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Polytope of Type {30,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,8}*1920d
if this polytope has a name.
Group : SmallGroup(1920,239473)
Rank : 3
Schlafli Type : {30,8}
Number of vertices, edges, etc : 120, 480, 32
Order of s0s1s2 : 30
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 : {30,8}*960a
   4-fold quotients : {30,4}*480
   5-fold quotients : {6,8}*384d
   8-fold quotients : {15,4}*240, {30,4}*240b, {30,4}*240c
   10-fold quotients : {6,8}*192a
   16-fold quotients : {15,4}*120, {30,2}*120
   20-fold quotients : {6,4}*96
   32-fold quotients : {15,2}*60
   40-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {10,2}*40
   80-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {5,2}*20
   160-fold quotients : {3,2}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  3,  4)(  5,  6)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 65)( 18, 66)
( 19, 68)( 20, 67)( 21, 70)( 22, 69)( 23, 71)( 24, 72)( 25, 77)( 26, 78)
( 27, 80)( 28, 79)( 29, 73)( 30, 74)( 31, 76)( 32, 75)( 33, 49)( 34, 50)
( 35, 52)( 36, 51)( 37, 54)( 38, 53)( 39, 55)( 40, 56)( 41, 61)( 42, 62)
( 43, 64)( 44, 63)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 81,161)( 82,162)
( 83,164)( 84,163)( 85,166)( 86,165)( 87,167)( 88,168)( 89,173)( 90,174)
( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,225)( 98,226)
( 99,228)(100,227)(101,230)(102,229)(103,231)(104,232)(105,237)(106,238)
(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)(113,209)(114,210)
(115,212)(116,211)(117,214)(118,213)(119,215)(120,216)(121,221)(122,222)
(123,224)(124,223)(125,217)(126,218)(127,220)(128,219)(129,193)(130,194)
(131,196)(132,195)(133,198)(134,197)(135,199)(136,200)(137,205)(138,206)
(139,208)(140,207)(141,201)(142,202)(143,204)(144,203)(145,177)(146,178)
(147,180)(148,179)(149,182)(150,181)(151,183)(152,184)(153,189)(154,190)
(155,192)(156,191)(157,185)(158,186)(159,188)(160,187)(243,244)(245,246)
(249,253)(250,254)(251,256)(252,255)(257,305)(258,306)(259,308)(260,307)
(261,310)(262,309)(263,311)(264,312)(265,317)(266,318)(267,320)(268,319)
(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)(275,292)(276,291)
(277,294)(278,293)(279,295)(280,296)(281,301)(282,302)(283,304)(284,303)
(285,297)(286,298)(287,300)(288,299)(321,401)(322,402)(323,404)(324,403)
(325,406)(326,405)(327,407)(328,408)(329,413)(330,414)(331,416)(332,415)
(333,409)(334,410)(335,412)(336,411)(337,465)(338,466)(339,468)(340,467)
(341,470)(342,469)(343,471)(344,472)(345,477)(346,478)(347,480)(348,479)
(349,473)(350,474)(351,476)(352,475)(353,449)(354,450)(355,452)(356,451)
(357,454)(358,453)(359,455)(360,456)(361,461)(362,462)(363,464)(364,463)
(365,457)(366,458)(367,460)(368,459)(369,433)(370,434)(371,436)(372,435)
(373,438)(374,437)(375,439)(376,440)(377,445)(378,446)(379,448)(380,447)
(381,441)(382,442)(383,444)(384,443)(385,417)(386,418)(387,420)(388,419)
(389,422)(390,421)(391,423)(392,424)(393,429)(394,430)(395,432)(396,431)
(397,425)(398,426)(399,428)(400,427)(483,484)(485,486)(489,493)(490,494)
(491,496)(492,495)(497,545)(498,546)(499,548)(500,547)(501,550)(502,549)
(503,551)(504,552)(505,557)(506,558)(507,560)(508,559)(509,553)(510,554)
(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)(517,534)(518,533)
(519,535)(520,536)(521,541)(522,542)(523,544)(524,543)(525,537)(526,538)
(527,540)(528,539)(561,641)(562,642)(563,644)(564,643)(565,646)(566,645)
(567,647)(568,648)(569,653)(570,654)(571,656)(572,655)(573,649)(574,650)
(575,652)(576,651)(577,705)(578,706)(579,708)(580,707)(581,710)(582,709)
(583,711)(584,712)(585,717)(586,718)(587,720)(588,719)(589,713)(590,714)
(591,716)(592,715)(593,689)(594,690)(595,692)(596,691)(597,694)(598,693)
(599,695)(600,696)(601,701)(602,702)(603,704)(604,703)(605,697)(606,698)
(607,700)(608,699)(609,673)(610,674)(611,676)(612,675)(613,678)(614,677)
(615,679)(616,680)(617,685)(618,686)(619,688)(620,687)(621,681)(622,682)
(623,684)(624,683)(625,657)(626,658)(627,660)(628,659)(629,662)(630,661)
(631,663)(632,664)(633,669)(634,670)(635,672)(636,671)(637,665)(638,666)
(639,668)(640,667)(723,724)(725,726)(729,733)(730,734)(731,736)(732,735)
(737,785)(738,786)(739,788)(740,787)(741,790)(742,789)(743,791)(744,792)
(745,797)(746,798)(747,800)(748,799)(749,793)(750,794)(751,796)(752,795)
(753,769)(754,770)(755,772)(756,771)(757,774)(758,773)(759,775)(760,776)
(761,781)(762,782)(763,784)(764,783)(765,777)(766,778)(767,780)(768,779)
(801,881)(802,882)(803,884)(804,883)(805,886)(806,885)(807,887)(808,888)
(809,893)(810,894)(811,896)(812,895)(813,889)(814,890)(815,892)(816,891)
(817,945)(818,946)(819,948)(820,947)(821,950)(822,949)(823,951)(824,952)
(825,957)(826,958)(827,960)(828,959)(829,953)(830,954)(831,956)(832,955)
(833,929)(834,930)(835,932)(836,931)(837,934)(838,933)(839,935)(840,936)
(841,941)(842,942)(843,944)(844,943)(845,937)(846,938)(847,940)(848,939)
(849,913)(850,914)(851,916)(852,915)(853,918)(854,917)(855,919)(856,920)
(857,925)(858,926)(859,928)(860,927)(861,921)(862,922)(863,924)(864,923)
(865,897)(866,898)(867,900)(868,899)(869,902)(870,901)(871,903)(872,904)
(873,909)(874,910)(875,912)(876,911)(877,905)(878,906)(879,908)(880,907);;
s1 := (  1,337)(  2,340)(  3,339)(  4,338)(  5,351)(  6,350)(  7,349)(  8,352)
(  9,347)( 10,346)( 11,345)( 12,348)( 13,343)( 14,342)( 15,341)( 16,344)
( 17,321)( 18,324)( 19,323)( 20,322)( 21,335)( 22,334)( 23,333)( 24,336)
( 25,331)( 26,330)( 27,329)( 28,332)( 29,327)( 30,326)( 31,325)( 32,328)
( 33,385)( 34,388)( 35,387)( 36,386)( 37,399)( 38,398)( 39,397)( 40,400)
( 41,395)( 42,394)( 43,393)( 44,396)( 45,391)( 46,390)( 47,389)( 48,392)
( 49,369)( 50,372)( 51,371)( 52,370)( 53,383)( 54,382)( 55,381)( 56,384)
( 57,379)( 58,378)( 59,377)( 60,380)( 61,375)( 62,374)( 63,373)( 64,376)
( 65,353)( 66,356)( 67,355)( 68,354)( 69,367)( 70,366)( 71,365)( 72,368)
( 73,363)( 74,362)( 75,361)( 76,364)( 77,359)( 78,358)( 79,357)( 80,360)
( 81,257)( 82,260)( 83,259)( 84,258)( 85,271)( 86,270)( 87,269)( 88,272)
( 89,267)( 90,266)( 91,265)( 92,268)( 93,263)( 94,262)( 95,261)( 96,264)
( 97,241)( 98,244)( 99,243)(100,242)(101,255)(102,254)(103,253)(104,256)
(105,251)(106,250)(107,249)(108,252)(109,247)(110,246)(111,245)(112,248)
(113,305)(114,308)(115,307)(116,306)(117,319)(118,318)(119,317)(120,320)
(121,315)(122,314)(123,313)(124,316)(125,311)(126,310)(127,309)(128,312)
(129,289)(130,292)(131,291)(132,290)(133,303)(134,302)(135,301)(136,304)
(137,299)(138,298)(139,297)(140,300)(141,295)(142,294)(143,293)(144,296)
(145,273)(146,276)(147,275)(148,274)(149,287)(150,286)(151,285)(152,288)
(153,283)(154,282)(155,281)(156,284)(157,279)(158,278)(159,277)(160,280)
(161,417)(162,420)(163,419)(164,418)(165,431)(166,430)(167,429)(168,432)
(169,427)(170,426)(171,425)(172,428)(173,423)(174,422)(175,421)(176,424)
(177,401)(178,404)(179,403)(180,402)(181,415)(182,414)(183,413)(184,416)
(185,411)(186,410)(187,409)(188,412)(189,407)(190,406)(191,405)(192,408)
(193,465)(194,468)(195,467)(196,466)(197,479)(198,478)(199,477)(200,480)
(201,475)(202,474)(203,473)(204,476)(205,471)(206,470)(207,469)(208,472)
(209,449)(210,452)(211,451)(212,450)(213,463)(214,462)(215,461)(216,464)
(217,459)(218,458)(219,457)(220,460)(221,455)(222,454)(223,453)(224,456)
(225,433)(226,436)(227,435)(228,434)(229,447)(230,446)(231,445)(232,448)
(233,443)(234,442)(235,441)(236,444)(237,439)(238,438)(239,437)(240,440)
(481,817)(482,820)(483,819)(484,818)(485,831)(486,830)(487,829)(488,832)
(489,827)(490,826)(491,825)(492,828)(493,823)(494,822)(495,821)(496,824)
(497,801)(498,804)(499,803)(500,802)(501,815)(502,814)(503,813)(504,816)
(505,811)(506,810)(507,809)(508,812)(509,807)(510,806)(511,805)(512,808)
(513,865)(514,868)(515,867)(516,866)(517,879)(518,878)(519,877)(520,880)
(521,875)(522,874)(523,873)(524,876)(525,871)(526,870)(527,869)(528,872)
(529,849)(530,852)(531,851)(532,850)(533,863)(534,862)(535,861)(536,864)
(537,859)(538,858)(539,857)(540,860)(541,855)(542,854)(543,853)(544,856)
(545,833)(546,836)(547,835)(548,834)(549,847)(550,846)(551,845)(552,848)
(553,843)(554,842)(555,841)(556,844)(557,839)(558,838)(559,837)(560,840)
(561,737)(562,740)(563,739)(564,738)(565,751)(566,750)(567,749)(568,752)
(569,747)(570,746)(571,745)(572,748)(573,743)(574,742)(575,741)(576,744)
(577,721)(578,724)(579,723)(580,722)(581,735)(582,734)(583,733)(584,736)
(585,731)(586,730)(587,729)(588,732)(589,727)(590,726)(591,725)(592,728)
(593,785)(594,788)(595,787)(596,786)(597,799)(598,798)(599,797)(600,800)
(601,795)(602,794)(603,793)(604,796)(605,791)(606,790)(607,789)(608,792)
(609,769)(610,772)(611,771)(612,770)(613,783)(614,782)(615,781)(616,784)
(617,779)(618,778)(619,777)(620,780)(621,775)(622,774)(623,773)(624,776)
(625,753)(626,756)(627,755)(628,754)(629,767)(630,766)(631,765)(632,768)
(633,763)(634,762)(635,761)(636,764)(637,759)(638,758)(639,757)(640,760)
(641,897)(642,900)(643,899)(644,898)(645,911)(646,910)(647,909)(648,912)
(649,907)(650,906)(651,905)(652,908)(653,903)(654,902)(655,901)(656,904)
(657,881)(658,884)(659,883)(660,882)(661,895)(662,894)(663,893)(664,896)
(665,891)(666,890)(667,889)(668,892)(669,887)(670,886)(671,885)(672,888)
(673,945)(674,948)(675,947)(676,946)(677,959)(678,958)(679,957)(680,960)
(681,955)(682,954)(683,953)(684,956)(685,951)(686,950)(687,949)(688,952)
(689,929)(690,932)(691,931)(692,930)(693,943)(694,942)(695,941)(696,944)
(697,939)(698,938)(699,937)(700,940)(701,935)(702,934)(703,933)(704,936)
(705,913)(706,916)(707,915)(708,914)(709,927)(710,926)(711,925)(712,928)
(713,923)(714,922)(715,921)(716,924)(717,919)(718,918)(719,917)(720,920);;
s2 := (  1,727)(  2,728)(  3,725)(  4,726)(  5,723)(  6,724)(  7,721)(  8,722)
(  9,733)( 10,734)( 11,735)( 12,736)( 13,729)( 14,730)( 15,731)( 16,732)
( 17,743)( 18,744)( 19,741)( 20,742)( 21,739)( 22,740)( 23,737)( 24,738)
( 25,749)( 26,750)( 27,751)( 28,752)( 29,745)( 30,746)( 31,747)( 32,748)
( 33,759)( 34,760)( 35,757)( 36,758)( 37,755)( 38,756)( 39,753)( 40,754)
( 41,765)( 42,766)( 43,767)( 44,768)( 45,761)( 46,762)( 47,763)( 48,764)
( 49,775)( 50,776)( 51,773)( 52,774)( 53,771)( 54,772)( 55,769)( 56,770)
( 57,781)( 58,782)( 59,783)( 60,784)( 61,777)( 62,778)( 63,779)( 64,780)
( 65,791)( 66,792)( 67,789)( 68,790)( 69,787)( 70,788)( 71,785)( 72,786)
( 73,797)( 74,798)( 75,799)( 76,800)( 77,793)( 78,794)( 79,795)( 80,796)
( 81,807)( 82,808)( 83,805)( 84,806)( 85,803)( 86,804)( 87,801)( 88,802)
( 89,813)( 90,814)( 91,815)( 92,816)( 93,809)( 94,810)( 95,811)( 96,812)
( 97,823)( 98,824)( 99,821)(100,822)(101,819)(102,820)(103,817)(104,818)
(105,829)(106,830)(107,831)(108,832)(109,825)(110,826)(111,827)(112,828)
(113,839)(114,840)(115,837)(116,838)(117,835)(118,836)(119,833)(120,834)
(121,845)(122,846)(123,847)(124,848)(125,841)(126,842)(127,843)(128,844)
(129,855)(130,856)(131,853)(132,854)(133,851)(134,852)(135,849)(136,850)
(137,861)(138,862)(139,863)(140,864)(141,857)(142,858)(143,859)(144,860)
(145,871)(146,872)(147,869)(148,870)(149,867)(150,868)(151,865)(152,866)
(153,877)(154,878)(155,879)(156,880)(157,873)(158,874)(159,875)(160,876)
(161,887)(162,888)(163,885)(164,886)(165,883)(166,884)(167,881)(168,882)
(169,893)(170,894)(171,895)(172,896)(173,889)(174,890)(175,891)(176,892)
(177,903)(178,904)(179,901)(180,902)(181,899)(182,900)(183,897)(184,898)
(185,909)(186,910)(187,911)(188,912)(189,905)(190,906)(191,907)(192,908)
(193,919)(194,920)(195,917)(196,918)(197,915)(198,916)(199,913)(200,914)
(201,925)(202,926)(203,927)(204,928)(205,921)(206,922)(207,923)(208,924)
(209,935)(210,936)(211,933)(212,934)(213,931)(214,932)(215,929)(216,930)
(217,941)(218,942)(219,943)(220,944)(221,937)(222,938)(223,939)(224,940)
(225,951)(226,952)(227,949)(228,950)(229,947)(230,948)(231,945)(232,946)
(233,957)(234,958)(235,959)(236,960)(237,953)(238,954)(239,955)(240,956)
(241,487)(242,488)(243,485)(244,486)(245,483)(246,484)(247,481)(248,482)
(249,493)(250,494)(251,495)(252,496)(253,489)(254,490)(255,491)(256,492)
(257,503)(258,504)(259,501)(260,502)(261,499)(262,500)(263,497)(264,498)
(265,509)(266,510)(267,511)(268,512)(269,505)(270,506)(271,507)(272,508)
(273,519)(274,520)(275,517)(276,518)(277,515)(278,516)(279,513)(280,514)
(281,525)(282,526)(283,527)(284,528)(285,521)(286,522)(287,523)(288,524)
(289,535)(290,536)(291,533)(292,534)(293,531)(294,532)(295,529)(296,530)
(297,541)(298,542)(299,543)(300,544)(301,537)(302,538)(303,539)(304,540)
(305,551)(306,552)(307,549)(308,550)(309,547)(310,548)(311,545)(312,546)
(313,557)(314,558)(315,559)(316,560)(317,553)(318,554)(319,555)(320,556)
(321,567)(322,568)(323,565)(324,566)(325,563)(326,564)(327,561)(328,562)
(329,573)(330,574)(331,575)(332,576)(333,569)(334,570)(335,571)(336,572)
(337,583)(338,584)(339,581)(340,582)(341,579)(342,580)(343,577)(344,578)
(345,589)(346,590)(347,591)(348,592)(349,585)(350,586)(351,587)(352,588)
(353,599)(354,600)(355,597)(356,598)(357,595)(358,596)(359,593)(360,594)
(361,605)(362,606)(363,607)(364,608)(365,601)(366,602)(367,603)(368,604)
(369,615)(370,616)(371,613)(372,614)(373,611)(374,612)(375,609)(376,610)
(377,621)(378,622)(379,623)(380,624)(381,617)(382,618)(383,619)(384,620)
(385,631)(386,632)(387,629)(388,630)(389,627)(390,628)(391,625)(392,626)
(393,637)(394,638)(395,639)(396,640)(397,633)(398,634)(399,635)(400,636)
(401,647)(402,648)(403,645)(404,646)(405,643)(406,644)(407,641)(408,642)
(409,653)(410,654)(411,655)(412,656)(413,649)(414,650)(415,651)(416,652)
(417,663)(418,664)(419,661)(420,662)(421,659)(422,660)(423,657)(424,658)
(425,669)(426,670)(427,671)(428,672)(429,665)(430,666)(431,667)(432,668)
(433,679)(434,680)(435,677)(436,678)(437,675)(438,676)(439,673)(440,674)
(441,685)(442,686)(443,687)(444,688)(445,681)(446,682)(447,683)(448,684)
(449,695)(450,696)(451,693)(452,694)(453,691)(454,692)(455,689)(456,690)
(457,701)(458,702)(459,703)(460,704)(461,697)(462,698)(463,699)(464,700)
(465,711)(466,712)(467,709)(468,710)(469,707)(470,708)(471,705)(472,706)
(473,717)(474,718)(475,719)(476,720)(477,713)(478,714)(479,715)(480,716);;
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(960)!(  3,  4)(  5,  6)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 65)
( 18, 66)( 19, 68)( 20, 67)( 21, 70)( 22, 69)( 23, 71)( 24, 72)( 25, 77)
( 26, 78)( 27, 80)( 28, 79)( 29, 73)( 30, 74)( 31, 76)( 32, 75)( 33, 49)
( 34, 50)( 35, 52)( 36, 51)( 37, 54)( 38, 53)( 39, 55)( 40, 56)( 41, 61)
( 42, 62)( 43, 64)( 44, 63)( 45, 57)( 46, 58)( 47, 60)( 48, 59)( 81,161)
( 82,162)( 83,164)( 84,163)( 85,166)( 86,165)( 87,167)( 88,168)( 89,173)
( 90,174)( 91,176)( 92,175)( 93,169)( 94,170)( 95,172)( 96,171)( 97,225)
( 98,226)( 99,228)(100,227)(101,230)(102,229)(103,231)(104,232)(105,237)
(106,238)(107,240)(108,239)(109,233)(110,234)(111,236)(112,235)(113,209)
(114,210)(115,212)(116,211)(117,214)(118,213)(119,215)(120,216)(121,221)
(122,222)(123,224)(124,223)(125,217)(126,218)(127,220)(128,219)(129,193)
(130,194)(131,196)(132,195)(133,198)(134,197)(135,199)(136,200)(137,205)
(138,206)(139,208)(140,207)(141,201)(142,202)(143,204)(144,203)(145,177)
(146,178)(147,180)(148,179)(149,182)(150,181)(151,183)(152,184)(153,189)
(154,190)(155,192)(156,191)(157,185)(158,186)(159,188)(160,187)(243,244)
(245,246)(249,253)(250,254)(251,256)(252,255)(257,305)(258,306)(259,308)
(260,307)(261,310)(262,309)(263,311)(264,312)(265,317)(266,318)(267,320)
(268,319)(269,313)(270,314)(271,316)(272,315)(273,289)(274,290)(275,292)
(276,291)(277,294)(278,293)(279,295)(280,296)(281,301)(282,302)(283,304)
(284,303)(285,297)(286,298)(287,300)(288,299)(321,401)(322,402)(323,404)
(324,403)(325,406)(326,405)(327,407)(328,408)(329,413)(330,414)(331,416)
(332,415)(333,409)(334,410)(335,412)(336,411)(337,465)(338,466)(339,468)
(340,467)(341,470)(342,469)(343,471)(344,472)(345,477)(346,478)(347,480)
(348,479)(349,473)(350,474)(351,476)(352,475)(353,449)(354,450)(355,452)
(356,451)(357,454)(358,453)(359,455)(360,456)(361,461)(362,462)(363,464)
(364,463)(365,457)(366,458)(367,460)(368,459)(369,433)(370,434)(371,436)
(372,435)(373,438)(374,437)(375,439)(376,440)(377,445)(378,446)(379,448)
(380,447)(381,441)(382,442)(383,444)(384,443)(385,417)(386,418)(387,420)
(388,419)(389,422)(390,421)(391,423)(392,424)(393,429)(394,430)(395,432)
(396,431)(397,425)(398,426)(399,428)(400,427)(483,484)(485,486)(489,493)
(490,494)(491,496)(492,495)(497,545)(498,546)(499,548)(500,547)(501,550)
(502,549)(503,551)(504,552)(505,557)(506,558)(507,560)(508,559)(509,553)
(510,554)(511,556)(512,555)(513,529)(514,530)(515,532)(516,531)(517,534)
(518,533)(519,535)(520,536)(521,541)(522,542)(523,544)(524,543)(525,537)
(526,538)(527,540)(528,539)(561,641)(562,642)(563,644)(564,643)(565,646)
(566,645)(567,647)(568,648)(569,653)(570,654)(571,656)(572,655)(573,649)
(574,650)(575,652)(576,651)(577,705)(578,706)(579,708)(580,707)(581,710)
(582,709)(583,711)(584,712)(585,717)(586,718)(587,720)(588,719)(589,713)
(590,714)(591,716)(592,715)(593,689)(594,690)(595,692)(596,691)(597,694)
(598,693)(599,695)(600,696)(601,701)(602,702)(603,704)(604,703)(605,697)
(606,698)(607,700)(608,699)(609,673)(610,674)(611,676)(612,675)(613,678)
(614,677)(615,679)(616,680)(617,685)(618,686)(619,688)(620,687)(621,681)
(622,682)(623,684)(624,683)(625,657)(626,658)(627,660)(628,659)(629,662)
(630,661)(631,663)(632,664)(633,669)(634,670)(635,672)(636,671)(637,665)
(638,666)(639,668)(640,667)(723,724)(725,726)(729,733)(730,734)(731,736)
(732,735)(737,785)(738,786)(739,788)(740,787)(741,790)(742,789)(743,791)
(744,792)(745,797)(746,798)(747,800)(748,799)(749,793)(750,794)(751,796)
(752,795)(753,769)(754,770)(755,772)(756,771)(757,774)(758,773)(759,775)
(760,776)(761,781)(762,782)(763,784)(764,783)(765,777)(766,778)(767,780)
(768,779)(801,881)(802,882)(803,884)(804,883)(805,886)(806,885)(807,887)
(808,888)(809,893)(810,894)(811,896)(812,895)(813,889)(814,890)(815,892)
(816,891)(817,945)(818,946)(819,948)(820,947)(821,950)(822,949)(823,951)
(824,952)(825,957)(826,958)(827,960)(828,959)(829,953)(830,954)(831,956)
(832,955)(833,929)(834,930)(835,932)(836,931)(837,934)(838,933)(839,935)
(840,936)(841,941)(842,942)(843,944)(844,943)(845,937)(846,938)(847,940)
(848,939)(849,913)(850,914)(851,916)(852,915)(853,918)(854,917)(855,919)
(856,920)(857,925)(858,926)(859,928)(860,927)(861,921)(862,922)(863,924)
(864,923)(865,897)(866,898)(867,900)(868,899)(869,902)(870,901)(871,903)
(872,904)(873,909)(874,910)(875,912)(876,911)(877,905)(878,906)(879,908)
(880,907);
s1 := Sym(960)!(  1,337)(  2,340)(  3,339)(  4,338)(  5,351)(  6,350)(  7,349)
(  8,352)(  9,347)( 10,346)( 11,345)( 12,348)( 13,343)( 14,342)( 15,341)
( 16,344)( 17,321)( 18,324)( 19,323)( 20,322)( 21,335)( 22,334)( 23,333)
( 24,336)( 25,331)( 26,330)( 27,329)( 28,332)( 29,327)( 30,326)( 31,325)
( 32,328)( 33,385)( 34,388)( 35,387)( 36,386)( 37,399)( 38,398)( 39,397)
( 40,400)( 41,395)( 42,394)( 43,393)( 44,396)( 45,391)( 46,390)( 47,389)
( 48,392)( 49,369)( 50,372)( 51,371)( 52,370)( 53,383)( 54,382)( 55,381)
( 56,384)( 57,379)( 58,378)( 59,377)( 60,380)( 61,375)( 62,374)( 63,373)
( 64,376)( 65,353)( 66,356)( 67,355)( 68,354)( 69,367)( 70,366)( 71,365)
( 72,368)( 73,363)( 74,362)( 75,361)( 76,364)( 77,359)( 78,358)( 79,357)
( 80,360)( 81,257)( 82,260)( 83,259)( 84,258)( 85,271)( 86,270)( 87,269)
( 88,272)( 89,267)( 90,266)( 91,265)( 92,268)( 93,263)( 94,262)( 95,261)
( 96,264)( 97,241)( 98,244)( 99,243)(100,242)(101,255)(102,254)(103,253)
(104,256)(105,251)(106,250)(107,249)(108,252)(109,247)(110,246)(111,245)
(112,248)(113,305)(114,308)(115,307)(116,306)(117,319)(118,318)(119,317)
(120,320)(121,315)(122,314)(123,313)(124,316)(125,311)(126,310)(127,309)
(128,312)(129,289)(130,292)(131,291)(132,290)(133,303)(134,302)(135,301)
(136,304)(137,299)(138,298)(139,297)(140,300)(141,295)(142,294)(143,293)
(144,296)(145,273)(146,276)(147,275)(148,274)(149,287)(150,286)(151,285)
(152,288)(153,283)(154,282)(155,281)(156,284)(157,279)(158,278)(159,277)
(160,280)(161,417)(162,420)(163,419)(164,418)(165,431)(166,430)(167,429)
(168,432)(169,427)(170,426)(171,425)(172,428)(173,423)(174,422)(175,421)
(176,424)(177,401)(178,404)(179,403)(180,402)(181,415)(182,414)(183,413)
(184,416)(185,411)(186,410)(187,409)(188,412)(189,407)(190,406)(191,405)
(192,408)(193,465)(194,468)(195,467)(196,466)(197,479)(198,478)(199,477)
(200,480)(201,475)(202,474)(203,473)(204,476)(205,471)(206,470)(207,469)
(208,472)(209,449)(210,452)(211,451)(212,450)(213,463)(214,462)(215,461)
(216,464)(217,459)(218,458)(219,457)(220,460)(221,455)(222,454)(223,453)
(224,456)(225,433)(226,436)(227,435)(228,434)(229,447)(230,446)(231,445)
(232,448)(233,443)(234,442)(235,441)(236,444)(237,439)(238,438)(239,437)
(240,440)(481,817)(482,820)(483,819)(484,818)(485,831)(486,830)(487,829)
(488,832)(489,827)(490,826)(491,825)(492,828)(493,823)(494,822)(495,821)
(496,824)(497,801)(498,804)(499,803)(500,802)(501,815)(502,814)(503,813)
(504,816)(505,811)(506,810)(507,809)(508,812)(509,807)(510,806)(511,805)
(512,808)(513,865)(514,868)(515,867)(516,866)(517,879)(518,878)(519,877)
(520,880)(521,875)(522,874)(523,873)(524,876)(525,871)(526,870)(527,869)
(528,872)(529,849)(530,852)(531,851)(532,850)(533,863)(534,862)(535,861)
(536,864)(537,859)(538,858)(539,857)(540,860)(541,855)(542,854)(543,853)
(544,856)(545,833)(546,836)(547,835)(548,834)(549,847)(550,846)(551,845)
(552,848)(553,843)(554,842)(555,841)(556,844)(557,839)(558,838)(559,837)
(560,840)(561,737)(562,740)(563,739)(564,738)(565,751)(566,750)(567,749)
(568,752)(569,747)(570,746)(571,745)(572,748)(573,743)(574,742)(575,741)
(576,744)(577,721)(578,724)(579,723)(580,722)(581,735)(582,734)(583,733)
(584,736)(585,731)(586,730)(587,729)(588,732)(589,727)(590,726)(591,725)
(592,728)(593,785)(594,788)(595,787)(596,786)(597,799)(598,798)(599,797)
(600,800)(601,795)(602,794)(603,793)(604,796)(605,791)(606,790)(607,789)
(608,792)(609,769)(610,772)(611,771)(612,770)(613,783)(614,782)(615,781)
(616,784)(617,779)(618,778)(619,777)(620,780)(621,775)(622,774)(623,773)
(624,776)(625,753)(626,756)(627,755)(628,754)(629,767)(630,766)(631,765)
(632,768)(633,763)(634,762)(635,761)(636,764)(637,759)(638,758)(639,757)
(640,760)(641,897)(642,900)(643,899)(644,898)(645,911)(646,910)(647,909)
(648,912)(649,907)(650,906)(651,905)(652,908)(653,903)(654,902)(655,901)
(656,904)(657,881)(658,884)(659,883)(660,882)(661,895)(662,894)(663,893)
(664,896)(665,891)(666,890)(667,889)(668,892)(669,887)(670,886)(671,885)
(672,888)(673,945)(674,948)(675,947)(676,946)(677,959)(678,958)(679,957)
(680,960)(681,955)(682,954)(683,953)(684,956)(685,951)(686,950)(687,949)
(688,952)(689,929)(690,932)(691,931)(692,930)(693,943)(694,942)(695,941)
(696,944)(697,939)(698,938)(699,937)(700,940)(701,935)(702,934)(703,933)
(704,936)(705,913)(706,916)(707,915)(708,914)(709,927)(710,926)(711,925)
(712,928)(713,923)(714,922)(715,921)(716,924)(717,919)(718,918)(719,917)
(720,920);
s2 := Sym(960)!(  1,727)(  2,728)(  3,725)(  4,726)(  5,723)(  6,724)(  7,721)
(  8,722)(  9,733)( 10,734)( 11,735)( 12,736)( 13,729)( 14,730)( 15,731)
( 16,732)( 17,743)( 18,744)( 19,741)( 20,742)( 21,739)( 22,740)( 23,737)
( 24,738)( 25,749)( 26,750)( 27,751)( 28,752)( 29,745)( 30,746)( 31,747)
( 32,748)( 33,759)( 34,760)( 35,757)( 36,758)( 37,755)( 38,756)( 39,753)
( 40,754)( 41,765)( 42,766)( 43,767)( 44,768)( 45,761)( 46,762)( 47,763)
( 48,764)( 49,775)( 50,776)( 51,773)( 52,774)( 53,771)( 54,772)( 55,769)
( 56,770)( 57,781)( 58,782)( 59,783)( 60,784)( 61,777)( 62,778)( 63,779)
( 64,780)( 65,791)( 66,792)( 67,789)( 68,790)( 69,787)( 70,788)( 71,785)
( 72,786)( 73,797)( 74,798)( 75,799)( 76,800)( 77,793)( 78,794)( 79,795)
( 80,796)( 81,807)( 82,808)( 83,805)( 84,806)( 85,803)( 86,804)( 87,801)
( 88,802)( 89,813)( 90,814)( 91,815)( 92,816)( 93,809)( 94,810)( 95,811)
( 96,812)( 97,823)( 98,824)( 99,821)(100,822)(101,819)(102,820)(103,817)
(104,818)(105,829)(106,830)(107,831)(108,832)(109,825)(110,826)(111,827)
(112,828)(113,839)(114,840)(115,837)(116,838)(117,835)(118,836)(119,833)
(120,834)(121,845)(122,846)(123,847)(124,848)(125,841)(126,842)(127,843)
(128,844)(129,855)(130,856)(131,853)(132,854)(133,851)(134,852)(135,849)
(136,850)(137,861)(138,862)(139,863)(140,864)(141,857)(142,858)(143,859)
(144,860)(145,871)(146,872)(147,869)(148,870)(149,867)(150,868)(151,865)
(152,866)(153,877)(154,878)(155,879)(156,880)(157,873)(158,874)(159,875)
(160,876)(161,887)(162,888)(163,885)(164,886)(165,883)(166,884)(167,881)
(168,882)(169,893)(170,894)(171,895)(172,896)(173,889)(174,890)(175,891)
(176,892)(177,903)(178,904)(179,901)(180,902)(181,899)(182,900)(183,897)
(184,898)(185,909)(186,910)(187,911)(188,912)(189,905)(190,906)(191,907)
(192,908)(193,919)(194,920)(195,917)(196,918)(197,915)(198,916)(199,913)
(200,914)(201,925)(202,926)(203,927)(204,928)(205,921)(206,922)(207,923)
(208,924)(209,935)(210,936)(211,933)(212,934)(213,931)(214,932)(215,929)
(216,930)(217,941)(218,942)(219,943)(220,944)(221,937)(222,938)(223,939)
(224,940)(225,951)(226,952)(227,949)(228,950)(229,947)(230,948)(231,945)
(232,946)(233,957)(234,958)(235,959)(236,960)(237,953)(238,954)(239,955)
(240,956)(241,487)(242,488)(243,485)(244,486)(245,483)(246,484)(247,481)
(248,482)(249,493)(250,494)(251,495)(252,496)(253,489)(254,490)(255,491)
(256,492)(257,503)(258,504)(259,501)(260,502)(261,499)(262,500)(263,497)
(264,498)(265,509)(266,510)(267,511)(268,512)(269,505)(270,506)(271,507)
(272,508)(273,519)(274,520)(275,517)(276,518)(277,515)(278,516)(279,513)
(280,514)(281,525)(282,526)(283,527)(284,528)(285,521)(286,522)(287,523)
(288,524)(289,535)(290,536)(291,533)(292,534)(293,531)(294,532)(295,529)
(296,530)(297,541)(298,542)(299,543)(300,544)(301,537)(302,538)(303,539)
(304,540)(305,551)(306,552)(307,549)(308,550)(309,547)(310,548)(311,545)
(312,546)(313,557)(314,558)(315,559)(316,560)(317,553)(318,554)(319,555)
(320,556)(321,567)(322,568)(323,565)(324,566)(325,563)(326,564)(327,561)
(328,562)(329,573)(330,574)(331,575)(332,576)(333,569)(334,570)(335,571)
(336,572)(337,583)(338,584)(339,581)(340,582)(341,579)(342,580)(343,577)
(344,578)(345,589)(346,590)(347,591)(348,592)(349,585)(350,586)(351,587)
(352,588)(353,599)(354,600)(355,597)(356,598)(357,595)(358,596)(359,593)
(360,594)(361,605)(362,606)(363,607)(364,608)(365,601)(366,602)(367,603)
(368,604)(369,615)(370,616)(371,613)(372,614)(373,611)(374,612)(375,609)
(376,610)(377,621)(378,622)(379,623)(380,624)(381,617)(382,618)(383,619)
(384,620)(385,631)(386,632)(387,629)(388,630)(389,627)(390,628)(391,625)
(392,626)(393,637)(394,638)(395,639)(396,640)(397,633)(398,634)(399,635)
(400,636)(401,647)(402,648)(403,645)(404,646)(405,643)(406,644)(407,641)
(408,642)(409,653)(410,654)(411,655)(412,656)(413,649)(414,650)(415,651)
(416,652)(417,663)(418,664)(419,661)(420,662)(421,659)(422,660)(423,657)
(424,658)(425,669)(426,670)(427,671)(428,672)(429,665)(430,666)(431,667)
(432,668)(433,679)(434,680)(435,677)(436,678)(437,675)(438,676)(439,673)
(440,674)(441,685)(442,686)(443,687)(444,688)(445,681)(446,682)(447,683)
(448,684)(449,695)(450,696)(451,693)(452,694)(453,691)(454,692)(455,689)
(456,690)(457,701)(458,702)(459,703)(460,704)(461,697)(462,698)(463,699)
(464,700)(465,711)(466,712)(467,709)(468,710)(469,707)(470,708)(471,705)
(472,706)(473,717)(474,718)(475,719)(476,720)(477,713)(478,714)(479,715)
(480,716);
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, s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope