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Polytope of Type {15,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,8}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240269)
Rank : 3
Schlafli Type : {15,8}
Number of vertices, edges, etc : 120, 480, 64
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 : {15,8}*960b, {15,8}*960c, {15,4}*960
   3-fold quotients : {5,8}*640a
   4-fold quotients : {15,4}*480
   6-fold quotients : {5,8}*320a, {5,8}*320b, {5,4}*320
   12-fold quotients : {5,4}*160
   32-fold quotients : {15,2}*60
   96-fold quotients : {5,2}*20
   160-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  5,  8)(  6,  7)(  9, 10)( 11, 12)( 13, 15)( 14, 16)( 17, 28)( 18, 27)
( 19, 26)( 20, 25)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33,129)( 34,130)
( 35,131)( 36,132)( 37,136)( 38,135)( 39,134)( 40,133)( 41,138)( 42,137)
( 43,140)( 44,139)( 45,143)( 46,144)( 47,141)( 48,142)( 49,156)( 50,155)
( 51,154)( 52,153)( 53,157)( 54,158)( 55,159)( 56,160)( 57,148)( 58,147)
( 59,146)( 60,145)( 61,149)( 62,150)( 63,151)( 64,152)( 65, 97)( 66, 98)
( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)( 72,101)( 73,106)( 74,105)
( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)( 80,110)( 81,124)( 82,123)
( 83,122)( 84,121)( 85,125)( 86,126)( 87,127)( 88,128)( 89,116)( 90,115)
( 91,114)( 92,113)( 93,117)( 94,118)( 95,119)( 96,120)(161,321)(162,322)
(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)(169,330)(170,329)
(171,332)(172,331)(173,335)(174,336)(175,333)(176,334)(177,348)(178,347)
(179,346)(180,345)(181,349)(182,350)(183,351)(184,352)(185,340)(186,339)
(187,338)(188,337)(189,341)(190,342)(191,343)(192,344)(193,449)(194,450)
(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)(201,458)(202,457)
(203,460)(204,459)(205,463)(206,464)(207,461)(208,462)(209,476)(210,475)
(211,474)(212,473)(213,477)(214,478)(215,479)(216,480)(217,468)(218,467)
(219,466)(220,465)(221,469)(222,470)(223,471)(224,472)(225,417)(226,418)
(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)(233,426)(234,425)
(235,428)(236,427)(237,431)(238,432)(239,429)(240,430)(241,444)(242,443)
(243,442)(244,441)(245,445)(246,446)(247,447)(248,448)(249,436)(250,435)
(251,434)(252,433)(253,437)(254,438)(255,439)(256,440)(257,385)(258,386)
(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,394)(266,393)
(267,396)(268,395)(269,399)(270,400)(271,397)(272,398)(273,412)(274,411)
(275,410)(276,409)(277,413)(278,414)(279,415)(280,416)(281,404)(282,403)
(283,402)(284,401)(285,405)(286,406)(287,407)(288,408)(289,353)(290,354)
(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,362)(298,361)
(299,364)(300,363)(301,367)(302,368)(303,365)(304,366)(305,380)(306,379)
(307,378)(308,377)(309,381)(310,382)(311,383)(312,384)(313,372)(314,371)
(315,370)(316,369)(317,373)(318,374)(319,375)(320,376)(485,488)(486,487)
(489,490)(491,492)(493,495)(494,496)(497,508)(498,507)(499,506)(500,505)
(501,509)(502,510)(503,511)(504,512)(513,609)(514,610)(515,611)(516,612)
(517,616)(518,615)(519,614)(520,613)(521,618)(522,617)(523,620)(524,619)
(525,623)(526,624)(527,621)(528,622)(529,636)(530,635)(531,634)(532,633)
(533,637)(534,638)(535,639)(536,640)(537,628)(538,627)(539,626)(540,625)
(541,629)(542,630)(543,631)(544,632)(545,577)(546,578)(547,579)(548,580)
(549,584)(550,583)(551,582)(552,581)(553,586)(554,585)(555,588)(556,587)
(557,591)(558,592)(559,589)(560,590)(561,604)(562,603)(563,602)(564,601)
(565,605)(566,606)(567,607)(568,608)(569,596)(570,595)(571,594)(572,593)
(573,597)(574,598)(575,599)(576,600)(641,801)(642,802)(643,803)(644,804)
(645,808)(646,807)(647,806)(648,805)(649,810)(650,809)(651,812)(652,811)
(653,815)(654,816)(655,813)(656,814)(657,828)(658,827)(659,826)(660,825)
(661,829)(662,830)(663,831)(664,832)(665,820)(666,819)(667,818)(668,817)
(669,821)(670,822)(671,823)(672,824)(673,929)(674,930)(675,931)(676,932)
(677,936)(678,935)(679,934)(680,933)(681,938)(682,937)(683,940)(684,939)
(685,943)(686,944)(687,941)(688,942)(689,956)(690,955)(691,954)(692,953)
(693,957)(694,958)(695,959)(696,960)(697,948)(698,947)(699,946)(700,945)
(701,949)(702,950)(703,951)(704,952)(705,897)(706,898)(707,899)(708,900)
(709,904)(710,903)(711,902)(712,901)(713,906)(714,905)(715,908)(716,907)
(717,911)(718,912)(719,909)(720,910)(721,924)(722,923)(723,922)(724,921)
(725,925)(726,926)(727,927)(728,928)(729,916)(730,915)(731,914)(732,913)
(733,917)(734,918)(735,919)(736,920)(737,865)(738,866)(739,867)(740,868)
(741,872)(742,871)(743,870)(744,869)(745,874)(746,873)(747,876)(748,875)
(749,879)(750,880)(751,877)(752,878)(753,892)(754,891)(755,890)(756,889)
(757,893)(758,894)(759,895)(760,896)(761,884)(762,883)(763,882)(764,881)
(765,885)(766,886)(767,887)(768,888)(769,833)(770,834)(771,835)(772,836)
(773,840)(774,839)(775,838)(776,837)(777,842)(778,841)(779,844)(780,843)
(781,847)(782,848)(783,845)(784,846)(785,860)(786,859)(787,858)(788,857)
(789,861)(790,862)(791,863)(792,864)(793,852)(794,851)(795,850)(796,849)
(797,853)(798,854)(799,855)(800,856);;
s1 := (  1,193)(  2,194)(  3,224)(  4,223)(  5,204)(  6,203)(  7,213)(  8,214)
(  9,220)( 10,219)( 11,198)( 12,197)( 13,210)( 14,209)( 15,208)( 16,207)
( 17,206)( 18,205)( 19,211)( 20,212)( 21,199)( 22,200)( 23,218)( 24,217)
( 25,216)( 26,215)( 27,202)( 28,201)( 29,222)( 30,221)( 31,196)( 32,195)
( 33,161)( 34,162)( 35,192)( 36,191)( 37,172)( 38,171)( 39,181)( 40,182)
( 41,188)( 42,187)( 43,166)( 44,165)( 45,178)( 46,177)( 47,176)( 48,175)
( 49,174)( 50,173)( 51,179)( 52,180)( 53,167)( 54,168)( 55,186)( 56,185)
( 57,184)( 58,183)( 59,170)( 60,169)( 61,190)( 62,189)( 63,164)( 64,163)
( 65,289)( 66,290)( 67,320)( 68,319)( 69,300)( 70,299)( 71,309)( 72,310)
( 73,316)( 74,315)( 75,294)( 76,293)( 77,306)( 78,305)( 79,304)( 80,303)
( 81,302)( 82,301)( 83,307)( 84,308)( 85,295)( 86,296)( 87,314)( 88,313)
( 89,312)( 90,311)( 91,298)( 92,297)( 93,318)( 94,317)( 95,292)( 96,291)
( 97,257)( 98,258)( 99,288)(100,287)(101,268)(102,267)(103,277)(104,278)
(105,284)(106,283)(107,262)(108,261)(109,274)(110,273)(111,272)(112,271)
(113,270)(114,269)(115,275)(116,276)(117,263)(118,264)(119,282)(120,281)
(121,280)(122,279)(123,266)(124,265)(125,286)(126,285)(127,260)(128,259)
(129,225)(130,226)(131,256)(132,255)(133,236)(134,235)(135,245)(136,246)
(137,252)(138,251)(139,230)(140,229)(141,242)(142,241)(143,240)(144,239)
(145,238)(146,237)(147,243)(148,244)(149,231)(150,232)(151,250)(152,249)
(153,248)(154,247)(155,234)(156,233)(157,254)(158,253)(159,228)(160,227)
(321,353)(322,354)(323,384)(324,383)(325,364)(326,363)(327,373)(328,374)
(329,380)(330,379)(331,358)(332,357)(333,370)(334,369)(335,368)(336,367)
(337,366)(338,365)(339,371)(340,372)(341,359)(342,360)(343,378)(344,377)
(345,376)(346,375)(347,362)(348,361)(349,382)(350,381)(351,356)(352,355)
(385,449)(386,450)(387,480)(388,479)(389,460)(390,459)(391,469)(392,470)
(393,476)(394,475)(395,454)(396,453)(397,466)(398,465)(399,464)(400,463)
(401,462)(402,461)(403,467)(404,468)(405,455)(406,456)(407,474)(408,473)
(409,472)(410,471)(411,458)(412,457)(413,478)(414,477)(415,452)(416,451)
(419,448)(420,447)(421,428)(422,427)(423,437)(424,438)(425,444)(426,443)
(429,434)(430,433)(431,432)(439,442)(440,441)(445,446)(481,673)(482,674)
(483,704)(484,703)(485,684)(486,683)(487,693)(488,694)(489,700)(490,699)
(491,678)(492,677)(493,690)(494,689)(495,688)(496,687)(497,686)(498,685)
(499,691)(500,692)(501,679)(502,680)(503,698)(504,697)(505,696)(506,695)
(507,682)(508,681)(509,702)(510,701)(511,676)(512,675)(513,641)(514,642)
(515,672)(516,671)(517,652)(518,651)(519,661)(520,662)(521,668)(522,667)
(523,646)(524,645)(525,658)(526,657)(527,656)(528,655)(529,654)(530,653)
(531,659)(532,660)(533,647)(534,648)(535,666)(536,665)(537,664)(538,663)
(539,650)(540,649)(541,670)(542,669)(543,644)(544,643)(545,769)(546,770)
(547,800)(548,799)(549,780)(550,779)(551,789)(552,790)(553,796)(554,795)
(555,774)(556,773)(557,786)(558,785)(559,784)(560,783)(561,782)(562,781)
(563,787)(564,788)(565,775)(566,776)(567,794)(568,793)(569,792)(570,791)
(571,778)(572,777)(573,798)(574,797)(575,772)(576,771)(577,737)(578,738)
(579,768)(580,767)(581,748)(582,747)(583,757)(584,758)(585,764)(586,763)
(587,742)(588,741)(589,754)(590,753)(591,752)(592,751)(593,750)(594,749)
(595,755)(596,756)(597,743)(598,744)(599,762)(600,761)(601,760)(602,759)
(603,746)(604,745)(605,766)(606,765)(607,740)(608,739)(609,705)(610,706)
(611,736)(612,735)(613,716)(614,715)(615,725)(616,726)(617,732)(618,731)
(619,710)(620,709)(621,722)(622,721)(623,720)(624,719)(625,718)(626,717)
(627,723)(628,724)(629,711)(630,712)(631,730)(632,729)(633,728)(634,727)
(635,714)(636,713)(637,734)(638,733)(639,708)(640,707)(801,833)(802,834)
(803,864)(804,863)(805,844)(806,843)(807,853)(808,854)(809,860)(810,859)
(811,838)(812,837)(813,850)(814,849)(815,848)(816,847)(817,846)(818,845)
(819,851)(820,852)(821,839)(822,840)(823,858)(824,857)(825,856)(826,855)
(827,842)(828,841)(829,862)(830,861)(831,836)(832,835)(865,929)(866,930)
(867,960)(868,959)(869,940)(870,939)(871,949)(872,950)(873,956)(874,955)
(875,934)(876,933)(877,946)(878,945)(879,944)(880,943)(881,942)(882,941)
(883,947)(884,948)(885,935)(886,936)(887,954)(888,953)(889,952)(890,951)
(891,938)(892,937)(893,958)(894,957)(895,932)(896,931)(899,928)(900,927)
(901,908)(902,907)(903,917)(904,918)(905,924)(906,923)(909,914)(910,913)
(911,912)(919,922)(920,921)(925,926);;
s2 := (  1,483)(  2,484)(  3,481)(  4,482)(  5,487)(  6,488)(  7,485)(  8,486)
(  9,491)( 10,492)( 11,489)( 12,490)( 13,495)( 14,496)( 15,493)( 16,494)
( 17,499)( 18,500)( 19,497)( 20,498)( 21,503)( 22,504)( 23,501)( 24,502)
( 25,507)( 26,508)( 27,505)( 28,506)( 29,511)( 30,512)( 31,509)( 32,510)
( 33,515)( 34,516)( 35,513)( 36,514)( 37,519)( 38,520)( 39,517)( 40,518)
( 41,523)( 42,524)( 43,521)( 44,522)( 45,527)( 46,528)( 47,525)( 48,526)
( 49,531)( 50,532)( 51,529)( 52,530)( 53,535)( 54,536)( 55,533)( 56,534)
( 57,539)( 58,540)( 59,537)( 60,538)( 61,543)( 62,544)( 63,541)( 64,542)
( 65,547)( 66,548)( 67,545)( 68,546)( 69,551)( 70,552)( 71,549)( 72,550)
( 73,555)( 74,556)( 75,553)( 76,554)( 77,559)( 78,560)( 79,557)( 80,558)
( 81,563)( 82,564)( 83,561)( 84,562)( 85,567)( 86,568)( 87,565)( 88,566)
( 89,571)( 90,572)( 91,569)( 92,570)( 93,575)( 94,576)( 95,573)( 96,574)
( 97,579)( 98,580)( 99,577)(100,578)(101,583)(102,584)(103,581)(104,582)
(105,587)(106,588)(107,585)(108,586)(109,591)(110,592)(111,589)(112,590)
(113,595)(114,596)(115,593)(116,594)(117,599)(118,600)(119,597)(120,598)
(121,603)(122,604)(123,601)(124,602)(125,607)(126,608)(127,605)(128,606)
(129,611)(130,612)(131,609)(132,610)(133,615)(134,616)(135,613)(136,614)
(137,619)(138,620)(139,617)(140,618)(141,623)(142,624)(143,621)(144,622)
(145,627)(146,628)(147,625)(148,626)(149,631)(150,632)(151,629)(152,630)
(153,635)(154,636)(155,633)(156,634)(157,639)(158,640)(159,637)(160,638)
(161,643)(162,644)(163,641)(164,642)(165,647)(166,648)(167,645)(168,646)
(169,651)(170,652)(171,649)(172,650)(173,655)(174,656)(175,653)(176,654)
(177,659)(178,660)(179,657)(180,658)(181,663)(182,664)(183,661)(184,662)
(185,667)(186,668)(187,665)(188,666)(189,671)(190,672)(191,669)(192,670)
(193,675)(194,676)(195,673)(196,674)(197,679)(198,680)(199,677)(200,678)
(201,683)(202,684)(203,681)(204,682)(205,687)(206,688)(207,685)(208,686)
(209,691)(210,692)(211,689)(212,690)(213,695)(214,696)(215,693)(216,694)
(217,699)(218,700)(219,697)(220,698)(221,703)(222,704)(223,701)(224,702)
(225,707)(226,708)(227,705)(228,706)(229,711)(230,712)(231,709)(232,710)
(233,715)(234,716)(235,713)(236,714)(237,719)(238,720)(239,717)(240,718)
(241,723)(242,724)(243,721)(244,722)(245,727)(246,728)(247,725)(248,726)
(249,731)(250,732)(251,729)(252,730)(253,735)(254,736)(255,733)(256,734)
(257,739)(258,740)(259,737)(260,738)(261,743)(262,744)(263,741)(264,742)
(265,747)(266,748)(267,745)(268,746)(269,751)(270,752)(271,749)(272,750)
(273,755)(274,756)(275,753)(276,754)(277,759)(278,760)(279,757)(280,758)
(281,763)(282,764)(283,761)(284,762)(285,767)(286,768)(287,765)(288,766)
(289,771)(290,772)(291,769)(292,770)(293,775)(294,776)(295,773)(296,774)
(297,779)(298,780)(299,777)(300,778)(301,783)(302,784)(303,781)(304,782)
(305,787)(306,788)(307,785)(308,786)(309,791)(310,792)(311,789)(312,790)
(313,795)(314,796)(315,793)(316,794)(317,799)(318,800)(319,797)(320,798)
(321,803)(322,804)(323,801)(324,802)(325,807)(326,808)(327,805)(328,806)
(329,811)(330,812)(331,809)(332,810)(333,815)(334,816)(335,813)(336,814)
(337,819)(338,820)(339,817)(340,818)(341,823)(342,824)(343,821)(344,822)
(345,827)(346,828)(347,825)(348,826)(349,831)(350,832)(351,829)(352,830)
(353,835)(354,836)(355,833)(356,834)(357,839)(358,840)(359,837)(360,838)
(361,843)(362,844)(363,841)(364,842)(365,847)(366,848)(367,845)(368,846)
(369,851)(370,852)(371,849)(372,850)(373,855)(374,856)(375,853)(376,854)
(377,859)(378,860)(379,857)(380,858)(381,863)(382,864)(383,861)(384,862)
(385,867)(386,868)(387,865)(388,866)(389,871)(390,872)(391,869)(392,870)
(393,875)(394,876)(395,873)(396,874)(397,879)(398,880)(399,877)(400,878)
(401,883)(402,884)(403,881)(404,882)(405,887)(406,888)(407,885)(408,886)
(409,891)(410,892)(411,889)(412,890)(413,895)(414,896)(415,893)(416,894)
(417,899)(418,900)(419,897)(420,898)(421,903)(422,904)(423,901)(424,902)
(425,907)(426,908)(427,905)(428,906)(429,911)(430,912)(431,909)(432,910)
(433,915)(434,916)(435,913)(436,914)(437,919)(438,920)(439,917)(440,918)
(441,923)(442,924)(443,921)(444,922)(445,927)(446,928)(447,925)(448,926)
(449,931)(450,932)(451,929)(452,930)(453,935)(454,936)(455,933)(456,934)
(457,939)(458,940)(459,937)(460,938)(461,943)(462,944)(463,941)(464,942)
(465,947)(466,948)(467,945)(468,946)(469,951)(470,952)(471,949)(472,950)
(473,955)(474,956)(475,953)(476,954)(477,959)(478,960)(479,957)(480,958);;
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(960)!(  5,  8)(  6,  7)(  9, 10)( 11, 12)( 13, 15)( 14, 16)( 17, 28)
( 18, 27)( 19, 26)( 20, 25)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33,129)
( 34,130)( 35,131)( 36,132)( 37,136)( 38,135)( 39,134)( 40,133)( 41,138)
( 42,137)( 43,140)( 44,139)( 45,143)( 46,144)( 47,141)( 48,142)( 49,156)
( 50,155)( 51,154)( 52,153)( 53,157)( 54,158)( 55,159)( 56,160)( 57,148)
( 58,147)( 59,146)( 60,145)( 61,149)( 62,150)( 63,151)( 64,152)( 65, 97)
( 66, 98)( 67, 99)( 68,100)( 69,104)( 70,103)( 71,102)( 72,101)( 73,106)
( 74,105)( 75,108)( 76,107)( 77,111)( 78,112)( 79,109)( 80,110)( 81,124)
( 82,123)( 83,122)( 84,121)( 85,125)( 86,126)( 87,127)( 88,128)( 89,116)
( 90,115)( 91,114)( 92,113)( 93,117)( 94,118)( 95,119)( 96,120)(161,321)
(162,322)(163,323)(164,324)(165,328)(166,327)(167,326)(168,325)(169,330)
(170,329)(171,332)(172,331)(173,335)(174,336)(175,333)(176,334)(177,348)
(178,347)(179,346)(180,345)(181,349)(182,350)(183,351)(184,352)(185,340)
(186,339)(187,338)(188,337)(189,341)(190,342)(191,343)(192,344)(193,449)
(194,450)(195,451)(196,452)(197,456)(198,455)(199,454)(200,453)(201,458)
(202,457)(203,460)(204,459)(205,463)(206,464)(207,461)(208,462)(209,476)
(210,475)(211,474)(212,473)(213,477)(214,478)(215,479)(216,480)(217,468)
(218,467)(219,466)(220,465)(221,469)(222,470)(223,471)(224,472)(225,417)
(226,418)(227,419)(228,420)(229,424)(230,423)(231,422)(232,421)(233,426)
(234,425)(235,428)(236,427)(237,431)(238,432)(239,429)(240,430)(241,444)
(242,443)(243,442)(244,441)(245,445)(246,446)(247,447)(248,448)(249,436)
(250,435)(251,434)(252,433)(253,437)(254,438)(255,439)(256,440)(257,385)
(258,386)(259,387)(260,388)(261,392)(262,391)(263,390)(264,389)(265,394)
(266,393)(267,396)(268,395)(269,399)(270,400)(271,397)(272,398)(273,412)
(274,411)(275,410)(276,409)(277,413)(278,414)(279,415)(280,416)(281,404)
(282,403)(283,402)(284,401)(285,405)(286,406)(287,407)(288,408)(289,353)
(290,354)(291,355)(292,356)(293,360)(294,359)(295,358)(296,357)(297,362)
(298,361)(299,364)(300,363)(301,367)(302,368)(303,365)(304,366)(305,380)
(306,379)(307,378)(308,377)(309,381)(310,382)(311,383)(312,384)(313,372)
(314,371)(315,370)(316,369)(317,373)(318,374)(319,375)(320,376)(485,488)
(486,487)(489,490)(491,492)(493,495)(494,496)(497,508)(498,507)(499,506)
(500,505)(501,509)(502,510)(503,511)(504,512)(513,609)(514,610)(515,611)
(516,612)(517,616)(518,615)(519,614)(520,613)(521,618)(522,617)(523,620)
(524,619)(525,623)(526,624)(527,621)(528,622)(529,636)(530,635)(531,634)
(532,633)(533,637)(534,638)(535,639)(536,640)(537,628)(538,627)(539,626)
(540,625)(541,629)(542,630)(543,631)(544,632)(545,577)(546,578)(547,579)
(548,580)(549,584)(550,583)(551,582)(552,581)(553,586)(554,585)(555,588)
(556,587)(557,591)(558,592)(559,589)(560,590)(561,604)(562,603)(563,602)
(564,601)(565,605)(566,606)(567,607)(568,608)(569,596)(570,595)(571,594)
(572,593)(573,597)(574,598)(575,599)(576,600)(641,801)(642,802)(643,803)
(644,804)(645,808)(646,807)(647,806)(648,805)(649,810)(650,809)(651,812)
(652,811)(653,815)(654,816)(655,813)(656,814)(657,828)(658,827)(659,826)
(660,825)(661,829)(662,830)(663,831)(664,832)(665,820)(666,819)(667,818)
(668,817)(669,821)(670,822)(671,823)(672,824)(673,929)(674,930)(675,931)
(676,932)(677,936)(678,935)(679,934)(680,933)(681,938)(682,937)(683,940)
(684,939)(685,943)(686,944)(687,941)(688,942)(689,956)(690,955)(691,954)
(692,953)(693,957)(694,958)(695,959)(696,960)(697,948)(698,947)(699,946)
(700,945)(701,949)(702,950)(703,951)(704,952)(705,897)(706,898)(707,899)
(708,900)(709,904)(710,903)(711,902)(712,901)(713,906)(714,905)(715,908)
(716,907)(717,911)(718,912)(719,909)(720,910)(721,924)(722,923)(723,922)
(724,921)(725,925)(726,926)(727,927)(728,928)(729,916)(730,915)(731,914)
(732,913)(733,917)(734,918)(735,919)(736,920)(737,865)(738,866)(739,867)
(740,868)(741,872)(742,871)(743,870)(744,869)(745,874)(746,873)(747,876)
(748,875)(749,879)(750,880)(751,877)(752,878)(753,892)(754,891)(755,890)
(756,889)(757,893)(758,894)(759,895)(760,896)(761,884)(762,883)(763,882)
(764,881)(765,885)(766,886)(767,887)(768,888)(769,833)(770,834)(771,835)
(772,836)(773,840)(774,839)(775,838)(776,837)(777,842)(778,841)(779,844)
(780,843)(781,847)(782,848)(783,845)(784,846)(785,860)(786,859)(787,858)
(788,857)(789,861)(790,862)(791,863)(792,864)(793,852)(794,851)(795,850)
(796,849)(797,853)(798,854)(799,855)(800,856);
s1 := Sym(960)!(  1,193)(  2,194)(  3,224)(  4,223)(  5,204)(  6,203)(  7,213)
(  8,214)(  9,220)( 10,219)( 11,198)( 12,197)( 13,210)( 14,209)( 15,208)
( 16,207)( 17,206)( 18,205)( 19,211)( 20,212)( 21,199)( 22,200)( 23,218)
( 24,217)( 25,216)( 26,215)( 27,202)( 28,201)( 29,222)( 30,221)( 31,196)
( 32,195)( 33,161)( 34,162)( 35,192)( 36,191)( 37,172)( 38,171)( 39,181)
( 40,182)( 41,188)( 42,187)( 43,166)( 44,165)( 45,178)( 46,177)( 47,176)
( 48,175)( 49,174)( 50,173)( 51,179)( 52,180)( 53,167)( 54,168)( 55,186)
( 56,185)( 57,184)( 58,183)( 59,170)( 60,169)( 61,190)( 62,189)( 63,164)
( 64,163)( 65,289)( 66,290)( 67,320)( 68,319)( 69,300)( 70,299)( 71,309)
( 72,310)( 73,316)( 74,315)( 75,294)( 76,293)( 77,306)( 78,305)( 79,304)
( 80,303)( 81,302)( 82,301)( 83,307)( 84,308)( 85,295)( 86,296)( 87,314)
( 88,313)( 89,312)( 90,311)( 91,298)( 92,297)( 93,318)( 94,317)( 95,292)
( 96,291)( 97,257)( 98,258)( 99,288)(100,287)(101,268)(102,267)(103,277)
(104,278)(105,284)(106,283)(107,262)(108,261)(109,274)(110,273)(111,272)
(112,271)(113,270)(114,269)(115,275)(116,276)(117,263)(118,264)(119,282)
(120,281)(121,280)(122,279)(123,266)(124,265)(125,286)(126,285)(127,260)
(128,259)(129,225)(130,226)(131,256)(132,255)(133,236)(134,235)(135,245)
(136,246)(137,252)(138,251)(139,230)(140,229)(141,242)(142,241)(143,240)
(144,239)(145,238)(146,237)(147,243)(148,244)(149,231)(150,232)(151,250)
(152,249)(153,248)(154,247)(155,234)(156,233)(157,254)(158,253)(159,228)
(160,227)(321,353)(322,354)(323,384)(324,383)(325,364)(326,363)(327,373)
(328,374)(329,380)(330,379)(331,358)(332,357)(333,370)(334,369)(335,368)
(336,367)(337,366)(338,365)(339,371)(340,372)(341,359)(342,360)(343,378)
(344,377)(345,376)(346,375)(347,362)(348,361)(349,382)(350,381)(351,356)
(352,355)(385,449)(386,450)(387,480)(388,479)(389,460)(390,459)(391,469)
(392,470)(393,476)(394,475)(395,454)(396,453)(397,466)(398,465)(399,464)
(400,463)(401,462)(402,461)(403,467)(404,468)(405,455)(406,456)(407,474)
(408,473)(409,472)(410,471)(411,458)(412,457)(413,478)(414,477)(415,452)
(416,451)(419,448)(420,447)(421,428)(422,427)(423,437)(424,438)(425,444)
(426,443)(429,434)(430,433)(431,432)(439,442)(440,441)(445,446)(481,673)
(482,674)(483,704)(484,703)(485,684)(486,683)(487,693)(488,694)(489,700)
(490,699)(491,678)(492,677)(493,690)(494,689)(495,688)(496,687)(497,686)
(498,685)(499,691)(500,692)(501,679)(502,680)(503,698)(504,697)(505,696)
(506,695)(507,682)(508,681)(509,702)(510,701)(511,676)(512,675)(513,641)
(514,642)(515,672)(516,671)(517,652)(518,651)(519,661)(520,662)(521,668)
(522,667)(523,646)(524,645)(525,658)(526,657)(527,656)(528,655)(529,654)
(530,653)(531,659)(532,660)(533,647)(534,648)(535,666)(536,665)(537,664)
(538,663)(539,650)(540,649)(541,670)(542,669)(543,644)(544,643)(545,769)
(546,770)(547,800)(548,799)(549,780)(550,779)(551,789)(552,790)(553,796)
(554,795)(555,774)(556,773)(557,786)(558,785)(559,784)(560,783)(561,782)
(562,781)(563,787)(564,788)(565,775)(566,776)(567,794)(568,793)(569,792)
(570,791)(571,778)(572,777)(573,798)(574,797)(575,772)(576,771)(577,737)
(578,738)(579,768)(580,767)(581,748)(582,747)(583,757)(584,758)(585,764)
(586,763)(587,742)(588,741)(589,754)(590,753)(591,752)(592,751)(593,750)
(594,749)(595,755)(596,756)(597,743)(598,744)(599,762)(600,761)(601,760)
(602,759)(603,746)(604,745)(605,766)(606,765)(607,740)(608,739)(609,705)
(610,706)(611,736)(612,735)(613,716)(614,715)(615,725)(616,726)(617,732)
(618,731)(619,710)(620,709)(621,722)(622,721)(623,720)(624,719)(625,718)
(626,717)(627,723)(628,724)(629,711)(630,712)(631,730)(632,729)(633,728)
(634,727)(635,714)(636,713)(637,734)(638,733)(639,708)(640,707)(801,833)
(802,834)(803,864)(804,863)(805,844)(806,843)(807,853)(808,854)(809,860)
(810,859)(811,838)(812,837)(813,850)(814,849)(815,848)(816,847)(817,846)
(818,845)(819,851)(820,852)(821,839)(822,840)(823,858)(824,857)(825,856)
(826,855)(827,842)(828,841)(829,862)(830,861)(831,836)(832,835)(865,929)
(866,930)(867,960)(868,959)(869,940)(870,939)(871,949)(872,950)(873,956)
(874,955)(875,934)(876,933)(877,946)(878,945)(879,944)(880,943)(881,942)
(882,941)(883,947)(884,948)(885,935)(886,936)(887,954)(888,953)(889,952)
(890,951)(891,938)(892,937)(893,958)(894,957)(895,932)(896,931)(899,928)
(900,927)(901,908)(902,907)(903,917)(904,918)(905,924)(906,923)(909,914)
(910,913)(911,912)(919,922)(920,921)(925,926);
s2 := Sym(960)!(  1,483)(  2,484)(  3,481)(  4,482)(  5,487)(  6,488)(  7,485)
(  8,486)(  9,491)( 10,492)( 11,489)( 12,490)( 13,495)( 14,496)( 15,493)
( 16,494)( 17,499)( 18,500)( 19,497)( 20,498)( 21,503)( 22,504)( 23,501)
( 24,502)( 25,507)( 26,508)( 27,505)( 28,506)( 29,511)( 30,512)( 31,509)
( 32,510)( 33,515)( 34,516)( 35,513)( 36,514)( 37,519)( 38,520)( 39,517)
( 40,518)( 41,523)( 42,524)( 43,521)( 44,522)( 45,527)( 46,528)( 47,525)
( 48,526)( 49,531)( 50,532)( 51,529)( 52,530)( 53,535)( 54,536)( 55,533)
( 56,534)( 57,539)( 58,540)( 59,537)( 60,538)( 61,543)( 62,544)( 63,541)
( 64,542)( 65,547)( 66,548)( 67,545)( 68,546)( 69,551)( 70,552)( 71,549)
( 72,550)( 73,555)( 74,556)( 75,553)( 76,554)( 77,559)( 78,560)( 79,557)
( 80,558)( 81,563)( 82,564)( 83,561)( 84,562)( 85,567)( 86,568)( 87,565)
( 88,566)( 89,571)( 90,572)( 91,569)( 92,570)( 93,575)( 94,576)( 95,573)
( 96,574)( 97,579)( 98,580)( 99,577)(100,578)(101,583)(102,584)(103,581)
(104,582)(105,587)(106,588)(107,585)(108,586)(109,591)(110,592)(111,589)
(112,590)(113,595)(114,596)(115,593)(116,594)(117,599)(118,600)(119,597)
(120,598)(121,603)(122,604)(123,601)(124,602)(125,607)(126,608)(127,605)
(128,606)(129,611)(130,612)(131,609)(132,610)(133,615)(134,616)(135,613)
(136,614)(137,619)(138,620)(139,617)(140,618)(141,623)(142,624)(143,621)
(144,622)(145,627)(146,628)(147,625)(148,626)(149,631)(150,632)(151,629)
(152,630)(153,635)(154,636)(155,633)(156,634)(157,639)(158,640)(159,637)
(160,638)(161,643)(162,644)(163,641)(164,642)(165,647)(166,648)(167,645)
(168,646)(169,651)(170,652)(171,649)(172,650)(173,655)(174,656)(175,653)
(176,654)(177,659)(178,660)(179,657)(180,658)(181,663)(182,664)(183,661)
(184,662)(185,667)(186,668)(187,665)(188,666)(189,671)(190,672)(191,669)
(192,670)(193,675)(194,676)(195,673)(196,674)(197,679)(198,680)(199,677)
(200,678)(201,683)(202,684)(203,681)(204,682)(205,687)(206,688)(207,685)
(208,686)(209,691)(210,692)(211,689)(212,690)(213,695)(214,696)(215,693)
(216,694)(217,699)(218,700)(219,697)(220,698)(221,703)(222,704)(223,701)
(224,702)(225,707)(226,708)(227,705)(228,706)(229,711)(230,712)(231,709)
(232,710)(233,715)(234,716)(235,713)(236,714)(237,719)(238,720)(239,717)
(240,718)(241,723)(242,724)(243,721)(244,722)(245,727)(246,728)(247,725)
(248,726)(249,731)(250,732)(251,729)(252,730)(253,735)(254,736)(255,733)
(256,734)(257,739)(258,740)(259,737)(260,738)(261,743)(262,744)(263,741)
(264,742)(265,747)(266,748)(267,745)(268,746)(269,751)(270,752)(271,749)
(272,750)(273,755)(274,756)(275,753)(276,754)(277,759)(278,760)(279,757)
(280,758)(281,763)(282,764)(283,761)(284,762)(285,767)(286,768)(287,765)
(288,766)(289,771)(290,772)(291,769)(292,770)(293,775)(294,776)(295,773)
(296,774)(297,779)(298,780)(299,777)(300,778)(301,783)(302,784)(303,781)
(304,782)(305,787)(306,788)(307,785)(308,786)(309,791)(310,792)(311,789)
(312,790)(313,795)(314,796)(315,793)(316,794)(317,799)(318,800)(319,797)
(320,798)(321,803)(322,804)(323,801)(324,802)(325,807)(326,808)(327,805)
(328,806)(329,811)(330,812)(331,809)(332,810)(333,815)(334,816)(335,813)
(336,814)(337,819)(338,820)(339,817)(340,818)(341,823)(342,824)(343,821)
(344,822)(345,827)(346,828)(347,825)(348,826)(349,831)(350,832)(351,829)
(352,830)(353,835)(354,836)(355,833)(356,834)(357,839)(358,840)(359,837)
(360,838)(361,843)(362,844)(363,841)(364,842)(365,847)(366,848)(367,845)
(368,846)(369,851)(370,852)(371,849)(372,850)(373,855)(374,856)(375,853)
(376,854)(377,859)(378,860)(379,857)(380,858)(381,863)(382,864)(383,861)
(384,862)(385,867)(386,868)(387,865)(388,866)(389,871)(390,872)(391,869)
(392,870)(393,875)(394,876)(395,873)(396,874)(397,879)(398,880)(399,877)
(400,878)(401,883)(402,884)(403,881)(404,882)(405,887)(406,888)(407,885)
(408,886)(409,891)(410,892)(411,889)(412,890)(413,895)(414,896)(415,893)
(416,894)(417,899)(418,900)(419,897)(420,898)(421,903)(422,904)(423,901)
(424,902)(425,907)(426,908)(427,905)(428,906)(429,911)(430,912)(431,909)
(432,910)(433,915)(434,916)(435,913)(436,914)(437,919)(438,920)(439,917)
(440,918)(441,923)(442,924)(443,921)(444,922)(445,927)(446,928)(447,925)
(448,926)(449,931)(450,932)(451,929)(452,930)(453,935)(454,936)(455,933)
(456,934)(457,939)(458,940)(459,937)(460,938)(461,943)(462,944)(463,941)
(464,942)(465,947)(466,948)(467,945)(468,946)(469,951)(470,952)(471,949)
(472,950)(473,955)(474,956)(475,953)(476,954)(477,959)(478,960)(479,957)
(480,958);
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*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s2, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*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 >; 
 
References : None.
to this polytope