Polytope of Type {120,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {120,4}*1920e
if this polytope has a name.
Group : SmallGroup(1920,239568)
Rank : 3
Schlafli Type : {120,4}
Number of vertices, edges, etc : 240, 480, 8
Order of s0s1s2 : 60
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {60,4}*960c
4-fold quotients : {30,4}*480
5-fold quotients : {24,4}*384e
8-fold quotients : {15,4}*240, {30,4}*240b, {30,4}*240c
10-fold quotients : {12,4}*192c
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 := ( 1,481)( 2,482)( 3,484)( 4,483)( 5,487)( 6,488)( 7,485)( 8,486)
( 9,513)( 10,514)( 11,516)( 12,515)( 13,519)( 14,520)( 15,517)( 16,518)
( 17,505)( 18,506)( 19,508)( 20,507)( 21,511)( 22,512)( 23,509)( 24,510)
( 25,497)( 26,498)( 27,500)( 28,499)( 29,503)( 30,504)( 31,501)( 32,502)
( 33,489)( 34,490)( 35,492)( 36,491)( 37,495)( 38,496)( 39,493)( 40,494)
( 41,561)( 42,562)( 43,564)( 44,563)( 45,567)( 46,568)( 47,565)( 48,566)
( 49,593)( 50,594)( 51,596)( 52,595)( 53,599)( 54,600)( 55,597)( 56,598)
( 57,585)( 58,586)( 59,588)( 60,587)( 61,591)( 62,592)( 63,589)( 64,590)
( 65,577)( 66,578)( 67,580)( 68,579)( 69,583)( 70,584)( 71,581)( 72,582)
( 73,569)( 74,570)( 75,572)( 76,571)( 77,575)( 78,576)( 79,573)( 80,574)
( 81,521)( 82,522)( 83,524)( 84,523)( 85,527)( 86,528)( 87,525)( 88,526)
( 89,553)( 90,554)( 91,556)( 92,555)( 93,559)( 94,560)( 95,557)( 96,558)
( 97,545)( 98,546)( 99,548)(100,547)(101,551)(102,552)(103,549)(104,550)
(105,537)(106,538)(107,540)(108,539)(109,543)(110,544)(111,541)(112,542)
(113,529)(114,530)(115,532)(116,531)(117,535)(118,536)(119,533)(120,534)
(121,602)(122,601)(123,603)(124,604)(125,608)(126,607)(127,606)(128,605)
(129,634)(130,633)(131,635)(132,636)(133,640)(134,639)(135,638)(136,637)
(137,626)(138,625)(139,627)(140,628)(141,632)(142,631)(143,630)(144,629)
(145,618)(146,617)(147,619)(148,620)(149,624)(150,623)(151,622)(152,621)
(153,610)(154,609)(155,611)(156,612)(157,616)(158,615)(159,614)(160,613)
(161,682)(162,681)(163,683)(164,684)(165,688)(166,687)(167,686)(168,685)
(169,714)(170,713)(171,715)(172,716)(173,720)(174,719)(175,718)(176,717)
(177,706)(178,705)(179,707)(180,708)(181,712)(182,711)(183,710)(184,709)
(185,698)(186,697)(187,699)(188,700)(189,704)(190,703)(191,702)(192,701)
(193,690)(194,689)(195,691)(196,692)(197,696)(198,695)(199,694)(200,693)
(201,642)(202,641)(203,643)(204,644)(205,648)(206,647)(207,646)(208,645)
(209,674)(210,673)(211,675)(212,676)(213,680)(214,679)(215,678)(216,677)
(217,666)(218,665)(219,667)(220,668)(221,672)(222,671)(223,670)(224,669)
(225,658)(226,657)(227,659)(228,660)(229,664)(230,663)(231,662)(232,661)
(233,650)(234,649)(235,651)(236,652)(237,656)(238,655)(239,654)(240,653)
(241,842)(242,841)(243,843)(244,844)(245,848)(246,847)(247,846)(248,845)
(249,874)(250,873)(251,875)(252,876)(253,880)(254,879)(255,878)(256,877)
(257,866)(258,865)(259,867)(260,868)(261,872)(262,871)(263,870)(264,869)
(265,858)(266,857)(267,859)(268,860)(269,864)(270,863)(271,862)(272,861)
(273,850)(274,849)(275,851)(276,852)(277,856)(278,855)(279,854)(280,853)
(281,922)(282,921)(283,923)(284,924)(285,928)(286,927)(287,926)(288,925)
(289,954)(290,953)(291,955)(292,956)(293,960)(294,959)(295,958)(296,957)
(297,946)(298,945)(299,947)(300,948)(301,952)(302,951)(303,950)(304,949)
(305,938)(306,937)(307,939)(308,940)(309,944)(310,943)(311,942)(312,941)
(313,930)(314,929)(315,931)(316,932)(317,936)(318,935)(319,934)(320,933)
(321,882)(322,881)(323,883)(324,884)(325,888)(326,887)(327,886)(328,885)
(329,914)(330,913)(331,915)(332,916)(333,920)(334,919)(335,918)(336,917)
(337,906)(338,905)(339,907)(340,908)(341,912)(342,911)(343,910)(344,909)
(345,898)(346,897)(347,899)(348,900)(349,904)(350,903)(351,902)(352,901)
(353,890)(354,889)(355,891)(356,892)(357,896)(358,895)(359,894)(360,893)
(361,722)(362,721)(363,723)(364,724)(365,728)(366,727)(367,726)(368,725)
(369,754)(370,753)(371,755)(372,756)(373,760)(374,759)(375,758)(376,757)
(377,746)(378,745)(379,747)(380,748)(381,752)(382,751)(383,750)(384,749)
(385,738)(386,737)(387,739)(388,740)(389,744)(390,743)(391,742)(392,741)
(393,730)(394,729)(395,731)(396,732)(397,736)(398,735)(399,734)(400,733)
(401,802)(402,801)(403,803)(404,804)(405,808)(406,807)(407,806)(408,805)
(409,834)(410,833)(411,835)(412,836)(413,840)(414,839)(415,838)(416,837)
(417,826)(418,825)(419,827)(420,828)(421,832)(422,831)(423,830)(424,829)
(425,818)(426,817)(427,819)(428,820)(429,824)(430,823)(431,822)(432,821)
(433,810)(434,809)(435,811)(436,812)(437,816)(438,815)(439,814)(440,813)
(441,762)(442,761)(443,763)(444,764)(445,768)(446,767)(447,766)(448,765)
(449,794)(450,793)(451,795)(452,796)(453,800)(454,799)(455,798)(456,797)
(457,786)(458,785)(459,787)(460,788)(461,792)(462,791)(463,790)(464,789)
(465,778)(466,777)(467,779)(468,780)(469,784)(470,783)(471,782)(472,781)
(473,770)(474,769)(475,771)(476,772)(477,776)(478,775)(479,774)(480,773);;
s1 := ( 1,289)( 2,290)( 3,295)( 4,296)( 5,294)( 6,293)( 7,291)( 8,292)
( 9,281)( 10,282)( 11,287)( 12,288)( 13,286)( 14,285)( 15,283)( 16,284)
( 17,313)( 18,314)( 19,319)( 20,320)( 21,318)( 22,317)( 23,315)( 24,316)
( 25,305)( 26,306)( 27,311)( 28,312)( 29,310)( 30,309)( 31,307)( 32,308)
( 33,297)( 34,298)( 35,303)( 36,304)( 37,302)( 38,301)( 39,299)( 40,300)
( 41,249)( 42,250)( 43,255)( 44,256)( 45,254)( 46,253)( 47,251)( 48,252)
( 49,241)( 50,242)( 51,247)( 52,248)( 53,246)( 54,245)( 55,243)( 56,244)
( 57,273)( 58,274)( 59,279)( 60,280)( 61,278)( 62,277)( 63,275)( 64,276)
( 65,265)( 66,266)( 67,271)( 68,272)( 69,270)( 70,269)( 71,267)( 72,268)
( 73,257)( 74,258)( 75,263)( 76,264)( 77,262)( 78,261)( 79,259)( 80,260)
( 81,329)( 82,330)( 83,335)( 84,336)( 85,334)( 86,333)( 87,331)( 88,332)
( 89,321)( 90,322)( 91,327)( 92,328)( 93,326)( 94,325)( 95,323)( 96,324)
( 97,353)( 98,354)( 99,359)(100,360)(101,358)(102,357)(103,355)(104,356)
(105,345)(106,346)(107,351)(108,352)(109,350)(110,349)(111,347)(112,348)
(113,337)(114,338)(115,343)(116,344)(117,342)(118,341)(119,339)(120,340)
(121,410)(122,409)(123,416)(124,415)(125,413)(126,414)(127,412)(128,411)
(129,402)(130,401)(131,408)(132,407)(133,405)(134,406)(135,404)(136,403)
(137,434)(138,433)(139,440)(140,439)(141,437)(142,438)(143,436)(144,435)
(145,426)(146,425)(147,432)(148,431)(149,429)(150,430)(151,428)(152,427)
(153,418)(154,417)(155,424)(156,423)(157,421)(158,422)(159,420)(160,419)
(161,370)(162,369)(163,376)(164,375)(165,373)(166,374)(167,372)(168,371)
(169,362)(170,361)(171,368)(172,367)(173,365)(174,366)(175,364)(176,363)
(177,394)(178,393)(179,400)(180,399)(181,397)(182,398)(183,396)(184,395)
(185,386)(186,385)(187,392)(188,391)(189,389)(190,390)(191,388)(192,387)
(193,378)(194,377)(195,384)(196,383)(197,381)(198,382)(199,380)(200,379)
(201,450)(202,449)(203,456)(204,455)(205,453)(206,454)(207,452)(208,451)
(209,442)(210,441)(211,448)(212,447)(213,445)(214,446)(215,444)(216,443)
(217,474)(218,473)(219,480)(220,479)(221,477)(222,478)(223,476)(224,475)
(225,466)(226,465)(227,472)(228,471)(229,469)(230,470)(231,468)(232,467)
(233,458)(234,457)(235,464)(236,463)(237,461)(238,462)(239,460)(240,459)
(481,770)(482,769)(483,776)(484,775)(485,773)(486,774)(487,772)(488,771)
(489,762)(490,761)(491,768)(492,767)(493,765)(494,766)(495,764)(496,763)
(497,794)(498,793)(499,800)(500,799)(501,797)(502,798)(503,796)(504,795)
(505,786)(506,785)(507,792)(508,791)(509,789)(510,790)(511,788)(512,787)
(513,778)(514,777)(515,784)(516,783)(517,781)(518,782)(519,780)(520,779)
(521,730)(522,729)(523,736)(524,735)(525,733)(526,734)(527,732)(528,731)
(529,722)(530,721)(531,728)(532,727)(533,725)(534,726)(535,724)(536,723)
(537,754)(538,753)(539,760)(540,759)(541,757)(542,758)(543,756)(544,755)
(545,746)(546,745)(547,752)(548,751)(549,749)(550,750)(551,748)(552,747)
(553,738)(554,737)(555,744)(556,743)(557,741)(558,742)(559,740)(560,739)
(561,810)(562,809)(563,816)(564,815)(565,813)(566,814)(567,812)(568,811)
(569,802)(570,801)(571,808)(572,807)(573,805)(574,806)(575,804)(576,803)
(577,834)(578,833)(579,840)(580,839)(581,837)(582,838)(583,836)(584,835)
(585,826)(586,825)(587,832)(588,831)(589,829)(590,830)(591,828)(592,827)
(593,818)(594,817)(595,824)(596,823)(597,821)(598,822)(599,820)(600,819)
(601,889)(602,890)(603,895)(604,896)(605,894)(606,893)(607,891)(608,892)
(609,881)(610,882)(611,887)(612,888)(613,886)(614,885)(615,883)(616,884)
(617,913)(618,914)(619,919)(620,920)(621,918)(622,917)(623,915)(624,916)
(625,905)(626,906)(627,911)(628,912)(629,910)(630,909)(631,907)(632,908)
(633,897)(634,898)(635,903)(636,904)(637,902)(638,901)(639,899)(640,900)
(641,849)(642,850)(643,855)(644,856)(645,854)(646,853)(647,851)(648,852)
(649,841)(650,842)(651,847)(652,848)(653,846)(654,845)(655,843)(656,844)
(657,873)(658,874)(659,879)(660,880)(661,878)(662,877)(663,875)(664,876)
(665,865)(666,866)(667,871)(668,872)(669,870)(670,869)(671,867)(672,868)
(673,857)(674,858)(675,863)(676,864)(677,862)(678,861)(679,859)(680,860)
(681,929)(682,930)(683,935)(684,936)(685,934)(686,933)(687,931)(688,932)
(689,921)(690,922)(691,927)(692,928)(693,926)(694,925)(695,923)(696,924)
(697,953)(698,954)(699,959)(700,960)(701,958)(702,957)(703,955)(704,956)
(705,945)(706,946)(707,951)(708,952)(709,950)(710,949)(711,947)(712,948)
(713,937)(714,938)(715,943)(716,944)(717,942)(718,941)(719,939)(720,940);;
s2 := ( 1,483)( 2,484)( 3,482)( 4,481)( 5,487)( 6,488)( 7,486)( 8,485)
( 9,491)( 10,492)( 11,490)( 12,489)( 13,495)( 14,496)( 15,494)( 16,493)
( 17,499)( 18,500)( 19,498)( 20,497)( 21,503)( 22,504)( 23,502)( 24,501)
( 25,507)( 26,508)( 27,506)( 28,505)( 29,511)( 30,512)( 31,510)( 32,509)
( 33,515)( 34,516)( 35,514)( 36,513)( 37,519)( 38,520)( 39,518)( 40,517)
( 41,523)( 42,524)( 43,522)( 44,521)( 45,527)( 46,528)( 47,526)( 48,525)
( 49,531)( 50,532)( 51,530)( 52,529)( 53,535)( 54,536)( 55,534)( 56,533)
( 57,539)( 58,540)( 59,538)( 60,537)( 61,543)( 62,544)( 63,542)( 64,541)
( 65,547)( 66,548)( 67,546)( 68,545)( 69,551)( 70,552)( 71,550)( 72,549)
( 73,555)( 74,556)( 75,554)( 76,553)( 77,559)( 78,560)( 79,558)( 80,557)
( 81,563)( 82,564)( 83,562)( 84,561)( 85,567)( 86,568)( 87,566)( 88,565)
( 89,571)( 90,572)( 91,570)( 92,569)( 93,575)( 94,576)( 95,574)( 96,573)
( 97,579)( 98,580)( 99,578)(100,577)(101,583)(102,584)(103,582)(104,581)
(105,587)(106,588)(107,586)(108,585)(109,591)(110,592)(111,590)(112,589)
(113,595)(114,596)(115,594)(116,593)(117,599)(118,600)(119,598)(120,597)
(121,604)(122,603)(123,601)(124,602)(125,608)(126,607)(127,605)(128,606)
(129,612)(130,611)(131,609)(132,610)(133,616)(134,615)(135,613)(136,614)
(137,620)(138,619)(139,617)(140,618)(141,624)(142,623)(143,621)(144,622)
(145,628)(146,627)(147,625)(148,626)(149,632)(150,631)(151,629)(152,630)
(153,636)(154,635)(155,633)(156,634)(157,640)(158,639)(159,637)(160,638)
(161,644)(162,643)(163,641)(164,642)(165,648)(166,647)(167,645)(168,646)
(169,652)(170,651)(171,649)(172,650)(173,656)(174,655)(175,653)(176,654)
(177,660)(178,659)(179,657)(180,658)(181,664)(182,663)(183,661)(184,662)
(185,668)(186,667)(187,665)(188,666)(189,672)(190,671)(191,669)(192,670)
(193,676)(194,675)(195,673)(196,674)(197,680)(198,679)(199,677)(200,678)
(201,684)(202,683)(203,681)(204,682)(205,688)(206,687)(207,685)(208,686)
(209,692)(210,691)(211,689)(212,690)(213,696)(214,695)(215,693)(216,694)
(217,700)(218,699)(219,697)(220,698)(221,704)(222,703)(223,701)(224,702)
(225,708)(226,707)(227,705)(228,706)(229,712)(230,711)(231,709)(232,710)
(233,716)(234,715)(235,713)(236,714)(237,720)(238,719)(239,717)(240,718)
(241,843)(242,844)(243,842)(244,841)(245,847)(246,848)(247,846)(248,845)
(249,851)(250,852)(251,850)(252,849)(253,855)(254,856)(255,854)(256,853)
(257,859)(258,860)(259,858)(260,857)(261,863)(262,864)(263,862)(264,861)
(265,867)(266,868)(267,866)(268,865)(269,871)(270,872)(271,870)(272,869)
(273,875)(274,876)(275,874)(276,873)(277,879)(278,880)(279,878)(280,877)
(281,883)(282,884)(283,882)(284,881)(285,887)(286,888)(287,886)(288,885)
(289,891)(290,892)(291,890)(292,889)(293,895)(294,896)(295,894)(296,893)
(297,899)(298,900)(299,898)(300,897)(301,903)(302,904)(303,902)(304,901)
(305,907)(306,908)(307,906)(308,905)(309,911)(310,912)(311,910)(312,909)
(313,915)(314,916)(315,914)(316,913)(317,919)(318,920)(319,918)(320,917)
(321,923)(322,924)(323,922)(324,921)(325,927)(326,928)(327,926)(328,925)
(329,931)(330,932)(331,930)(332,929)(333,935)(334,936)(335,934)(336,933)
(337,939)(338,940)(339,938)(340,937)(341,943)(342,944)(343,942)(344,941)
(345,947)(346,948)(347,946)(348,945)(349,951)(350,952)(351,950)(352,949)
(353,955)(354,956)(355,954)(356,953)(357,959)(358,960)(359,958)(360,957)
(361,723)(362,724)(363,722)(364,721)(365,727)(366,728)(367,726)(368,725)
(369,731)(370,732)(371,730)(372,729)(373,735)(374,736)(375,734)(376,733)
(377,739)(378,740)(379,738)(380,737)(381,743)(382,744)(383,742)(384,741)
(385,747)(386,748)(387,746)(388,745)(389,751)(390,752)(391,750)(392,749)
(393,755)(394,756)(395,754)(396,753)(397,759)(398,760)(399,758)(400,757)
(401,763)(402,764)(403,762)(404,761)(405,767)(406,768)(407,766)(408,765)
(409,771)(410,772)(411,770)(412,769)(413,775)(414,776)(415,774)(416,773)
(417,779)(418,780)(419,778)(420,777)(421,783)(422,784)(423,782)(424,781)
(425,787)(426,788)(427,786)(428,785)(429,791)(430,792)(431,790)(432,789)
(433,795)(434,796)(435,794)(436,793)(437,799)(438,800)(439,798)(440,797)
(441,803)(442,804)(443,802)(444,801)(445,807)(446,808)(447,806)(448,805)
(449,811)(450,812)(451,810)(452,809)(453,815)(454,816)(455,814)(456,813)
(457,819)(458,820)(459,818)(460,817)(461,823)(462,824)(463,822)(464,821)
(465,827)(466,828)(467,826)(468,825)(469,831)(470,832)(471,830)(472,829)
(473,835)(474,836)(475,834)(476,833)(477,839)(478,840)(479,838)(480,837);;
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*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*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*s2*s1*s0*s1*s0*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,481)( 2,482)( 3,484)( 4,483)( 5,487)( 6,488)( 7,485)
( 8,486)( 9,513)( 10,514)( 11,516)( 12,515)( 13,519)( 14,520)( 15,517)
( 16,518)( 17,505)( 18,506)( 19,508)( 20,507)( 21,511)( 22,512)( 23,509)
( 24,510)( 25,497)( 26,498)( 27,500)( 28,499)( 29,503)( 30,504)( 31,501)
( 32,502)( 33,489)( 34,490)( 35,492)( 36,491)( 37,495)( 38,496)( 39,493)
( 40,494)( 41,561)( 42,562)( 43,564)( 44,563)( 45,567)( 46,568)( 47,565)
( 48,566)( 49,593)( 50,594)( 51,596)( 52,595)( 53,599)( 54,600)( 55,597)
( 56,598)( 57,585)( 58,586)( 59,588)( 60,587)( 61,591)( 62,592)( 63,589)
( 64,590)( 65,577)( 66,578)( 67,580)( 68,579)( 69,583)( 70,584)( 71,581)
( 72,582)( 73,569)( 74,570)( 75,572)( 76,571)( 77,575)( 78,576)( 79,573)
( 80,574)( 81,521)( 82,522)( 83,524)( 84,523)( 85,527)( 86,528)( 87,525)
( 88,526)( 89,553)( 90,554)( 91,556)( 92,555)( 93,559)( 94,560)( 95,557)
( 96,558)( 97,545)( 98,546)( 99,548)(100,547)(101,551)(102,552)(103,549)
(104,550)(105,537)(106,538)(107,540)(108,539)(109,543)(110,544)(111,541)
(112,542)(113,529)(114,530)(115,532)(116,531)(117,535)(118,536)(119,533)
(120,534)(121,602)(122,601)(123,603)(124,604)(125,608)(126,607)(127,606)
(128,605)(129,634)(130,633)(131,635)(132,636)(133,640)(134,639)(135,638)
(136,637)(137,626)(138,625)(139,627)(140,628)(141,632)(142,631)(143,630)
(144,629)(145,618)(146,617)(147,619)(148,620)(149,624)(150,623)(151,622)
(152,621)(153,610)(154,609)(155,611)(156,612)(157,616)(158,615)(159,614)
(160,613)(161,682)(162,681)(163,683)(164,684)(165,688)(166,687)(167,686)
(168,685)(169,714)(170,713)(171,715)(172,716)(173,720)(174,719)(175,718)
(176,717)(177,706)(178,705)(179,707)(180,708)(181,712)(182,711)(183,710)
(184,709)(185,698)(186,697)(187,699)(188,700)(189,704)(190,703)(191,702)
(192,701)(193,690)(194,689)(195,691)(196,692)(197,696)(198,695)(199,694)
(200,693)(201,642)(202,641)(203,643)(204,644)(205,648)(206,647)(207,646)
(208,645)(209,674)(210,673)(211,675)(212,676)(213,680)(214,679)(215,678)
(216,677)(217,666)(218,665)(219,667)(220,668)(221,672)(222,671)(223,670)
(224,669)(225,658)(226,657)(227,659)(228,660)(229,664)(230,663)(231,662)
(232,661)(233,650)(234,649)(235,651)(236,652)(237,656)(238,655)(239,654)
(240,653)(241,842)(242,841)(243,843)(244,844)(245,848)(246,847)(247,846)
(248,845)(249,874)(250,873)(251,875)(252,876)(253,880)(254,879)(255,878)
(256,877)(257,866)(258,865)(259,867)(260,868)(261,872)(262,871)(263,870)
(264,869)(265,858)(266,857)(267,859)(268,860)(269,864)(270,863)(271,862)
(272,861)(273,850)(274,849)(275,851)(276,852)(277,856)(278,855)(279,854)
(280,853)(281,922)(282,921)(283,923)(284,924)(285,928)(286,927)(287,926)
(288,925)(289,954)(290,953)(291,955)(292,956)(293,960)(294,959)(295,958)
(296,957)(297,946)(298,945)(299,947)(300,948)(301,952)(302,951)(303,950)
(304,949)(305,938)(306,937)(307,939)(308,940)(309,944)(310,943)(311,942)
(312,941)(313,930)(314,929)(315,931)(316,932)(317,936)(318,935)(319,934)
(320,933)(321,882)(322,881)(323,883)(324,884)(325,888)(326,887)(327,886)
(328,885)(329,914)(330,913)(331,915)(332,916)(333,920)(334,919)(335,918)
(336,917)(337,906)(338,905)(339,907)(340,908)(341,912)(342,911)(343,910)
(344,909)(345,898)(346,897)(347,899)(348,900)(349,904)(350,903)(351,902)
(352,901)(353,890)(354,889)(355,891)(356,892)(357,896)(358,895)(359,894)
(360,893)(361,722)(362,721)(363,723)(364,724)(365,728)(366,727)(367,726)
(368,725)(369,754)(370,753)(371,755)(372,756)(373,760)(374,759)(375,758)
(376,757)(377,746)(378,745)(379,747)(380,748)(381,752)(382,751)(383,750)
(384,749)(385,738)(386,737)(387,739)(388,740)(389,744)(390,743)(391,742)
(392,741)(393,730)(394,729)(395,731)(396,732)(397,736)(398,735)(399,734)
(400,733)(401,802)(402,801)(403,803)(404,804)(405,808)(406,807)(407,806)
(408,805)(409,834)(410,833)(411,835)(412,836)(413,840)(414,839)(415,838)
(416,837)(417,826)(418,825)(419,827)(420,828)(421,832)(422,831)(423,830)
(424,829)(425,818)(426,817)(427,819)(428,820)(429,824)(430,823)(431,822)
(432,821)(433,810)(434,809)(435,811)(436,812)(437,816)(438,815)(439,814)
(440,813)(441,762)(442,761)(443,763)(444,764)(445,768)(446,767)(447,766)
(448,765)(449,794)(450,793)(451,795)(452,796)(453,800)(454,799)(455,798)
(456,797)(457,786)(458,785)(459,787)(460,788)(461,792)(462,791)(463,790)
(464,789)(465,778)(466,777)(467,779)(468,780)(469,784)(470,783)(471,782)
(472,781)(473,770)(474,769)(475,771)(476,772)(477,776)(478,775)(479,774)
(480,773);
s1 := Sym(960)!( 1,289)( 2,290)( 3,295)( 4,296)( 5,294)( 6,293)( 7,291)
( 8,292)( 9,281)( 10,282)( 11,287)( 12,288)( 13,286)( 14,285)( 15,283)
( 16,284)( 17,313)( 18,314)( 19,319)( 20,320)( 21,318)( 22,317)( 23,315)
( 24,316)( 25,305)( 26,306)( 27,311)( 28,312)( 29,310)( 30,309)( 31,307)
( 32,308)( 33,297)( 34,298)( 35,303)( 36,304)( 37,302)( 38,301)( 39,299)
( 40,300)( 41,249)( 42,250)( 43,255)( 44,256)( 45,254)( 46,253)( 47,251)
( 48,252)( 49,241)( 50,242)( 51,247)( 52,248)( 53,246)( 54,245)( 55,243)
( 56,244)( 57,273)( 58,274)( 59,279)( 60,280)( 61,278)( 62,277)( 63,275)
( 64,276)( 65,265)( 66,266)( 67,271)( 68,272)( 69,270)( 70,269)( 71,267)
( 72,268)( 73,257)( 74,258)( 75,263)( 76,264)( 77,262)( 78,261)( 79,259)
( 80,260)( 81,329)( 82,330)( 83,335)( 84,336)( 85,334)( 86,333)( 87,331)
( 88,332)( 89,321)( 90,322)( 91,327)( 92,328)( 93,326)( 94,325)( 95,323)
( 96,324)( 97,353)( 98,354)( 99,359)(100,360)(101,358)(102,357)(103,355)
(104,356)(105,345)(106,346)(107,351)(108,352)(109,350)(110,349)(111,347)
(112,348)(113,337)(114,338)(115,343)(116,344)(117,342)(118,341)(119,339)
(120,340)(121,410)(122,409)(123,416)(124,415)(125,413)(126,414)(127,412)
(128,411)(129,402)(130,401)(131,408)(132,407)(133,405)(134,406)(135,404)
(136,403)(137,434)(138,433)(139,440)(140,439)(141,437)(142,438)(143,436)
(144,435)(145,426)(146,425)(147,432)(148,431)(149,429)(150,430)(151,428)
(152,427)(153,418)(154,417)(155,424)(156,423)(157,421)(158,422)(159,420)
(160,419)(161,370)(162,369)(163,376)(164,375)(165,373)(166,374)(167,372)
(168,371)(169,362)(170,361)(171,368)(172,367)(173,365)(174,366)(175,364)
(176,363)(177,394)(178,393)(179,400)(180,399)(181,397)(182,398)(183,396)
(184,395)(185,386)(186,385)(187,392)(188,391)(189,389)(190,390)(191,388)
(192,387)(193,378)(194,377)(195,384)(196,383)(197,381)(198,382)(199,380)
(200,379)(201,450)(202,449)(203,456)(204,455)(205,453)(206,454)(207,452)
(208,451)(209,442)(210,441)(211,448)(212,447)(213,445)(214,446)(215,444)
(216,443)(217,474)(218,473)(219,480)(220,479)(221,477)(222,478)(223,476)
(224,475)(225,466)(226,465)(227,472)(228,471)(229,469)(230,470)(231,468)
(232,467)(233,458)(234,457)(235,464)(236,463)(237,461)(238,462)(239,460)
(240,459)(481,770)(482,769)(483,776)(484,775)(485,773)(486,774)(487,772)
(488,771)(489,762)(490,761)(491,768)(492,767)(493,765)(494,766)(495,764)
(496,763)(497,794)(498,793)(499,800)(500,799)(501,797)(502,798)(503,796)
(504,795)(505,786)(506,785)(507,792)(508,791)(509,789)(510,790)(511,788)
(512,787)(513,778)(514,777)(515,784)(516,783)(517,781)(518,782)(519,780)
(520,779)(521,730)(522,729)(523,736)(524,735)(525,733)(526,734)(527,732)
(528,731)(529,722)(530,721)(531,728)(532,727)(533,725)(534,726)(535,724)
(536,723)(537,754)(538,753)(539,760)(540,759)(541,757)(542,758)(543,756)
(544,755)(545,746)(546,745)(547,752)(548,751)(549,749)(550,750)(551,748)
(552,747)(553,738)(554,737)(555,744)(556,743)(557,741)(558,742)(559,740)
(560,739)(561,810)(562,809)(563,816)(564,815)(565,813)(566,814)(567,812)
(568,811)(569,802)(570,801)(571,808)(572,807)(573,805)(574,806)(575,804)
(576,803)(577,834)(578,833)(579,840)(580,839)(581,837)(582,838)(583,836)
(584,835)(585,826)(586,825)(587,832)(588,831)(589,829)(590,830)(591,828)
(592,827)(593,818)(594,817)(595,824)(596,823)(597,821)(598,822)(599,820)
(600,819)(601,889)(602,890)(603,895)(604,896)(605,894)(606,893)(607,891)
(608,892)(609,881)(610,882)(611,887)(612,888)(613,886)(614,885)(615,883)
(616,884)(617,913)(618,914)(619,919)(620,920)(621,918)(622,917)(623,915)
(624,916)(625,905)(626,906)(627,911)(628,912)(629,910)(630,909)(631,907)
(632,908)(633,897)(634,898)(635,903)(636,904)(637,902)(638,901)(639,899)
(640,900)(641,849)(642,850)(643,855)(644,856)(645,854)(646,853)(647,851)
(648,852)(649,841)(650,842)(651,847)(652,848)(653,846)(654,845)(655,843)
(656,844)(657,873)(658,874)(659,879)(660,880)(661,878)(662,877)(663,875)
(664,876)(665,865)(666,866)(667,871)(668,872)(669,870)(670,869)(671,867)
(672,868)(673,857)(674,858)(675,863)(676,864)(677,862)(678,861)(679,859)
(680,860)(681,929)(682,930)(683,935)(684,936)(685,934)(686,933)(687,931)
(688,932)(689,921)(690,922)(691,927)(692,928)(693,926)(694,925)(695,923)
(696,924)(697,953)(698,954)(699,959)(700,960)(701,958)(702,957)(703,955)
(704,956)(705,945)(706,946)(707,951)(708,952)(709,950)(710,949)(711,947)
(712,948)(713,937)(714,938)(715,943)(716,944)(717,942)(718,941)(719,939)
(720,940);
s2 := Sym(960)!( 1,483)( 2,484)( 3,482)( 4,481)( 5,487)( 6,488)( 7,486)
( 8,485)( 9,491)( 10,492)( 11,490)( 12,489)( 13,495)( 14,496)( 15,494)
( 16,493)( 17,499)( 18,500)( 19,498)( 20,497)( 21,503)( 22,504)( 23,502)
( 24,501)( 25,507)( 26,508)( 27,506)( 28,505)( 29,511)( 30,512)( 31,510)
( 32,509)( 33,515)( 34,516)( 35,514)( 36,513)( 37,519)( 38,520)( 39,518)
( 40,517)( 41,523)( 42,524)( 43,522)( 44,521)( 45,527)( 46,528)( 47,526)
( 48,525)( 49,531)( 50,532)( 51,530)( 52,529)( 53,535)( 54,536)( 55,534)
( 56,533)( 57,539)( 58,540)( 59,538)( 60,537)( 61,543)( 62,544)( 63,542)
( 64,541)( 65,547)( 66,548)( 67,546)( 68,545)( 69,551)( 70,552)( 71,550)
( 72,549)( 73,555)( 74,556)( 75,554)( 76,553)( 77,559)( 78,560)( 79,558)
( 80,557)( 81,563)( 82,564)( 83,562)( 84,561)( 85,567)( 86,568)( 87,566)
( 88,565)( 89,571)( 90,572)( 91,570)( 92,569)( 93,575)( 94,576)( 95,574)
( 96,573)( 97,579)( 98,580)( 99,578)(100,577)(101,583)(102,584)(103,582)
(104,581)(105,587)(106,588)(107,586)(108,585)(109,591)(110,592)(111,590)
(112,589)(113,595)(114,596)(115,594)(116,593)(117,599)(118,600)(119,598)
(120,597)(121,604)(122,603)(123,601)(124,602)(125,608)(126,607)(127,605)
(128,606)(129,612)(130,611)(131,609)(132,610)(133,616)(134,615)(135,613)
(136,614)(137,620)(138,619)(139,617)(140,618)(141,624)(142,623)(143,621)
(144,622)(145,628)(146,627)(147,625)(148,626)(149,632)(150,631)(151,629)
(152,630)(153,636)(154,635)(155,633)(156,634)(157,640)(158,639)(159,637)
(160,638)(161,644)(162,643)(163,641)(164,642)(165,648)(166,647)(167,645)
(168,646)(169,652)(170,651)(171,649)(172,650)(173,656)(174,655)(175,653)
(176,654)(177,660)(178,659)(179,657)(180,658)(181,664)(182,663)(183,661)
(184,662)(185,668)(186,667)(187,665)(188,666)(189,672)(190,671)(191,669)
(192,670)(193,676)(194,675)(195,673)(196,674)(197,680)(198,679)(199,677)
(200,678)(201,684)(202,683)(203,681)(204,682)(205,688)(206,687)(207,685)
(208,686)(209,692)(210,691)(211,689)(212,690)(213,696)(214,695)(215,693)
(216,694)(217,700)(218,699)(219,697)(220,698)(221,704)(222,703)(223,701)
(224,702)(225,708)(226,707)(227,705)(228,706)(229,712)(230,711)(231,709)
(232,710)(233,716)(234,715)(235,713)(236,714)(237,720)(238,719)(239,717)
(240,718)(241,843)(242,844)(243,842)(244,841)(245,847)(246,848)(247,846)
(248,845)(249,851)(250,852)(251,850)(252,849)(253,855)(254,856)(255,854)
(256,853)(257,859)(258,860)(259,858)(260,857)(261,863)(262,864)(263,862)
(264,861)(265,867)(266,868)(267,866)(268,865)(269,871)(270,872)(271,870)
(272,869)(273,875)(274,876)(275,874)(276,873)(277,879)(278,880)(279,878)
(280,877)(281,883)(282,884)(283,882)(284,881)(285,887)(286,888)(287,886)
(288,885)(289,891)(290,892)(291,890)(292,889)(293,895)(294,896)(295,894)
(296,893)(297,899)(298,900)(299,898)(300,897)(301,903)(302,904)(303,902)
(304,901)(305,907)(306,908)(307,906)(308,905)(309,911)(310,912)(311,910)
(312,909)(313,915)(314,916)(315,914)(316,913)(317,919)(318,920)(319,918)
(320,917)(321,923)(322,924)(323,922)(324,921)(325,927)(326,928)(327,926)
(328,925)(329,931)(330,932)(331,930)(332,929)(333,935)(334,936)(335,934)
(336,933)(337,939)(338,940)(339,938)(340,937)(341,943)(342,944)(343,942)
(344,941)(345,947)(346,948)(347,946)(348,945)(349,951)(350,952)(351,950)
(352,949)(353,955)(354,956)(355,954)(356,953)(357,959)(358,960)(359,958)
(360,957)(361,723)(362,724)(363,722)(364,721)(365,727)(366,728)(367,726)
(368,725)(369,731)(370,732)(371,730)(372,729)(373,735)(374,736)(375,734)
(376,733)(377,739)(378,740)(379,738)(380,737)(381,743)(382,744)(383,742)
(384,741)(385,747)(386,748)(387,746)(388,745)(389,751)(390,752)(391,750)
(392,749)(393,755)(394,756)(395,754)(396,753)(397,759)(398,760)(399,758)
(400,757)(401,763)(402,764)(403,762)(404,761)(405,767)(406,768)(407,766)
(408,765)(409,771)(410,772)(411,770)(412,769)(413,775)(414,776)(415,774)
(416,773)(417,779)(418,780)(419,778)(420,777)(421,783)(422,784)(423,782)
(424,781)(425,787)(426,788)(427,786)(428,785)(429,791)(430,792)(431,790)
(432,789)(433,795)(434,796)(435,794)(436,793)(437,799)(438,800)(439,798)
(440,797)(441,803)(442,804)(443,802)(444,801)(445,807)(446,808)(447,806)
(448,805)(449,811)(450,812)(451,810)(452,809)(453,815)(454,816)(455,814)
(456,813)(457,819)(458,820)(459,818)(460,817)(461,823)(462,824)(463,822)
(464,821)(465,827)(466,828)(467,826)(468,825)(469,831)(470,832)(471,830)
(472,829)(473,835)(474,836)(475,834)(476,833)(477,839)(478,840)(479,838)
(480,837);
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*s2*s1*s2*s1*s0*s1*s0*s1*s0*s2*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*s2*s1*s0*s1*s0*s1*s0*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 >;
References : None.
to this polytope