(175,424)(176,421)
(177,401)(178,404)(179,403)(180,402)(181,416)(182,413)(183,414)(184,415)
(185,411)(186,410)(187,409)(188,412)(189,406)(190,407)(191,408)(192,405)
(193,465)(194,468)(195,467)(196,466)(197,480)(198,477)(199,478)(200,479)
(201,475)(202,474)(203,473)(204,476)(205,470)(206,471)(207,472)(208,469)
(209,449)(210,452)(211,451)(212,450)(213,464)(214,461)(215,462)(216,463)
(217,459)(218,458)(219,457)(220,460)(221,454)(222,455)(223,456)(224,453)
(225,433)(226,436)(227,435)(228,434)(229,448)(230,445)(231,446)(232,447)
(233,443)(234,442)(235,441)(236,444)(237,438)(238,439)(239,440)(240,437)
(481,817)(482,820)(483,819)(484,818)(485,832)(486,829)(487,830)(488,831)
(489,827)(490,826)(491,825)(492,828)(493,822)(494,823)(495,824)(496,821)
(497,801)(498,804)(499,803)(500,802)(501,816)(502,813)(503,814)(504,815)
(505,811)(506,810)(507,809)(508,812)(509,806)(510,807)(511,808)(512,805)
(513,865)(514,868)(515,867)(516,866)(517,880)(518,877)(519,878)(520,879)
(521,875)(522,874)(523,873)(524,876)(525,870)(526,871)(527,872)(528,869)
(529,849)(530,852)(531,851)(532,850)(533,864)(534,861)(535,862)(536,863)
(537,859)(538,858)(539,857)(540,860)(541,854)(542,855)(543,856)(544,853)
(545,833)(546,836)(547,835)(548,834)(549,848)(550,845)(551,846)(552,847)
(553,843)(554,842)(555,841)(556,844)(557,838)(558,839)(559,840)(560,837)
(561,737)(562,740)(563,739)(564,738)(565,752)(566,749)(567,750)(568,751)
(569,747)(570,746)(571,745)(572,748)(573,742)(574,743)(575,744)(576,741)
(577,721)(578,724)(579,723)(580,722)(581,736)(582,733)(583,734)(584,735)
(585,731)(586,730)(587,729)(588,732)(589,726)(590,727)(591,728)(592,725)
(593,785)(594,788)(595,787)(596,786)(597,800)(598,797)(599,798)(600,799)
(601,795)(602,794)(603,793)(604,796)(605,790)(606,791)(607,792)(608,789)
(609,769)(610,772)(611,771)(612,770)(613,784)(614,781)(615,782)(616,783)
(617,779)(618,778)(619,777)(620,780)(621,774)(622,775)(623,776)(624,773)
(625,753)(626,756)(627,755)(628,754)(629,768)(630,765)(631,766)(632,767)
(633,763)(634,762)(635,761)(636,764)(637,758)(638,759)(639,760)(640,757)
(641,897)(642,900)(643,899)(644,898)(645,912)(646,909)(647,910)(648,911)
(649,907)(650,906)(651,905)(652,908)(653,902)(654,903)(655,904)(656,901)
(657,881)(658,884)(659,883)(660,882)(661,896)(662,893)(663,894)(664,895)
(665,891)(666,890)(667,889)(668,892)(669,886)(670,887)(671,888)(672,885)
(673,945)(674,948)(675,947)(676,946)(677,960)(678,957)(679,958)(680,959)
(681,955)(682,954)(683,953)(684,956)(685,950)(686,951)(687,952)(688,949)
(689,929)(690,932)(691,931)(692,930)(693,944)(694,941)(695,942)(696,943)
(697,939)(698,938)(699,937)(700,940)(701,934)(702,935)(703,936)(704,933)
(705,913)(706,916)(707,915)(708,914)(709,928)(710,925)(711,926)(712,927)
(713,923)(714,922)(715,921)(716,924)(717,918)(718,919)(719,920)(720,917);;
s2 := ( 1,485)( 2,486)( 3,487)( 4,488)( 5,481)( 6,482)( 7,483)( 8,484)
( 9,493)( 10,494)( 11,495)( 12,496)( 13,489)( 14,490)( 15,491)( 16,492)
( 17,501)( 18,502)( 19,503)( 20,504)( 21,497)( 22,498)( 23,499)( 24,500)
( 25,509)( 26,510)( 27,511)( 28,512)( 29,505)( 30,506)( 31,507)( 32,508)
( 33,517)( 34,518)( 35,519)( 36,520)( 37,513)( 38,514)( 39,515)( 40,516)
( 41,525)( 42,526)( 43,527)( 44,528)( 45,521)( 46,522)( 47,523)( 48,524)
( 49,533)( 50,534)( 51,535)( 52,536)( 53,529)( 54,530)( 55,531)( 56,532)
( 57,541)( 58,542)( 59,543)( 60,544)( 61,537)( 62,538)( 63,539)( 64,540)
( 65,549)( 66,550)( 67,551)( 68,552)( 69,545)( 70,546)( 71,547)( 72,548)
( 73,557)( 74,558)( 75,559)( 76,560)( 77,553)( 78,554)( 79,555)( 80,556)
( 81,565)( 82,566)( 83,567)( 84,568)( 85,561)( 86,562)( 87,563)( 88,564)
( 89,573)( 90,574)( 91,575)( 92,576)( 93,569)( 94,570)( 95,571)( 96,572)
( 97,581)( 98,582)( 99,583)(100,584)(101,577)(102,578)(103,579)(104,580)
(105,589)(106,590)(107,591)(108,592)(109,585)(110,586)(111,587)(112,588)
(113,597)(114,598)(115,599)(116,600)(117,593)(118,594)(119,595)(120,596)
(121,605)(122,606)(123,607)(124,608)(125,601)(126,602)(127,603)(128,604)
(129,613)(130,614)(131,615)(132,616)(133,609)(134,610)(135,611)(136,612)
(137,621)(138,622)(139,623)(140,624)(141,617)(142,618)(143,619)(144,620)
(145,629)(146,630)(147,631)(148,632)(149,625)(150,626)(151,627)(152,628)
(153,637)(154,638)(155,639)(156,640)(157,633)(158,634)(159,635)(160,636)
(161,645)(162,646)(163,647)(164,648)(165,641)(166,642)(167,643)(168,644)
(169,653)(170,654)(171,655)(172,656)(173,649)(174,650)(175,651)(176,652)
(177,661)(178,662)(179,663)(180,664)(181,657)(182,658)(183,659)(184,660)
(185,669)(186,670)(187,671)(188,672)(189,665)(190,666)(191,667)(192,668)
(193,677)(194,678)(195,679)(196,680)(197,673)(198,674)(199,675)(200,676)
(201,685)(202,686)(203,687)(204,688)(205,681)(206,682)(207,683)(208,684)
(209,693)(210,694)(211,695)(212,696)(213,689)(214,690)(215,691)(216,692)
(217,701)(218,702)(219,703)(220,704)(221,697)(222,698)(223,699)(224,700)
(225,709)(226,710)(227,711)(228,712)(229,705)(230,706)(231,707)(232,708)
(233,717)(234,718)(235,719)(236,720)(237,713)(238,714)(239,715)(240,716)
(241,725)(242,726)(243,727)(244,728)(245,721)(246,722)(247,723)(248,724)
(249,733)(250,734)(251,735)(252,736)(253,729)(254,730)(255,731)(256,732)
(257,741)(258,742)(259,743)(260,744)(261,737)(262,738)(263,739)(264,740)
(265,749)(266,750)(267,751)(268,752)(269,745)(270,746)(271,747)(272,748)
(273,757)(274,758)(275,759)(276,760)(277,753)(278,754)(279,755)(280,756)
(281,765)(282,766)(283,767)(284,768)(285,761)(286,762)(287,763)(288,764)
(289,773)(290,774)(291,775)(292,776)(293,769)(294,770)(295,771)(296,772)
(297,781)(298,782)(299,783)(300,784)(301,777)(302,778)(303,779)(304,780)
(305,789)(306,790)(307,791)(308,792)(309,785)(310,786)(311,787)(312,788)
(313,797)(314,798)(315,799)(316,800)(317,793)(318,794)(319,795)(320,796)
(321,805)(322,806)(323,807)(324,808)(325,801)(326,802)(327,803)(328,804)
(329,813)(330,814)(331,815)(332,816)(333,809)(334,810)(335,811)(336,812)
(337,821)(338,822)(339,823)(340,824)(341,817)(342,818)(343,819)(344,820)
(345,829)(346,830)(347,831)(348,832)(349,825)(350,826)(351,827)(352,828)
(353,837)(354,838)(355,839)(356,840)(357,833)(358,834)(359,835)(360,836)
(361,845)(362,846)(363,847)(364,848)(365,841)(366,842)(367,843)(368,844)
(369,853)(370,854)(371,855)(372,856)(373,849)(374,850)(375,851)(376,852)
(377,861)(378,862)(379,863)(380,864)(381,857)(382,858)(383,859)(384,860)
(385,869)(386,870)(387,871)(388,872)(389,865)(390,866)(391,867)(392,868)
(393,877)(394,878)(395,879)(396,880)(397,873)(398,874)(399,875)(400,876)
(401,885)(402,886)(403,887)(404,888)(405,881)(406,882)(407,883)(408,884)
(409,893)(410,894)(411,895)(412,896)(413,889)(414,890)(415,891)(416,892)
(417,901)(418,902)(419,903)(420,904)(421,897)(422,898)(423,899)(424,900)
(425,909)(426,910)(427,911)(428,912)(429,905)(430,906)(431,907)(432,908)
(433,917)(434,918)(435,919)(436,920)(437,913)(438,914)(439,915)(440,916)
(441,925)(442,926)(443,927)(444,928)(445,921)(446,922)(447,923)(448,924)
(449,933)(450,934)(451,935)(452,936)(453,929)(454,930)(455,931)(456,932)
(457,941)(458,942)(459,943)(460,944)(461,937)(462,938)(463,939)(464,940)
(465,949)(466,950)(467,951)(468,952)(469,945)(470,946)(471,947)(472,948)
(473,957)(474,958)(475,959)(476,960)(477,953)(478,954)(479,955)(480,956);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 3, 4)( 7, 8)( 9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 65)
( 18, 66)( 19, 68)( 20, 67)( 21, 69)( 22, 70)( 23, 72)( 24, 71)( 25, 77)
( 26, 78)( 27, 80)( 28, 79)( 29, 73)( 30, 74)( 31, 76)( 32, 75)( 33, 49)
( 34, 50)( 35, 52)( 36, 51)( 37, 53)( 38, 54)( 39, 56)( 40, 55)( 41, 61)
( 42, 62)( 43, 64)( 44, 63)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 81,161)
( 82,162)( 83,164)( 84,163)( 85,165)( 86,166)( 87,168)( 88,167)( 89,173)
( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,225)
( 98,226)( 99,228)(100,227)(101,229)(102,230)(103,232)(104,231)(105,237)
(106,238)(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)(113,209)
(114,210)(115,212)(116,211)(117,213)(118,214)(119,216)(120,215)(121,221)
(122,222)(123,224)(124,223)(125,217)(126,218)(127,220)(128,219)(129,193)
(130,194)(131,196)(132,195)(133,197)(134,198)(135,200)(136,199)(137,205)
(138,206)(139,208)(140,207)(141,201)(142,202)(143,204)(144,203)(145,177)
(146,178)(147,180)(148,179)(149,181)(150,182)(151,184)(152,183)(153,189)
(154,190)(155,192)(156,191)(157,185)(158,186)(159,188)(160,187)(243,244)
(247,248)(249,253)(250,254)(251,256)(252,255)(257,305)(258,306)(259,308)
(260,307)(261,309)(262,310)(263,312)(264,311)(265,317)(266,318)(267,320)
(268,319)(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)(275,292)
(276,291)(277,293)(278,294)(279,296)(280,295)(281,301)(282,302)(283,304)
(284,303)(285,297)(286,298)(287,300)(288,299)(321,401)(322,402)(323,404)
(324,403)(325,405)(326,406)(327,408)(328,407)(329,413)(330,414)(331,416)
(332,415)(333,409)(334,410)(335,412)(336,411)(337,465)(338,466)(339,468)
(340,467)(341,469)(342,470)(343,472)(344,471)(345,477)(346,478)(347,480)
(348,479)(349,473)(350,474)(351,476)(352,475)(353,449)(354,450)(355,452)
(356,451)(357,453)(358,454)(359,456)(360,455)(361,461)(362,462)(363,464)
(364,463)(365,457)(366,458)(367,460)(368,459)(369,433)(370,434)(371,436)
(372,435)(373,437)(374,438)(375,440)(376,439)(377,445)(378,446)(379,448)
(380,447)(381,441)(382,442)(383,444)(384,443)(385,417)(386,418)(387,420)
(388,419)(389,421)(390,422)(391,424)(392,423)(393,429)(394,430)(395,432)
(396,431)(397,425)(398,426)(399,428)(400,427)(483,484)(487,488)(489,493)
(490,494)(491,496)(492,495)(497,545)(498,546)(499,548)(500,547)(501,549)
(502,550)(503,552)(504,551)(505,557)(506,558)(507,560)(508,559)(509,553)
(510,554)(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)(517,533)
(518,534)(519,536)(520,535)(521,541)(522,542)(523,544)(524,543)(525,537)
(526,538)(527,540)(528,539)(561,641)(562,642)(563,644)(564,643)(565,645)
(566,646)(567,648)(568,647)(569,653)(570,654)(571,656)(572,655)(573,649)
(574,650)(575,652)(576,651)(577,705)(578,706)(579,708)(580,707)(581,709)
(582,710)(583,712)(584,711)(585,717)(586,718)(587,720)(588,719)(589,713)
(590,714)(591,716)(592,715)(593,689)(594,690)(595,692)(596,691)(597,693)
(598,694)(599,696)(600,695)(601,701)(602,702)(603,704)(604,703)(605,697)
(606,698)(607,700)(608,699)(609,673)(610,674)(611,676)(612,675)(613,677)
(614,678)(615,680)(616,679)(617,685)(618,686)(619,688)(620,687)(621,681)
(622,682)(623,684)(624,683)(625,657)(626,658)(627,660)(628,659)(629,661)
(630,662)(631,664)(632,663)(633,669)(634,670)(635,672)(636,671)(637,665)
(638,666)(639,668)(640,667)(723,724)(727,728)(729,733)(730,734)(731,736)
(732,735)(737,785)(738,786)(739,788)(740,787)(741,789)(742,790)(743,792)
(744,791)(745,797)(746,798)(747,800)(748,799)(749,793)(750,794)(751,796)
(752,795)(753,769)(754,770)(755,772)(756,771)(757,773)(758,774)(759,776)
(760,775)(761,781)(762,782)(763,784)(764,783)(765,777)(766,778)(767,780)
(768,779)(801,881)(802,882)(803,884)(804,883)(805,885)(806,886)(807,888)
(808,887)(809,893)(810,894)(811,896)(812,895)(813,889)(814,890)(815,892)
(816,891)(817,945)(818,946)(819,948)(820,947)(821,949)(822,950)(823,952)
(824,951)(825,957)(826,958)(827,960)(828,959)(829,953)(830,954)(831,956)
(832,955)(833,929)(834,930)(835,932)(836,931)(837,933)(838,934)(839,936)
(840,935)(841,941)(842,942)(843,944)(844,943)(845,937)(846,938)(847,940)
(848,939)(849,913)(850,914)(851,916)(852,915)(853,917)(854,918)(855,920)
(856,919)(857,925)(858,926)(859,928)(860,927)(861,921)(862,922)(863,924)
(864,923)(865,897)(866,898)(867,900)(868,899)(869,901)(870,902)(871,904)
(872,903)(873,909)(874,910)(875,912)(876,911)(877,905)(878,906)(879,908)
(880,907);
s1 := Sym(960)!( 1,337)( 2,340)( 3,339)( 4,338)( 5,352)( 6,349)( 7,350)
( 8,351)( 9,347)( 10,346)( 11,345)( 12,348)( 13,342)( 14,343)( 15,344)
( 16,341)( 17,321)( 18,324)( 19,323)( 20,322)( 21,336)( 22,333)( 23,334)
( 24,335)( 25,331)( 26,330)( 27,329)( 28,332)( 29,326)( 30,327)( 31,328)
( 32,325)( 33,385)( 34,388)( 35,387)( 36,386)( 37,400)( 38,397)( 39,398)
( 40,399)( 41,395)( 42,394)( 43,393)( 44,396)( 45,390)( 46,391)( 47,392)
( 48,389)( 49,369)( 50,372)( 51,371)( 52,370)( 53,384)( 54,381)( 55,382)
( 56,383)( 57,379)( 58,378)( 59,377)( 60,380)( 61,374)( 62,375)( 63,376)
( 64,373)( 65,353)( 66,356)( 67,355)( 68,354)( 69,368)( 70,365)( 71,366)
( 72,367)( 73,363)( 74,362)( 75,361)( 76,364)( 77,358)( 78,359)( 79,360)
( 80,357)( 81,257)( 82,260)( 83,259)( 84,258)( 85,272)( 86,269)( 87,270)
( 88,271)( 89,267)( 90,266)( 91,265)( 92,268)( 93,262)( 94,263)( 95,264)
( 96,261)( 97,241)( 98,244)( 99,243)(100,242)(101,256)(102,253)(103,254)
(104,255)(105,251)(106,250)(107,249)(108,252)(109,246)(110,247)(111,248)
(112,245)(113,305)(114,308)(115,307)(116,306)(117,320)(118,317)(119,318)
(120,319)(121,315)(122,314)(123,313)(124,316)(125,310)(126,311)(127,312)
(128,309)(129,289)(130,292)(131,291)(132,290)(133,304)(134,301)(135,302)
(136,303)(137,299)(138,298)(139,297)(140,300)(141,294)(142,295)(143,296)
(144,293)(145,273)(146,276)(147,275)(148,274)(149,288)(150,285)(151,286)
(152,287)(153,283)(154,282)(155,281)(156,284)(157,278)(158,279)(159,280)
(160,277)(161,417)(162,420)(163,419)(164,418)(165,432)(166,429)(167,430)
(168,431)(169,427)(170,426)(171,425)(172,428)(173,422)(174,423)(175,424)
(176,421)(177,401)(178,404)(179,403)(180,402)(181,416)(182,413)(183,414)
(184,415)(185,411)(186,410)(187,409)(188,412)(189,406)(190,407)(191,408)
(192,405)(193,465)(194,468)(195,467)(196,466)(197,480)(198,477)(199,478)
(200,479)(201,475)(202,474)(203,473)(204,476)(205,470)(206,471)(207,472)
(208,469)(209,449)(210,452)(211,451)(212,450)(213,464)(214,461)(215,462)
(216,463)(217,459)(218,458)(219,457)(220,460)(221,454)(222,455)(223,456)
(224,453)(225,433)(226,436)(227,435)(228,434)(229,448)(230,445)(231,446)
(232,447)(233,443)(234,442)(235,441)(236,444)(237,438)(238,439)(239,440)
(240,437)(481,817)(482,820)(483,819)(484,818)(485,832)(486,829)(487,830)
(488,831)(489,827)(490,826)(491,825)(492,828)(493,822)(494,823)(495,824)
(496,821)(497,801)(498,804)(499,803)(500,802)(501,816)(502,813)(503,814)
(504,815)(505,811)(506,810)(507,809)(508,812)(509,806)(510,807)(511,808)
(512,805)(513,865)(514,868)(515,867)(516,866)(517,880)(518,877)(519,878)
(520,879)(521,875)(522,874)(523,873)(524,876)(525,870)(526,871)(527,872)
(528,869)(529,849)(530,852)(531,851)(532,850)(533,864)(534,861)(535,862)
(536,863)(537,859)(538,858)(539,857)(540,860)(541,854)(542,855)(543,856)
(544,853)(545,833)(546,836)(547,835)(548,834)(549,848)(550,845)(551,846)
(552,847)(553,843)(554,842)(555,841)(556,844)(557,838)(558,839)(559,840)
(560,837)(561,737)(562,740)(563,739)(564,738)(565,752)(566,749)(567,750)
(568,751)(569,747)(570,746)(571,745)(572,748)(573,742)(574,743)(575,744)
(576,741)(577,721)(578,724)(579,723)(580,722)(581,736)(582,733)(583,734)
(584,735)(585,731)(586,730)(587,729)(588,732)(589,726)(590,727)(591,728)
(592,725)(593,785)(594,788)(595,787)(596,786)(597,800)(598,797)(599,798)
(600,799)(601,795)(602,794)(603,793)(604,796)(605,790)(606,791)(607,792)
(608,789)(609,769)(610,772)(611,771)(612,770)(613,784)(614,781)(615,782)
(616,783)(617,779)(618,778)(619,777)(620,780)(621,774)(622,775)(623,776)
(624,773)(625,753)(626,756)(627,755)(628,754)(629,768)(630,765)(631,766)
(632,767)(633,763)(634,762)(635,761)(636,764)(637,758)(638,759)(639,760)
(640,757)(641,897)(642,900)(643,899)(644,898)(645,912)(646,909)(647,910)
(648,911)(649,907)(650,906)(651,905)(652,908)(653,902)(654,903)(655,904)
(656,901)(657,881)(658,884)(659,883)(660,882)(661,896)(662,893)(663,894)
(664,895)(665,891)(666,890)(667,889)(668,892)(669,886)(670,887)(671,888)
(672,885)(673,945)(674,948)(675,947)(676,946)(677,960)(678,957)(679,958)
(680,959)(681,955)(682,954)(683,953)(684,956)(685,950)(686,951)(687,952)
(688,949)(689,929)(690,932)(691,931)(692,930)(693,944)(694,941)(695,942)
(696,943)(697,939)(698,938)(699,937)(700,940)(701,934)(702,935)(703,936)
(704,933)(705,913)(706,916)(707,915)(708,914)(709,928)(710,925)(711,926)
(712,927)(713,923)(714,922)(715,921)(716,924)(717,918)(718,919)(719,920)
(720,917);
s2 := Sym(960)!( 1,485)( 2,486)( 3,487)( 4,488)( 5,481)( 6,482)( 7,483)
( 8,484)( 9,493)( 10,494)( 11,495)( 12,496)( 13,489)( 14,490)( 15,491)
( 16,492)( 17,501)( 18,502)( 19,503)( 20,504)( 21,497)( 22,498)( 23,499)
( 24,500)( 25,509)( 26,510)( 27,511)( 28,512)( 29,505)( 30,506)( 31,507)
( 32,508)( 33,517)( 34,518)( 35,519)( 36,520)( 37,513)( 38,514)( 39,515)
( 40,516)( 41,525)( 42,526)( 43,527)( 44,528)( 45,521)( 46,522)( 47,523)
( 48,524)( 49,533)( 50,534)( 51,535)( 52,536)( 53,529)( 54,530)( 55,531)
( 56,532)( 57,541)( 58,542)( 59,543)( 60,544)( 61,537)( 62,538)( 63,539)
( 64,540)( 65,549)( 66,550)( 67,551)( 68,552)( 69,545)( 70,546)( 71,547)
( 72,548)( 73,557)( 74,558)( 75,559)( 76,560)( 77,553)( 78,554)( 79,555)
( 80,556)( 81,565)( 82,566)( 83,567)( 84,568)( 85,561)( 86,562)( 87,563)
( 88,564)( 89,573)( 90,574)( 91,575)( 92,576)( 93,569)( 94,570)( 95,571)
( 96,572)( 97,581)( 98,582)( 99,583)(100,584)(101,577)(102,578)(103,579)
(104,580)(105,589)(106,590)(107,591)(108,592)(109,585)(110,586)(111,587)
(112,588)(113,597)(114,598)(115,599)(116,600)(117,593)(118,594)(119,595)
(120,596)(121,605)(122,606)(123,607)(124,608)(125,601)(126,602)(127,603)
(128,604)(129,613)(130,614)(131,615)(132,616)(133,609)(134,610)(135,611)
(136,612)(137,621)(138,622)(139,623)(140,624)(141,617)(142,618)(143,619)
(144,620)(145,629)(146,630)(147,631)(148,632)(149,625)(150,626)(151,627)
(152,628)(153,637)(154,638)(155,639)(156,640)(157,633)(158,634)(159,635)
(160,636)(161,645)(162,646)(163,647)(164,648)(165,641)(166,642)(167,643)
(168,644)(169,653)(170,654)(171,655)(172,656)(173,649)(174,650)(175,651)
(176,652)(177,661)(178,662)(179,663)(180,664)(181,657)(182,658)(183,659)
(184,660)(185,669)(186,670)(187,671)(188,672)(189,665)(190,666)(191,667)
(192,668)(193,677)(194,678)(195,679)(196,680)(197,673)(198,674)(199,675)
(200,676)(201,685)(202,686)(203,687)(204,688)(205,681)(206,682)(207,683)
(208,684)(209,693)(210,694)(211,695)(212,696)(213,689)(214,690)(215,691)
(216,692)(217,701)(218,702)(219,703)(220,704)(221,697)(222,698)(223,699)
(224,700)(225,709)(226,710)(227,711)(228,712)(229,705)(230,706)(231,707)
(232,708)(233,717)(234,718)(235,719)(236,720)(237,713)(238,714)(239,715)
(240,716)(241,725)(242,726)(243,727)(244,728)(245,721)(246,722)(247,723)
(248,724)(249,733)(250,734)(251,735)(252,736)(253,729)(254,730)(255,731)
(256,732)(257,741)(258,742)(259,743)(260,744)(261,737)(262,738)(263,739)
(264,740)(265,749)(266,750)(267,751)(268,752)(269,745)(270,746)(271,747)
(272,748)(273,757)(274,758)(275,759)(276,760)(277,753)(278,754)(279,755)
(280,756)(281,765)(282,766)(283,767)(284,768)(285,761)(286,762)(287,763)
(288,764)(289,773)(290,774)(291,775)(292,776)(293,769)(294,770)(295,771)
(296,772)(297,781)(298,782)(299,783)(300,784)(301,777)(302,778)(303,779)
(304,780)(305,789)(306,790)(307,791)(308,792)(309,785)(310,786)(311,787)
(312,788)(313,797)(314,798)(315,799)(316,800)(317,793)(318,794)(319,795)
(320,796)(321,805)(322,806)(323,807)(324,808)(325,801)(326,802)(327,803)
(328,804)(329,813)(330,814)(331,815)(332,816)(333,809)(334,810)(335,811)
(336,812)(337,821)(338,822)(339,823)(340,824)(341,817)(342,818)(343,819)
(344,820)(345,829)(346,830)(347,831)(348,832)(349,825)(350,826)(351,827)
(352,828)(353,837)(354,838)(355,839)(356,840)(357,833)(358,834)(359,835)
(360,836)(361,845)(362,846)(363,847)(364,848)(365,841)(366,842)(367,843)
(368,844)(369,853)(370,854)(371,855)(372,856)(373,849)(374,850)(375,851)
(376,852)(377,861)(378,862)(379,863)(380,864)(381,857)(382,858)(383,859)
(384,860)(385,869)(386,870)(387,871)(388,872)(389,865)(390,866)(391,867)
(392,868)(393,877)(394,878)(395,879)(396,880)(397,873)(398,874)(399,875)
(400,876)(401,885)(402,886)(403,887)(404,888)(405,881)(406,882)(407,883)
(408,884)(409,893)(410,894)(411,895)(412,896)(413,889)(414,890)(415,891)
(416,892)(417,901)(418,902)(419,903)(420,904)(421,897)(422,898)(423,899)
(424,900)(425,909)(426,910)(427,911)(428,912)(429,905)(430,906)(431,907)
(432,908)(433,917)(434,918)(435,919)(436,920)(437,913)(438,914)(439,915)
(440,916)(441,925)(442,926)(443,927)(444,928)(445,921)(446,922)(447,923)
(448,924)(449,933)(450,934)(451,935)(452,936)(453,929)(454,930)(455,931)
(456,932)(457,941)(458,942)(459,943)(460,944)(461,937)(462,938)(463,939)
(464,940)(465,949)(466,950)(467,951)(468,952)(469,945)(470,946)(471,947)
(472,948)(473,957)(474,958)(475,959)(476,960)(477,953)(478,954)(479,955)
(480,956);
poly := sub<Sym(960)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope