Polytope of Type {20,48}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {20,48}*1920a
Also Known As : {20,48|2}. if this polytope has another name.
Group : SmallGroup(1920,41749)
Rank : 3
Schlafli Type : {20,48}
Number of vertices, edges, etc : 20, 480, 48
Order of s0s1s2 : 240
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 : {10,48}*960, {20,24}*960a
3-fold quotients : {20,16}*640a
4-fold quotients : {10,24}*480, {20,12}*480
5-fold quotients : {4,48}*384a
6-fold quotients : {20,8}*320a, {10,16}*320
8-fold quotients : {10,12}*240, {20,6}*240a
10-fold quotients : {4,24}*192a, {2,48}*192
12-fold quotients : {20,4}*160, {10,8}*160
15-fold quotients : {4,16}*128a
16-fold quotients : {10,6}*120
20-fold quotients : {4,12}*96a, {2,24}*96
24-fold quotients : {20,2}*80, {10,4}*80
30-fold quotients : {4,8}*64a, {2,16}*64
40-fold quotients : {2,12}*48, {4,6}*48a
48-fold quotients : {10,2}*40
60-fold quotients : {4,4}*32, {2,8}*32
80-fold quotients : {2,6}*24
96-fold quotients : {5,2}*20
120-fold quotients : {2,4}*16, {4,2}*16
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 := ( 1,241)( 2,245)( 3,244)( 4,243)( 5,242)( 6,246)( 7,250)( 8,249)
( 9,248)( 10,247)( 11,251)( 12,255)( 13,254)( 14,253)( 15,252)( 16,256)
( 17,260)( 18,259)( 19,258)( 20,257)( 21,261)( 22,265)( 23,264)( 24,263)
( 25,262)( 26,266)( 27,270)( 28,269)( 29,268)( 30,267)( 31,271)( 32,275)
( 33,274)( 34,273)( 35,272)( 36,276)( 37,280)( 38,279)( 39,278)( 40,277)
( 41,281)( 42,285)( 43,284)( 44,283)( 45,282)( 46,286)( 47,290)( 48,289)
( 49,288)( 50,287)( 51,291)( 52,295)( 53,294)( 54,293)( 55,292)( 56,296)
( 57,300)( 58,299)( 59,298)( 60,297)( 61,301)( 62,305)( 63,304)( 64,303)
( 65,302)( 66,306)( 67,310)( 68,309)( 69,308)( 70,307)( 71,311)( 72,315)
( 73,314)( 74,313)( 75,312)( 76,316)( 77,320)( 78,319)( 79,318)( 80,317)
( 81,321)( 82,325)( 83,324)( 84,323)( 85,322)( 86,326)( 87,330)( 88,329)
( 89,328)( 90,327)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)( 96,336)
( 97,340)( 98,339)( 99,338)(100,337)(101,341)(102,345)(103,344)(104,343)
(105,342)(106,346)(107,350)(108,349)(109,348)(110,347)(111,351)(112,355)
(113,354)(114,353)(115,352)(116,356)(117,360)(118,359)(119,358)(120,357)
(121,361)(122,365)(123,364)(124,363)(125,362)(126,366)(127,370)(128,369)
(129,368)(130,367)(131,371)(132,375)(133,374)(134,373)(135,372)(136,376)
(137,380)(138,379)(139,378)(140,377)(141,381)(142,385)(143,384)(144,383)
(145,382)(146,386)(147,390)(148,389)(149,388)(150,387)(151,391)(152,395)
(153,394)(154,393)(155,392)(156,396)(157,400)(158,399)(159,398)(160,397)
(161,401)(162,405)(163,404)(164,403)(165,402)(166,406)(167,410)(168,409)
(169,408)(170,407)(171,411)(172,415)(173,414)(174,413)(175,412)(176,416)
(177,420)(178,419)(179,418)(180,417)(181,421)(182,425)(183,424)(184,423)
(185,422)(186,426)(187,430)(188,429)(189,428)(190,427)(191,431)(192,435)
(193,434)(194,433)(195,432)(196,436)(197,440)(198,439)(199,438)(200,437)
(201,441)(202,445)(203,444)(204,443)(205,442)(206,446)(207,450)(208,449)
(209,448)(210,447)(211,451)(212,455)(213,454)(214,453)(215,452)(216,456)
(217,460)(218,459)(219,458)(220,457)(221,461)(222,465)(223,464)(224,463)
(225,462)(226,466)(227,470)(228,469)(229,468)(230,467)(231,471)(232,475)
(233,474)(234,473)(235,472)(236,476)(237,480)(238,479)(239,478)(240,477)
(481,721)(482,725)(483,724)(484,723)(485,722)(486,726)(487,730)(488,729)
(489,728)(490,727)(491,731)(492,735)(493,734)(494,733)(495,732)(496,736)
(497,740)(498,739)(499,738)(500,737)(501,741)(502,745)(503,744)(504,743)
(505,742)(506,746)(507,750)(508,749)(509,748)(510,747)(511,751)(512,755)
(513,754)(514,753)(515,752)(516,756)(517,760)(518,759)(519,758)(520,757)
(521,761)(522,765)(523,764)(524,763)(525,762)(526,766)(527,770)(528,769)
(529,768)(530,767)(531,771)(532,775)(533,774)(534,773)(535,772)(536,776)
(537,780)(538,779)(539,778)(540,777)(541,781)(542,785)(543,784)(544,783)
(545,782)(546,786)(547,790)(548,789)(549,788)(550,787)(551,791)(552,795)
(553,794)(554,793)(555,792)(556,796)(557,800)(558,799)(559,798)(560,797)
(561,801)(562,805)(563,804)(564,803)(565,802)(566,806)(567,810)(568,809)
(569,808)(570,807)(571,811)(572,815)(573,814)(574,813)(575,812)(576,816)
(577,820)(578,819)(579,818)(580,817)(581,821)(582,825)(583,824)(584,823)
(585,822)(586,826)(587,830)(588,829)(589,828)(590,827)(591,831)(592,835)
(593,834)(594,833)(595,832)(596,836)(597,840)(598,839)(599,838)(600,837)
(601,841)(602,845)(603,844)(604,843)(605,842)(606,846)(607,850)(608,849)
(609,848)(610,847)(611,851)(612,855)(613,854)(614,853)(615,852)(616,856)
(617,860)(618,859)(619,858)(620,857)(621,861)(622,865)(623,864)(624,863)
(625,862)(626,866)(627,870)(628,869)(629,868)(630,867)(631,871)(632,875)
(633,874)(634,873)(635,872)(636,876)(637,880)(638,879)(639,878)(640,877)
(641,881)(642,885)(643,884)(644,883)(645,882)(646,886)(647,890)(648,889)
(649,888)(650,887)(651,891)(652,895)(653,894)(654,893)(655,892)(656,896)
(657,900)(658,899)(659,898)(660,897)(661,901)(662,905)(663,904)(664,903)
(665,902)(666,906)(667,910)(668,909)(669,908)(670,907)(671,911)(672,915)
(673,914)(674,913)(675,912)(676,916)(677,920)(678,919)(679,918)(680,917)
(681,921)(682,925)(683,924)(684,923)(685,922)(686,926)(687,930)(688,929)
(689,928)(690,927)(691,931)(692,935)(693,934)(694,933)(695,932)(696,936)
(697,940)(698,939)(699,938)(700,937)(701,941)(702,945)(703,944)(704,943)
(705,942)(706,946)(707,950)(708,949)(709,948)(710,947)(711,951)(712,955)
(713,954)(714,953)(715,952)(716,956)(717,960)(718,959)(719,958)(720,957);;
s1 := ( 1, 2)( 3, 5)( 6, 12)( 7, 11)( 8, 15)( 9, 14)( 10, 13)( 16, 17)
( 18, 20)( 21, 27)( 22, 26)( 23, 30)( 24, 29)( 25, 28)( 31, 47)( 32, 46)
( 33, 50)( 34, 49)( 35, 48)( 36, 57)( 37, 56)( 38, 60)( 39, 59)( 40, 58)
( 41, 52)( 42, 51)( 43, 55)( 44, 54)( 45, 53)( 61, 62)( 63, 65)( 66, 72)
( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 77)( 78, 80)( 81, 87)( 82, 86)
( 83, 90)( 84, 89)( 85, 88)( 91,107)( 92,106)( 93,110)( 94,109)( 95,108)
( 96,117)( 97,116)( 98,120)( 99,119)(100,118)(101,112)(102,111)(103,115)
(104,114)(105,113)(121,152)(122,151)(123,155)(124,154)(125,153)(126,162)
(127,161)(128,165)(129,164)(130,163)(131,157)(132,156)(133,160)(134,159)
(135,158)(136,167)(137,166)(138,170)(139,169)(140,168)(141,177)(142,176)
(143,180)(144,179)(145,178)(146,172)(147,171)(148,175)(149,174)(150,173)
(181,212)(182,211)(183,215)(184,214)(185,213)(186,222)(187,221)(188,225)
(189,224)(190,223)(191,217)(192,216)(193,220)(194,219)(195,218)(196,227)
(197,226)(198,230)(199,229)(200,228)(201,237)(202,236)(203,240)(204,239)
(205,238)(206,232)(207,231)(208,235)(209,234)(210,233)(241,302)(242,301)
(243,305)(244,304)(245,303)(246,312)(247,311)(248,315)(249,314)(250,313)
(251,307)(252,306)(253,310)(254,309)(255,308)(256,317)(257,316)(258,320)
(259,319)(260,318)(261,327)(262,326)(263,330)(264,329)(265,328)(266,322)
(267,321)(268,325)(269,324)(270,323)(271,347)(272,346)(273,350)(274,349)
(275,348)(276,357)(277,356)(278,360)(279,359)(280,358)(281,352)(282,351)
(283,355)(284,354)(285,353)(286,332)(287,331)(288,335)(289,334)(290,333)
(291,342)(292,341)(293,345)(294,344)(295,343)(296,337)(297,336)(298,340)
(299,339)(300,338)(361,452)(362,451)(363,455)(364,454)(365,453)(366,462)
(367,461)(368,465)(369,464)(370,463)(371,457)(372,456)(373,460)(374,459)
(375,458)(376,467)(377,466)(378,470)(379,469)(380,468)(381,477)(382,476)
(383,480)(384,479)(385,478)(386,472)(387,471)(388,475)(389,474)(390,473)
(391,422)(392,421)(393,425)(394,424)(395,423)(396,432)(397,431)(398,435)
(399,434)(400,433)(401,427)(402,426)(403,430)(404,429)(405,428)(406,437)
(407,436)(408,440)(409,439)(410,438)(411,447)(412,446)(413,450)(414,449)
(415,448)(416,442)(417,441)(418,445)(419,444)(420,443)(481,602)(482,601)
(483,605)(484,604)(485,603)(486,612)(487,611)(488,615)(489,614)(490,613)
(491,607)(492,606)(493,610)(494,609)(495,608)(496,617)(497,616)(498,620)
(499,619)(500,618)(501,627)(502,626)(503,630)(504,629)(505,628)(506,622)
(507,621)(508,625)(509,624)(510,623)(511,647)(512,646)(513,650)(514,649)
(515,648)(516,657)(517,656)(518,660)(519,659)(520,658)(521,652)(522,651)
(523,655)(524,654)(525,653)(526,632)(527,631)(528,635)(529,634)(530,633)
(531,642)(532,641)(533,645)(534,644)(535,643)(536,637)(537,636)(538,640)
(539,639)(540,638)(541,662)(542,661)(543,665)(544,664)(545,663)(546,672)
(547,671)(548,675)(549,674)(550,673)(551,667)(552,666)(553,670)(554,669)
(555,668)(556,677)(557,676)(558,680)(559,679)(560,678)(561,687)(562,686)
(563,690)(564,689)(565,688)(566,682)(567,681)(568,685)(569,684)(570,683)
(571,707)(572,706)(573,710)(574,709)(575,708)(576,717)(577,716)(578,720)
(579,719)(580,718)(581,712)(582,711)(583,715)(584,714)(585,713)(586,692)
(587,691)(588,695)(589,694)(590,693)(591,702)(592,701)(593,705)(594,704)
(595,703)(596,697)(597,696)(598,700)(599,699)(600,698)(721,902)(722,901)
(723,905)(724,904)(725,903)(726,912)(727,911)(728,915)(729,914)(730,913)
(731,907)(732,906)(733,910)(734,909)(735,908)(736,917)(737,916)(738,920)
(739,919)(740,918)(741,927)(742,926)(743,930)(744,929)(745,928)(746,922)
(747,921)(748,925)(749,924)(750,923)(751,947)(752,946)(753,950)(754,949)
(755,948)(756,957)(757,956)(758,960)(759,959)(760,958)(761,952)(762,951)
(763,955)(764,954)(765,953)(766,932)(767,931)(768,935)(769,934)(770,933)
(771,942)(772,941)(773,945)(774,944)(775,943)(776,937)(777,936)(778,940)
(779,939)(780,938)(781,842)(782,841)(783,845)(784,844)(785,843)(786,852)
(787,851)(788,855)(789,854)(790,853)(791,847)(792,846)(793,850)(794,849)
(795,848)(796,857)(797,856)(798,860)(799,859)(800,858)(801,867)(802,866)
(803,870)(804,869)(805,868)(806,862)(807,861)(808,865)(809,864)(810,863)
(811,887)(812,886)(813,890)(814,889)(815,888)(816,897)(817,896)(818,900)
(819,899)(820,898)(821,892)(822,891)(823,895)(824,894)(825,893)(826,872)
(827,871)(828,875)(829,874)(830,873)(831,882)(832,881)(833,885)(834,884)
(835,883)(836,877)(837,876)(838,880)(839,879)(840,878);;
s2 := ( 1,726)( 2,727)( 3,728)( 4,729)( 5,730)( 6,721)( 7,722)( 8,723)
( 9,724)( 10,725)( 11,731)( 12,732)( 13,733)( 14,734)( 15,735)( 16,741)
( 17,742)( 18,743)( 19,744)( 20,745)( 21,736)( 22,737)( 23,738)( 24,739)
( 25,740)( 26,746)( 27,747)( 28,748)( 29,749)( 30,750)( 31,771)( 32,772)
( 33,773)( 34,774)( 35,775)( 36,766)( 37,767)( 38,768)( 39,769)( 40,770)
( 41,776)( 42,777)( 43,778)( 44,779)( 45,780)( 46,756)( 47,757)( 48,758)
( 49,759)( 50,760)( 51,751)( 52,752)( 53,753)( 54,754)( 55,755)( 56,761)
( 57,762)( 58,763)( 59,764)( 60,765)( 61,786)( 62,787)( 63,788)( 64,789)
( 65,790)( 66,781)( 67,782)( 68,783)( 69,784)( 70,785)( 71,791)( 72,792)
( 73,793)( 74,794)( 75,795)( 76,801)( 77,802)( 78,803)( 79,804)( 80,805)
( 81,796)( 82,797)( 83,798)( 84,799)( 85,800)( 86,806)( 87,807)( 88,808)
( 89,809)( 90,810)( 91,831)( 92,832)( 93,833)( 94,834)( 95,835)( 96,826)
( 97,827)( 98,828)( 99,829)(100,830)(101,836)(102,837)(103,838)(104,839)
(105,840)(106,816)(107,817)(108,818)(109,819)(110,820)(111,811)(112,812)
(113,813)(114,814)(115,815)(116,821)(117,822)(118,823)(119,824)(120,825)
(121,876)(122,877)(123,878)(124,879)(125,880)(126,871)(127,872)(128,873)
(129,874)(130,875)(131,881)(132,882)(133,883)(134,884)(135,885)(136,891)
(137,892)(138,893)(139,894)(140,895)(141,886)(142,887)(143,888)(144,889)
(145,890)(146,896)(147,897)(148,898)(149,899)(150,900)(151,846)(152,847)
(153,848)(154,849)(155,850)(156,841)(157,842)(158,843)(159,844)(160,845)
(161,851)(162,852)(163,853)(164,854)(165,855)(166,861)(167,862)(168,863)
(169,864)(170,865)(171,856)(172,857)(173,858)(174,859)(175,860)(176,866)
(177,867)(178,868)(179,869)(180,870)(181,936)(182,937)(183,938)(184,939)
(185,940)(186,931)(187,932)(188,933)(189,934)(190,935)(191,941)(192,942)
(193,943)(194,944)(195,945)(196,951)(197,952)(198,953)(199,954)(200,955)
(201,946)(202,947)(203,948)(204,949)(205,950)(206,956)(207,957)(208,958)
(209,959)(210,960)(211,906)(212,907)(213,908)(214,909)(215,910)(216,901)
(217,902)(218,903)(219,904)(220,905)(221,911)(222,912)(223,913)(224,914)
(225,915)(226,921)(227,922)(228,923)(229,924)(230,925)(231,916)(232,917)
(233,918)(234,919)(235,920)(236,926)(237,927)(238,928)(239,929)(240,930)
(241,486)(242,487)(243,488)(244,489)(245,490)(246,481)(247,482)(248,483)
(249,484)(250,485)(251,491)(252,492)(253,493)(254,494)(255,495)(256,501)
(257,502)(258,503)(259,504)(260,505)(261,496)(262,497)(263,498)(264,499)
(265,500)(266,506)(267,507)(268,508)(269,509)(270,510)(271,531)(272,532)
(273,533)(274,534)(275,535)(276,526)(277,527)(278,528)(279,529)(280,530)
(281,536)(282,537)(283,538)(284,539)(285,540)(286,516)(287,517)(288,518)
(289,519)(290,520)(291,511)(292,512)(293,513)(294,514)(295,515)(296,521)
(297,522)(298,523)(299,524)(300,525)(301,546)(302,547)(303,548)(304,549)
(305,550)(306,541)(307,542)(308,543)(309,544)(310,545)(311,551)(312,552)
(313,553)(314,554)(315,555)(316,561)(317,562)(318,563)(319,564)(320,565)
(321,556)(322,557)(323,558)(324,559)(325,560)(326,566)(327,567)(328,568)
(329,569)(330,570)(331,591)(332,592)(333,593)(334,594)(335,595)(336,586)
(337,587)(338,588)(339,589)(340,590)(341,596)(342,597)(343,598)(344,599)
(345,600)(346,576)(347,577)(348,578)(349,579)(350,580)(351,571)(352,572)
(353,573)(354,574)(355,575)(356,581)(357,582)(358,583)(359,584)(360,585)
(361,636)(362,637)(363,638)(364,639)(365,640)(366,631)(367,632)(368,633)
(369,634)(370,635)(371,641)(372,642)(373,643)(374,644)(375,645)(376,651)
(377,652)(378,653)(379,654)(380,655)(381,646)(382,647)(383,648)(384,649)
(385,650)(386,656)(387,657)(388,658)(389,659)(390,660)(391,606)(392,607)
(393,608)(394,609)(395,610)(396,601)(397,602)(398,603)(399,604)(400,605)
(401,611)(402,612)(403,613)(404,614)(405,615)(406,621)(407,622)(408,623)
(409,624)(410,625)(411,616)(412,617)(413,618)(414,619)(415,620)(416,626)
(417,627)(418,628)(419,629)(420,630)(421,696)(422,697)(423,698)(424,699)
(425,700)(426,691)(427,692)(428,693)(429,694)(430,695)(431,701)(432,702)
(433,703)(434,704)(435,705)(436,711)(437,712)(438,713)(439,714)(440,715)
(441,706)(442,707)(443,708)(444,709)(445,710)(446,716)(447,717)(448,718)
(449,719)(450,720)(451,666)(452,667)(453,668)(454,669)(455,670)(456,661)
(457,662)(458,663)(459,664)(460,665)(461,671)(462,672)(463,673)(464,674)
(465,675)(466,681)(467,682)(468,683)(469,684)(470,685)(471,676)(472,677)
(473,678)(474,679)(475,680)(476,686)(477,687)(478,688)(479,689)(480,690);;
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,
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*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)( 6,246)( 7,250)
( 8,249)( 9,248)( 10,247)( 11,251)( 12,255)( 13,254)( 14,253)( 15,252)
( 16,256)( 17,260)( 18,259)( 19,258)( 20,257)( 21,261)( 22,265)( 23,264)
( 24,263)( 25,262)( 26,266)( 27,270)( 28,269)( 29,268)( 30,267)( 31,271)
( 32,275)( 33,274)( 34,273)( 35,272)( 36,276)( 37,280)( 38,279)( 39,278)
( 40,277)( 41,281)( 42,285)( 43,284)( 44,283)( 45,282)( 46,286)( 47,290)
( 48,289)( 49,288)( 50,287)( 51,291)( 52,295)( 53,294)( 54,293)( 55,292)
( 56,296)( 57,300)( 58,299)( 59,298)( 60,297)( 61,301)( 62,305)( 63,304)
( 64,303)( 65,302)( 66,306)( 67,310)( 68,309)( 69,308)( 70,307)( 71,311)
( 72,315)( 73,314)( 74,313)( 75,312)( 76,316)( 77,320)( 78,319)( 79,318)
( 80,317)( 81,321)( 82,325)( 83,324)( 84,323)( 85,322)( 86,326)( 87,330)
( 88,329)( 89,328)( 90,327)( 91,331)( 92,335)( 93,334)( 94,333)( 95,332)
( 96,336)( 97,340)( 98,339)( 99,338)(100,337)(101,341)(102,345)(103,344)
(104,343)(105,342)(106,346)(107,350)(108,349)(109,348)(110,347)(111,351)
(112,355)(113,354)(114,353)(115,352)(116,356)(117,360)(118,359)(119,358)
(120,357)(121,361)(122,365)(123,364)(124,363)(125,362)(126,366)(127,370)
(128,369)(129,368)(130,367)(131,371)(132,375)(133,374)(134,373)(135,372)
(136,376)(137,380)(138,379)(139,378)(140,377)(141,381)(142,385)(143,384)
(144,383)(145,382)(146,386)(147,390)(148,389)(149,388)(150,387)(151,391)
(152,395)(153,394)(154,393)(155,392)(156,396)(157,400)(158,399)(159,398)
(160,397)(161,401)(162,405)(163,404)(164,403)(165,402)(166,406)(167,410)
(168,409)(169,408)(170,407)(171,411)(172,415)(173,414)(174,413)(175,412)
(176,416)(177,420)(178,419)(179,418)(180,417)(181,421)(182,425)(183,424)
(184,423)(185,422)(186,426)(187,430)(188,429)(189,428)(190,427)(191,431)
(192,435)(193,434)(194,433)(195,432)(196,436)(197,440)(198,439)(199,438)
(200,437)(201,441)(202,445)(203,444)(204,443)(205,442)(206,446)(207,450)
(208,449)(209,448)(210,447)(211,451)(212,455)(213,454)(214,453)(215,452)
(216,456)(217,460)(218,459)(219,458)(220,457)(221,461)(222,465)(223,464)
(224,463)(225,462)(226,466)(227,470)(228,469)(229,468)(230,467)(231,471)
(232,475)(233,474)(234,473)(235,472)(236,476)(237,480)(238,479)(239,478)
(240,477)(481,721)(482,725)(483,724)(484,723)(485,722)(486,726)(487,730)
(488,729)(489,728)(490,727)(491,731)(492,735)(493,734)(494,733)(495,732)
(496,736)(497,740)(498,739)(499,738)(500,737)(501,741)(502,745)(503,744)
(504,743)(505,742)(506,746)(507,750)(508,749)(509,748)(510,747)(511,751)
(512,755)(513,754)(514,753)(515,752)(516,756)(517,760)(518,759)(519,758)
(520,757)(521,761)(522,765)(523,764)(524,763)(525,762)(526,766)(527,770)
(528,769)(529,768)(530,767)(531,771)(532,775)(533,774)(534,773)(535,772)
(536,776)(537,780)(538,779)(539,778)(540,777)(541,781)(542,785)(543,784)
(544,783)(545,782)(546,786)(547,790)(548,789)(549,788)(550,787)(551,791)
(552,795)(553,794)(554,793)(555,792)(556,796)(557,800)(558,799)(559,798)
(560,797)(561,801)(562,805)(563,804)(564,803)(565,802)(566,806)(567,810)
(568,809)(569,808)(570,807)(571,811)(572,815)(573,814)(574,813)(575,812)
(576,816)(577,820)(578,819)(579,818)(580,817)(581,821)(582,825)(583,824)
(584,823)(585,822)(586,826)(587,830)(588,829)(589,828)(590,827)(591,831)
(592,835)(593,834)(594,833)(595,832)(596,836)(597,840)(598,839)(599,838)
(600,837)(601,841)(602,845)(603,844)(604,843)(605,842)(606,846)(607,850)
(608,849)(609,848)(610,847)(611,851)(612,855)(613,854)(614,853)(615,852)
(616,856)(617,860)(618,859)(619,858)(620,857)(621,861)(622,865)(623,864)
(624,863)(625,862)(626,866)(627,870)(628,869)(629,868)(630,867)(631,871)
(632,875)(633,874)(634,873)(635,872)(636,876)(637,880)(638,879)(639,878)
(640,877)(641,881)(642,885)(643,884)(644,883)(645,882)(646,886)(647,890)
(648,889)(649,888)(650,887)(651,891)(652,895)(653,894)(654,893)(655,892)
(656,896)(657,900)(658,899)(659,898)(660,897)(661,901)(662,905)(663,904)
(664,903)(665,902)(666,906)(667,910)(668,909)(669,908)(670,907)(671,911)
(672,915)(673,914)(674,913)(675,912)(676,916)(677,920)(678,919)(679,918)
(680,917)(681,921)(682,925)(683,924)(684,923)(685,922)(686,926)(687,930)
(688,929)(689,928)(690,927)(691,931)(692,935)(693,934)(694,933)(695,932)
(696,936)(697,940)(698,939)(699,938)(700,937)(701,941)(702,945)(703,944)
(704,943)(705,942)(706,946)(707,950)(708,949)(709,948)(710,947)(711,951)
(712,955)(713,954)(714,953)(715,952)(716,956)(717,960)(718,959)(719,958)
(720,957);
s1 := Sym(960)!( 1, 2)( 3, 5)( 6, 12)( 7, 11)( 8, 15)( 9, 14)( 10, 13)
( 16, 17)( 18, 20)( 21, 27)( 22, 26)( 23, 30)( 24, 29)( 25, 28)( 31, 47)
( 32, 46)( 33, 50)( 34, 49)( 35, 48)( 36, 57)( 37, 56)( 38, 60)( 39, 59)
( 40, 58)( 41, 52)( 42, 51)( 43, 55)( 44, 54)( 45, 53)( 61, 62)( 63, 65)
( 66, 72)( 67, 71)( 68, 75)( 69, 74)( 70, 73)( 76, 77)( 78, 80)( 81, 87)
( 82, 86)( 83, 90)( 84, 89)( 85, 88)( 91,107)( 92,106)( 93,110)( 94,109)
( 95,108)( 96,117)( 97,116)( 98,120)( 99,119)(100,118)(101,112)(102,111)
(103,115)(104,114)(105,113)(121,152)(122,151)(123,155)(124,154)(125,153)
(126,162)(127,161)(128,165)(129,164)(130,163)(131,157)(132,156)(133,160)
(134,159)(135,158)(136,167)(137,166)(138,170)(139,169)(140,168)(141,177)
(142,176)(143,180)(144,179)(145,178)(146,172)(147,171)(148,175)(149,174)
(150,173)(181,212)(182,211)(183,215)(184,214)(185,213)(186,222)(187,221)
(188,225)(189,224)(190,223)(191,217)(192,216)(193,220)(194,219)(195,218)
(196,227)(197,226)(198,230)(199,229)(200,228)(201,237)(202,236)(203,240)
(204,239)(205,238)(206,232)(207,231)(208,235)(209,234)(210,233)(241,302)
(242,301)(243,305)(244,304)(245,303)(246,312)(247,311)(248,315)(249,314)
(250,313)(251,307)(252,306)(253,310)(254,309)(255,308)(256,317)(257,316)
(258,320)(259,319)(260,318)(261,327)(262,326)(263,330)(264,329)(265,328)
(266,322)(267,321)(268,325)(269,324)(270,323)(271,347)(272,346)(273,350)
(274,349)(275,348)(276,357)(277,356)(278,360)(279,359)(280,358)(281,352)
(282,351)(283,355)(284,354)(285,353)(286,332)(287,331)(288,335)(289,334)
(290,333)(291,342)(292,341)(293,345)(294,344)(295,343)(296,337)(297,336)
(298,340)(299,339)(300,338)(361,452)(362,451)(363,455)(364,454)(365,453)
(366,462)(367,461)(368,465)(369,464)(370,463)(371,457)(372,456)(373,460)
(374,459)(375,458)(376,467)(377,466)(378,470)(379,469)(380,468)(381,477)
(382,476)(383,480)(384,479)(385,478)(386,472)(387,471)(388,475)(389,474)
(390,473)(391,422)(392,421)(393,425)(394,424)(395,423)(396,432)(397,431)
(398,435)(399,434)(400,433)(401,427)(402,426)(403,430)(404,429)(405,428)
(406,437)(407,436)(408,440)(409,439)(410,438)(411,447)(412,446)(413,450)
(414,449)(415,448)(416,442)(417,441)(418,445)(419,444)(420,443)(481,602)
(482,601)(483,605)(484,604)(485,603)(486,612)(487,611)(488,615)(489,614)
(490,613)(491,607)(492,606)(493,610)(494,609)(495,608)(496,617)(497,616)
(498,620)(499,619)(500,618)(501,627)(502,626)(503,630)(504,629)(505,628)
(506,622)(507,621)(508,625)(509,624)(510,623)(511,647)(512,646)(513,650)
(514,649)(515,648)(516,657)(517,656)(518,660)(519,659)(520,658)(521,652)
(522,651)(523,655)(524,654)(525,653)(526,632)(527,631)(528,635)(529,634)
(530,633)(531,642)(532,641)(533,645)(534,644)(535,643)(536,637)(537,636)
(538,640)(539,639)(540,638)(541,662)(542,661)(543,665)(544,664)(545,663)
(546,672)(547,671)(548,675)(549,674)(550,673)(551,667)(552,666)(553,670)
(554,669)(555,668)(556,677)(557,676)(558,680)(559,679)(560,678)(561,687)
(562,686)(563,690)(564,689)(565,688)(566,682)(567,681)(568,685)(569,684)
(570,683)(571,707)(572,706)(573,710)(574,709)(575,708)(576,717)(577,716)
(578,720)(579,719)(580,718)(581,712)(582,711)(583,715)(584,714)(585,713)
(586,692)(587,691)(588,695)(589,694)(590,693)(591,702)(592,701)(593,705)
(594,704)(595,703)(596,697)(597,696)(598,700)(599,699)(600,698)(721,902)
(722,901)(723,905)(724,904)(725,903)(726,912)(727,911)(728,915)(729,914)
(730,913)(731,907)(732,906)(733,910)(734,909)(735,908)(736,917)(737,916)
(738,920)(739,919)(740,918)(741,927)(742,926)(743,930)(744,929)(745,928)
(746,922)(747,921)(748,925)(749,924)(750,923)(751,947)(752,946)(753,950)
(754,949)(755,948)(756,957)(757,956)(758,960)(759,959)(760,958)(761,952)
(762,951)(763,955)(764,954)(765,953)(766,932)(767,931)(768,935)(769,934)
(770,933)(771,942)(772,941)(773,945)(774,944)(775,943)(776,937)(777,936)
(778,940)(779,939)(780,938)(781,842)(782,841)(783,845)(784,844)(785,843)
(786,852)(787,851)(788,855)(789,854)(790,853)(791,847)(792,846)(793,850)
(794,849)(795,848)(796,857)(797,856)(798,860)(799,859)(800,858)(801,867)
(802,866)(803,870)(804,869)(805,868)(806,862)(807,861)(808,865)(809,864)
(810,863)(811,887)(812,886)(813,890)(814,889)(815,888)(816,897)(817,896)
(818,900)(819,899)(820,898)(821,892)(822,891)(823,895)(824,894)(825,893)
(826,872)(827,871)(828,875)(829,874)(830,873)(831,882)(832,881)(833,885)
(834,884)(835,883)(836,877)(837,876)(838,880)(839,879)(840,878);
s2 := Sym(960)!( 1,726)( 2,727)( 3,728)( 4,729)( 5,730)( 6,721)( 7,722)
( 8,723)( 9,724)( 10,725)( 11,731)( 12,732)( 13,733)( 14,734)( 15,735)
( 16,741)( 17,742)( 18,743)( 19,744)( 20,745)( 21,736)( 22,737)( 23,738)
( 24,739)( 25,740)( 26,746)( 27,747)( 28,748)( 29,749)( 30,750)( 31,771)
( 32,772)( 33,773)( 34,774)( 35,775)( 36,766)( 37,767)( 38,768)( 39,769)
( 40,770)( 41,776)( 42,777)( 43,778)( 44,779)( 45,780)( 46,756)( 47,757)
( 48,758)( 49,759)( 50,760)( 51,751)( 52,752)( 53,753)( 54,754)( 55,755)
( 56,761)( 57,762)( 58,763)( 59,764)( 60,765)( 61,786)( 62,787)( 63,788)
( 64,789)( 65,790)( 66,781)( 67,782)( 68,783)( 69,784)( 70,785)( 71,791)
( 72,792)( 73,793)( 74,794)( 75,795)( 76,801)( 77,802)( 78,803)( 79,804)
( 80,805)( 81,796)( 82,797)( 83,798)( 84,799)( 85,800)( 86,806)( 87,807)
( 88,808)( 89,809)( 90,810)( 91,831)( 92,832)( 93,833)( 94,834)( 95,835)
( 96,826)( 97,827)( 98,828)( 99,829)(100,830)(101,836)(102,837)(103,838)
(104,839)(105,840)(106,816)(107,817)(108,818)(109,819)(110,820)(111,811)
(112,812)(113,813)(114,814)(115,815)(116,821)(117,822)(118,823)(119,824)
(120,825)(121,876)(122,877)(123,878)(124,879)(125,880)(126,871)(127,872)
(128,873)(129,874)(130,875)(131,881)(132,882)(133,883)(134,884)(135,885)
(136,891)(137,892)(138,893)(139,894)(140,895)(141,886)(142,887)(143,888)
(144,889)(145,890)(146,896)(147,897)(148,898)(149,899)(150,900)(151,846)
(152,847)(153,848)(154,849)(155,850)(156,841)(157,842)(158,843)(159,844)
(160,845)(161,851)(162,852)(163,853)(164,854)(165,855)(166,861)(167,862)
(168,863)(169,864)(170,865)(171,856)(172,857)(173,858)(174,859)(175,860)
(176,866)(177,867)(178,868)(179,869)(180,870)(181,936)(182,937)(183,938)
(184,939)(185,940)(186,931)(187,932)(188,933)(189,934)(190,935)(191,941)
(192,942)(193,943)(194,944)(195,945)(196,951)(197,952)(198,953)(199,954)
(200,955)(201,946)(202,947)(203,948)(204,949)(205,950)(206,956)(207,957)
(208,958)(209,959)(210,960)(211,906)(212,907)(213,908)(214,909)(215,910)
(216,901)(217,902)(218,903)(219,904)(220,905)(221,911)(222,912)(223,913)
(224,914)(225,915)(226,921)(227,922)(228,923)(229,924)(230,925)(231,916)
(232,917)(233,918)(234,919)(235,920)(236,926)(237,927)(238,928)(239,929)
(240,930)(241,486)(242,487)(243,488)(244,489)(245,490)(246,481)(247,482)
(248,483)(249,484)(250,485)(251,491)(252,492)(253,493)(254,494)(255,495)
(256,501)(257,502)(258,503)(259,504)(260,505)(261,496)(262,497)(263,498)
(264,499)(265,500)(266,506)(267,507)(268,508)(269,509)(270,510)(271,531)
(272,532)(273,533)(274,534)(275,535)(276,526)(277,527)(278,528)(279,529)
(280,530)(281,536)(282,537)(283,538)(284,539)(285,540)(286,516)(287,517)
(288,518)(289,519)(290,520)(291,511)(292,512)(293,513)(294,514)(295,515)
(296,521)(297,522)(298,523)(299,524)(300,525)(301,546)(302,547)(303,548)
(304,549)(305,550)(306,541)(307,542)(308,543)(309,544)(310,545)(311,551)
(312,552)(313,553)(314,554)(315,555)(316,561)(317,562)(318,563)(319,564)
(320,565)(321,556)(322,557)(323,558)(324,559)(325,560)(326,566)(327,567)
(328,568)(329,569)(330,570)(331,591)(332,592)(333,593)(334,594)(335,595)
(336,586)(337,587)(338,588)(339,589)(340,590)(341,596)(342,597)(343,598)
(344,599)(345,600)(346,576)(347,577)(348,578)(349,579)(350,580)(351,571)
(352,572)(353,573)(354,574)(355,575)(356,581)(357,582)(358,583)(359,584)
(360,585)(361,636)(362,637)(363,638)(364,639)(365,640)(366,631)(367,632)
(368,633)(369,634)(370,635)(371,641)(372,642)(373,643)(374,644)(375,645)
(376,651)(377,652)(378,653)(379,654)(380,655)(381,646)(382,647)(383,648)
(384,649)(385,650)(386,656)(387,657)(388,658)(389,659)(390,660)(391,606)
(392,607)(393,608)(394,609)(395,610)(396,601)(397,602)(398,603)(399,604)
(400,605)(401,611)(402,612)(403,613)(404,614)(405,615)(406,621)(407,622)
(408,623)(409,624)(410,625)(411,616)(412,617)(413,618)(414,619)(415,620)
(416,626)(417,627)(418,628)(419,629)(420,630)(421,696)(422,697)(423,698)
(424,699)(425,700)(426,691)(427,692)(428,693)(429,694)(430,695)(431,701)
(432,702)(433,703)(434,704)(435,705)(436,711)(437,712)(438,713)(439,714)
(440,715)(441,706)(442,707)(443,708)(444,709)(445,710)(446,716)(447,717)
(448,718)(449,719)(450,720)(451,666)(452,667)(453,668)(454,669)(455,670)
(456,661)(457,662)(458,663)(459,664)(460,665)(461,671)(462,672)(463,673)
(464,674)(465,675)(466,681)(467,682)(468,683)(469,684)(470,685)(471,676)
(472,677)(473,678)(474,679)(475,680)(476,686)(477,687)(478,688)(479,689)
(480,690);
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,
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*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