Polytope of Type {30,32}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,32}*1920
Also Known As : {30,32|2}. if this polytope has another name.
Group : SmallGroup(1920,44837)
Rank : 3
Schlafli Type : {30,32}
Number of vertices, edges, etc : 30, 480, 32
Order of s0s1s2 : 480
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
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 : {30,16}*960
3-fold quotients : {10,32}*640
4-fold quotients : {30,8}*480
5-fold quotients : {6,32}*384
6-fold quotients : {10,16}*320
8-fold quotients : {30,4}*240a
10-fold quotients : {6,16}*192
12-fold quotients : {10,8}*160
15-fold quotients : {2,32}*128
16-fold quotients : {30,2}*120
20-fold quotients : {6,8}*96
24-fold quotients : {10,4}*80
30-fold quotients : {2,16}*64
32-fold quotients : {15,2}*60
40-fold quotients : {6,4}*48a
48-fold quotients : {10,2}*40
60-fold quotients : {2,8}*32
80-fold quotients : {6,2}*24
96-fold quotients : {5,2}*20
120-fold quotients : {2,4}*16
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 := ( 1,241)( 2,245)( 3,244)( 4,243)( 5,242)( 6,251)( 7,255)( 8,254)
( 9,253)( 10,252)( 11,246)( 12,250)( 13,249)( 14,248)( 15,247)( 16,256)
( 17,260)( 18,259)( 19,258)( 20,257)( 21,266)( 22,270)( 23,269)( 24,268)
( 25,267)( 26,261)( 27,265)( 28,264)( 29,263)( 30,262)( 31,271)( 32,275)
( 33,274)( 34,273)( 35,272)( 36,281)( 37,285)( 38,284)( 39,283)( 40,282)
( 41,276)( 42,280)( 43,279)( 44,278)( 45,277)( 46,286)( 47,290)( 48,289)
( 49,288)( 50,287)( 51,296)( 52,300)( 53,299)( 54,298)( 55,297)( 56,291)
( 57,295)( 58,294)( 59,293)( 60,292)( 61,301)( 62,305)( 63,304)( 64,303)
( 65,302)( 66,311)( 67,315)( 68,314)( 69,313)( 70,312)( 71,306)( 72,310)
( 73,309)( 74,308)( 75,307)( 76,316)( 77,320)( 78,319)( 79,318)( 80,317)
( 81,326)( 82,330)( 83,329)( 84,328)( 85,327)( 86,321)( 87,325)( 88,324)
( 89,323)( 90,322)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)( 96,341)
( 97,345)( 98,344)( 99,343)(100,342)(101,336)(102,340)(103,339)(104,338)
(105,337)(106,346)(107,350)(108,349)(109,348)(110,347)(111,356)(112,360)
(113,359)(114,358)(115,357)(116,351)(117,355)(118,354)(119,353)(120,352)
(121,361)(122,365)(123,364)(124,363)(125,362)(126,371)(127,375)(128,374)
(129,373)(130,372)(131,366)(132,370)(133,369)(134,368)(135,367)(136,376)
(137,380)(138,379)(139,378)(140,377)(141,386)(142,390)(143,389)(144,388)
(145,387)(146,381)(147,385)(148,384)(149,383)(150,382)(151,391)(152,395)
(153,394)(154,393)(155,392)(156,401)(157,405)(158,404)(159,403)(160,402)
(161,396)(162,400)(163,399)(164,398)(165,397)(166,406)(167,410)(168,409)
(169,408)(170,407)(171,416)(172,420)(173,419)(174,418)(175,417)(176,411)
(177,415)(178,414)(179,413)(180,412)(181,421)(182,425)(183,424)(184,423)
(185,422)(186,431)(187,435)(188,434)(189,433)(190,432)(191,426)(192,430)
(193,429)(194,428)(195,427)(196,436)(197,440)(198,439)(199,438)(200,437)
(201,446)(202,450)(203,449)(204,448)(205,447)(206,441)(207,445)(208,444)
(209,443)(210,442)(211,451)(212,455)(213,454)(214,453)(215,452)(216,461)
(217,465)(218,464)(219,463)(220,462)(221,456)(222,460)(223,459)(224,458)
(225,457)(226,466)(227,470)(228,469)(229,468)(230,467)(231,476)(232,480)
(233,479)(234,478)(235,477)(236,471)(237,475)(238,474)(239,473)(240,472)
(481,721)(482,725)(483,724)(484,723)(485,722)(486,731)(487,735)(488,734)
(489,733)(490,732)(491,726)(492,730)(493,729)(494,728)(495,727)(496,736)
(497,740)(498,739)(499,738)(500,737)(501,746)(502,750)(503,749)(504,748)
(505,747)(506,741)(507,745)(508,744)(509,743)(510,742)(511,751)(512,755)
(513,754)(514,753)(515,752)(516,761)(517,765)(518,764)(519,763)(520,762)
(521,756)(522,760)(523,759)(524,758)(525,757)(526,766)(527,770)(528,769)
(529,768)(530,767)(531,776)(532,780)(533,779)(534,778)(535,777)(536,771)
(537,775)(538,774)(539,773)(540,772)(541,781)(542,785)(543,784)(544,783)
(545,782)(546,791)(547,795)(548,794)(549,793)(550,792)(551,786)(552,790)
(553,789)(554,788)(555,787)(556,796)(557,800)(558,799)(559,798)(560,797)
(561,806)(562,810)(563,809)(564,808)(565,807)(566,801)(567,805)(568,804)
(569,803)(570,802)(571,811)(572,815)(573,814)(574,813)(575,812)(576,821)
(577,825)(578,824)(579,823)(580,822)(581,816)(582,820)(583,819)(584,818)
(585,817)(586,826)(587,830)(588,829)(589,828)(590,827)(591,836)(592,840)
(593,839)(594,838)(595,837)(596,831)(597,835)(598,834)(599,833)(600,832)
(601,841)(602,845)(603,844)(604,843)(605,842)(606,851)(607,855)(608,854)
(609,853)(610,852)(611,846)(612,850)(613,849)(614,848)(615,847)(616,856)
(617,860)(618,859)(619,858)(620,857)(621,866)(622,870)(623,869)(624,868)
(625,867)(626,861)(627,865)(628,864)(629,863)(630,862)(631,871)(632,875)
(633,874)(634,873)(635,872)(636,881)(637,885)(638,884)(639,883)(640,882)
(641,876)(642,880)(643,879)(644,878)(645,877)(646,886)(647,890)(648,889)
(649,888)(650,887)(651,896)(652,900)(653,899)(654,898)(655,897)(656,891)
(657,895)(658,894)(659,893)(660,892)(661,901)(662,905)(663,904)(664,903)
(665,902)(666,911)(667,915)(668,914)(669,913)(670,912)(671,906)(672,910)
(673,909)(674,908)(675,907)(676,916)(677,920)(678,919)(679,918)(680,917)
(681,926)(682,930)(683,929)(684,928)(685,927)(686,921)(687,925)(688,924)
(689,923)(690,922)(691,931)(692,935)(693,934)(694,933)(695,932)(696,941)
(697,945)(698,944)(699,943)(700,942)(701,936)(702,940)(703,939)(704,938)
(705,937)(706,946)(707,950)(708,949)(709,948)(710,947)(711,956)(712,960)
(713,959)(714,958)(715,957)(716,951)(717,955)(718,954)(719,953)(720,952);;
s1 := ( 1,247)( 2,246)( 3,250)( 4,249)( 5,248)( 6,242)( 7,241)( 8,245)
( 9,244)( 10,243)( 11,252)( 12,251)( 13,255)( 14,254)( 15,253)( 16,262)
( 17,261)( 18,265)( 19,264)( 20,263)( 21,257)( 22,256)( 23,260)( 24,259)
( 25,258)( 26,267)( 27,266)( 28,270)( 29,269)( 30,268)( 31,292)( 32,291)
( 33,295)( 34,294)( 35,293)( 36,287)( 37,286)( 38,290)( 39,289)( 40,288)
( 41,297)( 42,296)( 43,300)( 44,299)( 45,298)( 46,277)( 47,276)( 48,280)
( 49,279)( 50,278)( 51,272)( 52,271)( 53,275)( 54,274)( 55,273)( 56,282)
( 57,281)( 58,285)( 59,284)( 60,283)( 61,337)( 62,336)( 63,340)( 64,339)
( 65,338)( 66,332)( 67,331)( 68,335)( 69,334)( 70,333)( 71,342)( 72,341)
( 73,345)( 74,344)( 75,343)( 76,352)( 77,351)( 78,355)( 79,354)( 80,353)
( 81,347)( 82,346)( 83,350)( 84,349)( 85,348)( 86,357)( 87,356)( 88,360)
( 89,359)( 90,358)( 91,307)( 92,306)( 93,310)( 94,309)( 95,308)( 96,302)
( 97,301)( 98,305)( 99,304)(100,303)(101,312)(102,311)(103,315)(104,314)
(105,313)(106,322)(107,321)(108,325)(109,324)(110,323)(111,317)(112,316)
(113,320)(114,319)(115,318)(116,327)(117,326)(118,330)(119,329)(120,328)
(121,427)(122,426)(123,430)(124,429)(125,428)(126,422)(127,421)(128,425)
(129,424)(130,423)(131,432)(132,431)(133,435)(134,434)(135,433)(136,442)
(137,441)(138,445)(139,444)(140,443)(141,437)(142,436)(143,440)(144,439)
(145,438)(146,447)(147,446)(148,450)(149,449)(150,448)(151,472)(152,471)
(153,475)(154,474)(155,473)(156,467)(157,466)(158,470)(159,469)(160,468)
(161,477)(162,476)(163,480)(164,479)(165,478)(166,457)(167,456)(168,460)
(169,459)(170,458)(171,452)(172,451)(173,455)(174,454)(175,453)(176,462)
(177,461)(178,465)(179,464)(180,463)(181,367)(182,366)(183,370)(184,369)
(185,368)(186,362)(187,361)(188,365)(189,364)(190,363)(191,372)(192,371)
(193,375)(194,374)(195,373)(196,382)(197,381)(198,385)(199,384)(200,383)
(201,377)(202,376)(203,380)(204,379)(205,378)(206,387)(207,386)(208,390)
(209,389)(210,388)(211,412)(212,411)(213,415)(214,414)(215,413)(216,407)
(217,406)(218,410)(219,409)(220,408)(221,417)(222,416)(223,420)(224,419)
(225,418)(226,397)(227,396)(228,400)(229,399)(230,398)(231,392)(232,391)
(233,395)(234,394)(235,393)(236,402)(237,401)(238,405)(239,404)(240,403)
(481,847)(482,846)(483,850)(484,849)(485,848)(486,842)(487,841)(488,845)
(489,844)(490,843)(491,852)(492,851)(493,855)(494,854)(495,853)(496,862)
(497,861)(498,865)(499,864)(500,863)(501,857)(502,856)(503,860)(504,859)
(505,858)(506,867)(507,866)(508,870)(509,869)(510,868)(511,892)(512,891)
(513,895)(514,894)(515,893)(516,887)(517,886)(518,890)(519,889)(520,888)
(521,897)(522,896)(523,900)(524,899)(525,898)(526,877)(527,876)(528,880)
(529,879)(530,878)(531,872)(532,871)(533,875)(534,874)(535,873)(536,882)
(537,881)(538,885)(539,884)(540,883)(541,937)(542,936)(543,940)(544,939)
(545,938)(546,932)(547,931)(548,935)(549,934)(550,933)(551,942)(552,941)
(553,945)(554,944)(555,943)(556,952)(557,951)(558,955)(559,954)(560,953)
(561,947)(562,946)(563,950)(564,949)(565,948)(566,957)(567,956)(568,960)
(569,959)(570,958)(571,907)(572,906)(573,910)(574,909)(575,908)(576,902)
(577,901)(578,905)(579,904)(580,903)(581,912)(582,911)(583,915)(584,914)
(585,913)(586,922)(587,921)(588,925)(589,924)(590,923)(591,917)(592,916)
(593,920)(594,919)(595,918)(596,927)(597,926)(598,930)(599,929)(600,928)
(601,727)(602,726)(603,730)(604,729)(605,728)(606,722)(607,721)(608,725)
(609,724)(610,723)(611,732)(612,731)(613,735)(614,734)(615,733)(616,742)
(617,741)(618,745)(619,744)(620,743)(621,737)(622,736)(623,740)(624,739)
(625,738)(626,747)(627,746)(628,750)(629,749)(630,748)(631,772)(632,771)
(633,775)(634,774)(635,773)(636,767)(637,766)(638,770)(639,769)(640,768)
(641,777)(642,776)(643,780)(644,779)(645,778)(646,757)(647,756)(648,760)
(649,759)(650,758)(651,752)(652,751)(653,755)(654,754)(655,753)(656,762)
(657,761)(658,765)(659,764)(660,763)(661,817)(662,816)(663,820)(664,819)
(665,818)(666,812)(667,811)(668,815)(669,814)(670,813)(671,822)(672,821)
(673,825)(674,824)(675,823)(676,832)(677,831)(678,835)(679,834)(680,833)
(681,827)(682,826)(683,830)(684,829)(685,828)(686,837)(687,836)(688,840)
(689,839)(690,838)(691,787)(692,786)(693,790)(694,789)(695,788)(696,782)
(697,781)(698,785)(699,784)(700,783)(701,792)(702,791)(703,795)(704,794)
(705,793)(706,802)(707,801)(708,805)(709,804)(710,803)(711,797)(712,796)
(713,800)(714,799)(715,798)(716,807)(717,806)(718,810)(719,809)(720,808);;
s2 := ( 1,481)( 2,482)( 3,483)( 4,484)( 5,485)( 6,486)( 7,487)( 8,488)
( 9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)
( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)( 24,504)
( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,526)( 32,527)
( 33,528)( 34,529)( 35,530)( 36,531)( 37,532)( 38,533)( 39,534)( 40,535)
( 41,536)( 42,537)( 43,538)( 44,539)( 45,540)( 46,511)( 47,512)( 48,513)
( 49,514)( 50,515)( 51,516)( 52,517)( 53,518)( 54,519)( 55,520)( 56,521)
( 57,522)( 58,523)( 59,524)( 60,525)( 61,571)( 62,572)( 63,573)( 64,574)
( 65,575)( 66,576)( 67,577)( 68,578)( 69,579)( 70,580)( 71,581)( 72,582)
( 73,583)( 74,584)( 75,585)( 76,586)( 77,587)( 78,588)( 79,589)( 80,590)
( 81,591)( 82,592)( 83,593)( 84,594)( 85,595)( 86,596)( 87,597)( 88,598)
( 89,599)( 90,600)( 91,541)( 92,542)( 93,543)( 94,544)( 95,545)( 96,546)
( 97,547)( 98,548)( 99,549)(100,550)(101,551)(102,552)(103,553)(104,554)
(105,555)(106,556)(107,557)(108,558)(109,559)(110,560)(111,561)(112,562)
(113,563)(114,564)(115,565)(116,566)(117,567)(118,568)(119,569)(120,570)
(121,661)(122,662)(123,663)(124,664)(125,665)(126,666)(127,667)(128,668)
(129,669)(130,670)(131,671)(132,672)(133,673)(134,674)(135,675)(136,676)
(137,677)(138,678)(139,679)(140,680)(141,681)(142,682)(143,683)(144,684)
(145,685)(146,686)(147,687)(148,688)(149,689)(150,690)(151,706)(152,707)
(153,708)(154,709)(155,710)(156,711)(157,712)(158,713)(159,714)(160,715)
(161,716)(162,717)(163,718)(164,719)(165,720)(166,691)(167,692)(168,693)
(169,694)(170,695)(171,696)(172,697)(173,698)(174,699)(175,700)(176,701)
(177,702)(178,703)(179,704)(180,705)(181,601)(182,602)(183,603)(184,604)
(185,605)(186,606)(187,607)(188,608)(189,609)(190,610)(191,611)(192,612)
(193,613)(194,614)(195,615)(196,616)(197,617)(198,618)(199,619)(200,620)
(201,621)(202,622)(203,623)(204,624)(205,625)(206,626)(207,627)(208,628)
(209,629)(210,630)(211,646)(212,647)(213,648)(214,649)(215,650)(216,651)
(217,652)(218,653)(219,654)(220,655)(221,656)(222,657)(223,658)(224,659)
(225,660)(226,631)(227,632)(228,633)(229,634)(230,635)(231,636)(232,637)
(233,638)(234,639)(235,640)(236,641)(237,642)(238,643)(239,644)(240,645)
(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)(248,728)
(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)(256,736)
(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)(264,744)
(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,766)(272,767)
(273,768)(274,769)(275,770)(276,771)(277,772)(278,773)(279,774)(280,775)
(281,776)(282,777)(283,778)(284,779)(285,780)(286,751)(287,752)(288,753)
(289,754)(290,755)(291,756)(292,757)(293,758)(294,759)(295,760)(296,761)
(297,762)(298,763)(299,764)(300,765)(301,811)(302,812)(303,813)(304,814)
(305,815)(306,816)(307,817)(308,818)(309,819)(310,820)(311,821)(312,822)
(313,823)(314,824)(315,825)(316,826)(317,827)(318,828)(319,829)(320,830)
(321,831)(322,832)(323,833)(324,834)(325,835)(326,836)(327,837)(328,838)
(329,839)(330,840)(331,781)(332,782)(333,783)(334,784)(335,785)(336,786)
(337,787)(338,788)(339,789)(340,790)(341,791)(342,792)(343,793)(344,794)
(345,795)(346,796)(347,797)(348,798)(349,799)(350,800)(351,801)(352,802)
(353,803)(354,804)(355,805)(356,806)(357,807)(358,808)(359,809)(360,810)
(361,901)(362,902)(363,903)(364,904)(365,905)(366,906)(367,907)(368,908)
(369,909)(370,910)(371,911)(372,912)(373,913)(374,914)(375,915)(376,916)
(377,917)(378,918)(379,919)(380,920)(381,921)(382,922)(383,923)(384,924)
(385,925)(386,926)(387,927)(388,928)(389,929)(390,930)(391,946)(392,947)
(393,948)(394,949)(395,950)(396,951)(397,952)(398,953)(399,954)(400,955)
(401,956)(402,957)(403,958)(404,959)(405,960)(406,931)(407,932)(408,933)
(409,934)(410,935)(411,936)(412,937)(413,938)(414,939)(415,940)(416,941)
(417,942)(418,943)(419,944)(420,945)(421,841)(422,842)(423,843)(424,844)
(425,845)(426,846)(427,847)(428,848)(429,849)(430,850)(431,851)(432,852)
(433,853)(434,854)(435,855)(436,856)(437,857)(438,858)(439,859)(440,860)
(441,861)(442,862)(443,863)(444,864)(445,865)(446,866)(447,867)(448,868)
(449,869)(450,870)(451,886)(452,887)(453,888)(454,889)(455,890)(456,891)
(457,892)(458,893)(459,894)(460,895)(461,896)(462,897)(463,898)(464,899)
(465,900)(466,871)(467,872)(468,873)(469,874)(470,875)(471,876)(472,877)
(473,878)(474,879)(475,880)(476,881)(477,882)(478,883)(479,884)(480,885);;
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*s2*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,
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*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,241)( 2,245)( 3,244)( 4,243)( 5,242)( 6,251)( 7,255)
( 8,254)( 9,253)( 10,252)( 11,246)( 12,250)( 13,249)( 14,248)( 15,247)
( 16,256)( 17,260)( 18,259)( 19,258)( 20,257)( 21,266)( 22,270)( 23,269)
( 24,268)( 25,267)( 26,261)( 27,265)( 28,264)( 29,263)( 30,262)( 31,271)
( 32,275)( 33,274)( 34,273)( 35,272)( 36,281)( 37,285)( 38,284)( 39,283)
( 40,282)( 41,276)( 42,280)( 43,279)( 44,278)( 45,277)( 46,286)( 47,290)
( 48,289)( 49,288)( 50,287)( 51,296)( 52,300)( 53,299)( 54,298)( 55,297)
( 56,291)( 57,295)( 58,294)( 59,293)( 60,292)( 61,301)( 62,305)( 63,304)
( 64,303)( 65,302)( 66,311)( 67,315)( 68,314)( 69,313)( 70,312)( 71,306)
( 72,310)( 73,309)( 74,308)( 75,307)( 76,316)( 77,320)( 78,319)( 79,318)
( 80,317)( 81,326)( 82,330)( 83,329)( 84,328)( 85,327)( 86,321)( 87,325)
( 88,324)( 89,323)( 90,322)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)
( 96,341)( 97,345)( 98,344)( 99,343)(100,342)(101,336)(102,340)(103,339)
(104,338)(105,337)(106,346)(107,350)(108,349)(109,348)(110,347)(111,356)
(112,360)(113,359)(114,358)(115,357)(116,351)(117,355)(118,354)(119,353)
(120,352)(121,361)(122,365)(123,364)(124,363)(125,362)(126,371)(127,375)
(128,374)(129,373)(130,372)(131,366)(132,370)(133,369)(134,368)(135,367)
(136,376)(137,380)(138,379)(139,378)(140,377)(141,386)(142,390)(143,389)
(144,388)(145,387)(146,381)(147,385)(148,384)(149,383)(150,382)(151,391)
(152,395)(153,394)(154,393)(155,392)(156,401)(157,405)(158,404)(159,403)
(160,402)(161,396)(162,400)(163,399)(164,398)(165,397)(166,406)(167,410)
(168,409)(169,408)(170,407)(171,416)(172,420)(173,419)(174,418)(175,417)
(176,411)(177,415)(178,414)(179,413)(180,412)(181,421)(182,425)(183,424)
(184,423)(185,422)(186,431)(187,435)(188,434)(189,433)(190,432)(191,426)
(192,430)(193,429)(194,428)(195,427)(196,436)(197,440)(198,439)(199,438)
(200,437)(201,446)(202,450)(203,449)(204,448)(205,447)(206,441)(207,445)
(208,444)(209,443)(210,442)(211,451)(212,455)(213,454)(214,453)(215,452)
(216,461)(217,465)(218,464)(219,463)(220,462)(221,456)(222,460)(223,459)
(224,458)(225,457)(226,466)(227,470)(228,469)(229,468)(230,467)(231,476)
(232,480)(233,479)(234,478)(235,477)(236,471)(237,475)(238,474)(239,473)
(240,472)(481,721)(482,725)(483,724)(484,723)(485,722)(486,731)(487,735)
(488,734)(489,733)(490,732)(491,726)(492,730)(493,729)(494,728)(495,727)
(496,736)(497,740)(498,739)(499,738)(500,737)(501,746)(502,750)(503,749)
(504,748)(505,747)(506,741)(507,745)(508,744)(509,743)(510,742)(511,751)
(512,755)(513,754)(514,753)(515,752)(516,761)(517,765)(518,764)(519,763)
(520,762)(521,756)(522,760)(523,759)(524,758)(525,757)(526,766)(527,770)
(528,769)(529,768)(530,767)(531,776)(532,780)(533,779)(534,778)(535,777)
(536,771)(537,775)(538,774)(539,773)(540,772)(541,781)(542,785)(543,784)
(544,783)(545,782)(546,791)(547,795)(548,794)(549,793)(550,792)(551,786)
(552,790)(553,789)(554,788)(555,787)(556,796)(557,800)(558,799)(559,798)
(560,797)(561,806)(562,810)(563,809)(564,808)(565,807)(566,801)(567,805)
(568,804)(569,803)(570,802)(571,811)(572,815)(573,814)(574,813)(575,812)
(576,821)(577,825)(578,824)(579,823)(580,822)(581,816)(582,820)(583,819)
(584,818)(585,817)(586,826)(587,830)(588,829)(589,828)(590,827)(591,836)
(592,840)(593,839)(594,838)(595,837)(596,831)(597,835)(598,834)(599,833)
(600,832)(601,841)(602,845)(603,844)(604,843)(605,842)(606,851)(607,855)
(608,854)(609,853)(610,852)(611,846)(612,850)(613,849)(614,848)(615,847)
(616,856)(617,860)(618,859)(619,858)(620,857)(621,866)(622,870)(623,869)
(624,868)(625,867)(626,861)(627,865)(628,864)(629,863)(630,862)(631,871)
(632,875)(633,874)(634,873)(635,872)(636,881)(637,885)(638,884)(639,883)
(640,882)(641,876)(642,880)(643,879)(644,878)(645,877)(646,886)(647,890)
(648,889)(649,888)(650,887)(651,896)(652,900)(653,899)(654,898)(655,897)
(656,891)(657,895)(658,894)(659,893)(660,892)(661,901)(662,905)(663,904)
(664,903)(665,902)(666,911)(667,915)(668,914)(669,913)(670,912)(671,906)
(672,910)(673,909)(674,908)(675,907)(676,916)(677,920)(678,919)(679,918)
(680,917)(681,926)(682,930)(683,929)(684,928)(685,927)(686,921)(687,925)
(688,924)(689,923)(690,922)(691,931)(692,935)(693,934)(694,933)(695,932)
(696,941)(697,945)(698,944)(699,943)(700,942)(701,936)(702,940)(703,939)
(704,938)(705,937)(706,946)(707,950)(708,949)(709,948)(710,947)(711,956)
(712,960)(713,959)(714,958)(715,957)(716,951)(717,955)(718,954)(719,953)
(720,952);
s1 := Sym(960)!( 1,247)( 2,246)( 3,250)( 4,249)( 5,248)( 6,242)( 7,241)
( 8,245)( 9,244)( 10,243)( 11,252)( 12,251)( 13,255)( 14,254)( 15,253)
( 16,262)( 17,261)( 18,265)( 19,264)( 20,263)( 21,257)( 22,256)( 23,260)
( 24,259)( 25,258)( 26,267)( 27,266)( 28,270)( 29,269)( 30,268)( 31,292)
( 32,291)( 33,295)( 34,294)( 35,293)( 36,287)( 37,286)( 38,290)( 39,289)
( 40,288)( 41,297)( 42,296)( 43,300)( 44,299)( 45,298)( 46,277)( 47,276)
( 48,280)( 49,279)( 50,278)( 51,272)( 52,271)( 53,275)( 54,274)( 55,273)
( 56,282)( 57,281)( 58,285)( 59,284)( 60,283)( 61,337)( 62,336)( 63,340)
( 64,339)( 65,338)( 66,332)( 67,331)( 68,335)( 69,334)( 70,333)( 71,342)
( 72,341)( 73,345)( 74,344)( 75,343)( 76,352)( 77,351)( 78,355)( 79,354)
( 80,353)( 81,347)( 82,346)( 83,350)( 84,349)( 85,348)( 86,357)( 87,356)
( 88,360)( 89,359)( 90,358)( 91,307)( 92,306)( 93,310)( 94,309)( 95,308)
( 96,302)( 97,301)( 98,305)( 99,304)(100,303)(101,312)(102,311)(103,315)
(104,314)(105,313)(106,322)(107,321)(108,325)(109,324)(110,323)(111,317)
(112,316)(113,320)(114,319)(115,318)(116,327)(117,326)(118,330)(119,329)
(120,328)(121,427)(122,426)(123,430)(124,429)(125,428)(126,422)(127,421)
(128,425)(129,424)(130,423)(131,432)(132,431)(133,435)(134,434)(135,433)
(136,442)(137,441)(138,445)(139,444)(140,443)(141,437)(142,436)(143,440)
(144,439)(145,438)(146,447)(147,446)(148,450)(149,449)(150,448)(151,472)
(152,471)(153,475)(154,474)(155,473)(156,467)(157,466)(158,470)(159,469)
(160,468)(161,477)(162,476)(163,480)(164,479)(165,478)(166,457)(167,456)
(168,460)(169,459)(170,458)(171,452)(172,451)(173,455)(174,454)(175,453)
(176,462)(177,461)(178,465)(179,464)(180,463)(181,367)(182,366)(183,370)
(184,369)(185,368)(186,362)(187,361)(188,365)(189,364)(190,363)(191,372)
(192,371)(193,375)(194,374)(195,373)(196,382)(197,381)(198,385)(199,384)
(200,383)(201,377)(202,376)(203,380)(204,379)(205,378)(206,387)(207,386)
(208,390)(209,389)(210,388)(211,412)(212,411)(213,415)(214,414)(215,413)
(216,407)(217,406)(218,410)(219,409)(220,408)(221,417)(222,416)(223,420)
(224,419)(225,418)(226,397)(227,396)(228,400)(229,399)(230,398)(231,392)
(232,391)(233,395)(234,394)(235,393)(236,402)(237,401)(238,405)(239,404)
(240,403)(481,847)(482,846)(483,850)(484,849)(485,848)(486,842)(487,841)
(488,845)(489,844)(490,843)(491,852)(492,851)(493,855)(494,854)(495,853)
(496,862)(497,861)(498,865)(499,864)(500,863)(501,857)(502,856)(503,860)
(504,859)(505,858)(506,867)(507,866)(508,870)(509,869)(510,868)(511,892)
(512,891)(513,895)(514,894)(515,893)(516,887)(517,886)(518,890)(519,889)
(520,888)(521,897)(522,896)(523,900)(524,899)(525,898)(526,877)(527,876)
(528,880)(529,879)(530,878)(531,872)(532,871)(533,875)(534,874)(535,873)
(536,882)(537,881)(538,885)(539,884)(540,883)(541,937)(542,936)(543,940)
(544,939)(545,938)(546,932)(547,931)(548,935)(549,934)(550,933)(551,942)
(552,941)(553,945)(554,944)(555,943)(556,952)(557,951)(558,955)(559,954)
(560,953)(561,947)(562,946)(563,950)(564,949)(565,948)(566,957)(567,956)
(568,960)(569,959)(570,958)(571,907)(572,906)(573,910)(574,909)(575,908)
(576,902)(577,901)(578,905)(579,904)(580,903)(581,912)(582,911)(583,915)
(584,914)(585,913)(586,922)(587,921)(588,925)(589,924)(590,923)(591,917)
(592,916)(593,920)(594,919)(595,918)(596,927)(597,926)(598,930)(599,929)
(600,928)(601,727)(602,726)(603,730)(604,729)(605,728)(606,722)(607,721)
(608,725)(609,724)(610,723)(611,732)(612,731)(613,735)(614,734)(615,733)
(616,742)(617,741)(618,745)(619,744)(620,743)(621,737)(622,736)(623,740)
(624,739)(625,738)(626,747)(627,746)(628,750)(629,749)(630,748)(631,772)
(632,771)(633,775)(634,774)(635,773)(636,767)(637,766)(638,770)(639,769)
(640,768)(641,777)(642,776)(643,780)(644,779)(645,778)(646,757)(647,756)
(648,760)(649,759)(650,758)(651,752)(652,751)(653,755)(654,754)(655,753)
(656,762)(657,761)(658,765)(659,764)(660,763)(661,817)(662,816)(663,820)
(664,819)(665,818)(666,812)(667,811)(668,815)(669,814)(670,813)(671,822)
(672,821)(673,825)(674,824)(675,823)(676,832)(677,831)(678,835)(679,834)
(680,833)(681,827)(682,826)(683,830)(684,829)(685,828)(686,837)(687,836)
(688,840)(689,839)(690,838)(691,787)(692,786)(693,790)(694,789)(695,788)
(696,782)(697,781)(698,785)(699,784)(700,783)(701,792)(702,791)(703,795)
(704,794)(705,793)(706,802)(707,801)(708,805)(709,804)(710,803)(711,797)
(712,796)(713,800)(714,799)(715,798)(716,807)(717,806)(718,810)(719,809)
(720,808);
s2 := Sym(960)!( 1,481)( 2,482)( 3,483)( 4,484)( 5,485)( 6,486)( 7,487)
( 8,488)( 9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)
( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)( 21,501)( 22,502)( 23,503)
( 24,504)( 25,505)( 26,506)( 27,507)( 28,508)( 29,509)( 30,510)( 31,526)
( 32,527)( 33,528)( 34,529)( 35,530)( 36,531)( 37,532)( 38,533)( 39,534)
( 40,535)( 41,536)( 42,537)( 43,538)( 44,539)( 45,540)( 46,511)( 47,512)
( 48,513)( 49,514)( 50,515)( 51,516)( 52,517)( 53,518)( 54,519)( 55,520)
( 56,521)( 57,522)( 58,523)( 59,524)( 60,525)( 61,571)( 62,572)( 63,573)
( 64,574)( 65,575)( 66,576)( 67,577)( 68,578)( 69,579)( 70,580)( 71,581)
( 72,582)( 73,583)( 74,584)( 75,585)( 76,586)( 77,587)( 78,588)( 79,589)
( 80,590)( 81,591)( 82,592)( 83,593)( 84,594)( 85,595)( 86,596)( 87,597)
( 88,598)( 89,599)( 90,600)( 91,541)( 92,542)( 93,543)( 94,544)( 95,545)
( 96,546)( 97,547)( 98,548)( 99,549)(100,550)(101,551)(102,552)(103,553)
(104,554)(105,555)(106,556)(107,557)(108,558)(109,559)(110,560)(111,561)
(112,562)(113,563)(114,564)(115,565)(116,566)(117,567)(118,568)(119,569)
(120,570)(121,661)(122,662)(123,663)(124,664)(125,665)(126,666)(127,667)
(128,668)(129,669)(130,670)(131,671)(132,672)(133,673)(134,674)(135,675)
(136,676)(137,677)(138,678)(139,679)(140,680)(141,681)(142,682)(143,683)
(144,684)(145,685)(146,686)(147,687)(148,688)(149,689)(150,690)(151,706)
(152,707)(153,708)(154,709)(155,710)(156,711)(157,712)(158,713)(159,714)
(160,715)(161,716)(162,717)(163,718)(164,719)(165,720)(166,691)(167,692)
(168,693)(169,694)(170,695)(171,696)(172,697)(173,698)(174,699)(175,700)
(176,701)(177,702)(178,703)(179,704)(180,705)(181,601)(182,602)(183,603)
(184,604)(185,605)(186,606)(187,607)(188,608)(189,609)(190,610)(191,611)
(192,612)(193,613)(194,614)(195,615)(196,616)(197,617)(198,618)(199,619)
(200,620)(201,621)(202,622)(203,623)(204,624)(205,625)(206,626)(207,627)
(208,628)(209,629)(210,630)(211,646)(212,647)(213,648)(214,649)(215,650)
(216,651)(217,652)(218,653)(219,654)(220,655)(221,656)(222,657)(223,658)
(224,659)(225,660)(226,631)(227,632)(228,633)(229,634)(230,635)(231,636)
(232,637)(233,638)(234,639)(235,640)(236,641)(237,642)(238,643)(239,644)
(240,645)(241,721)(242,722)(243,723)(244,724)(245,725)(246,726)(247,727)
(248,728)(249,729)(250,730)(251,731)(252,732)(253,733)(254,734)(255,735)
(256,736)(257,737)(258,738)(259,739)(260,740)(261,741)(262,742)(263,743)
(264,744)(265,745)(266,746)(267,747)(268,748)(269,749)(270,750)(271,766)
(272,767)(273,768)(274,769)(275,770)(276,771)(277,772)(278,773)(279,774)
(280,775)(281,776)(282,777)(283,778)(284,779)(285,780)(286,751)(287,752)
(288,753)(289,754)(290,755)(291,756)(292,757)(293,758)(294,759)(295,760)
(296,761)(297,762)(298,763)(299,764)(300,765)(301,811)(302,812)(303,813)
(304,814)(305,815)(306,816)(307,817)(308,818)(309,819)(310,820)(311,821)
(312,822)(313,823)(314,824)(315,825)(316,826)(317,827)(318,828)(319,829)
(320,830)(321,831)(322,832)(323,833)(324,834)(325,835)(326,836)(327,837)
(328,838)(329,839)(330,840)(331,781)(332,782)(333,783)(334,784)(335,785)
(336,786)(337,787)(338,788)(339,789)(340,790)(341,791)(342,792)(343,793)
(344,794)(345,795)(346,796)(347,797)(348,798)(349,799)(350,800)(351,801)
(352,802)(353,803)(354,804)(355,805)(356,806)(357,807)(358,808)(359,809)
(360,810)(361,901)(362,902)(363,903)(364,904)(365,905)(366,906)(367,907)
(368,908)(369,909)(370,910)(371,911)(372,912)(373,913)(374,914)(375,915)
(376,916)(377,917)(378,918)(379,919)(380,920)(381,921)(382,922)(383,923)
(384,924)(385,925)(386,926)(387,927)(388,928)(389,929)(390,930)(391,946)
(392,947)(393,948)(394,949)(395,950)(396,951)(397,952)(398,953)(399,954)
(400,955)(401,956)(402,957)(403,958)(404,959)(405,960)(406,931)(407,932)
(408,933)(409,934)(410,935)(411,936)(412,937)(413,938)(414,939)(415,940)
(416,941)(417,942)(418,943)(419,944)(420,945)(421,841)(422,842)(423,843)
(424,844)(425,845)(426,846)(427,847)(428,848)(429,849)(430,850)(431,851)
(432,852)(433,853)(434,854)(435,855)(436,856)(437,857)(438,858)(439,859)
(440,860)(441,861)(442,862)(443,863)(444,864)(445,865)(446,866)(447,867)
(448,868)(449,869)(450,870)(451,886)(452,887)(453,888)(454,889)(455,890)
(456,891)(457,892)(458,893)(459,894)(460,895)(461,896)(462,897)(463,898)
(464,899)(465,900)(466,871)(467,872)(468,873)(469,874)(470,875)(471,876)
(472,877)(473,878)(474,879)(475,880)(476,881)(477,882)(478,883)(479,884)
(480,885);
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*s2*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,
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*s1*s2*s1*s2 >;
References : None.
to this polytope