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