Polytope of Type {8,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,15}*1920c
if this polytope has a name.
Group : SmallGroup(1920,240273)
Rank : 3
Schlafli Type : {8,15}
Number of vertices, edges, etc : 64, 480, 120
Order of s0s1s2 : 60
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {4,15}*960
3-fold quotients : {8,5}*640b
4-fold quotients : {4,15}*480
6-fold quotients : {4,5}*320
12-fold quotients : {4,5}*160
32-fold quotients : {2,15}*60
96-fold quotients : {2,5}*20
160-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,497)( 2,498)( 3,500)( 4,499)( 5,502)( 6,501)( 7,503)( 8,504)
( 9,505)( 10,506)( 11,508)( 12,507)( 13,510)( 14,509)( 15,511)( 16,512)
( 17,482)( 18,481)( 19,483)( 20,484)( 21,485)( 22,486)( 23,488)( 24,487)
( 25,490)( 26,489)( 27,491)( 28,492)( 29,493)( 30,494)( 31,496)( 32,495)
( 33,529)( 34,530)( 35,532)( 36,531)( 37,534)( 38,533)( 39,535)( 40,536)
( 41,537)( 42,538)( 43,540)( 44,539)( 45,542)( 46,541)( 47,543)( 48,544)
( 49,514)( 50,513)( 51,515)( 52,516)( 53,517)( 54,518)( 55,520)( 56,519)
( 57,522)( 58,521)( 59,523)( 60,524)( 61,525)( 62,526)( 63,528)( 64,527)
( 65,561)( 66,562)( 67,564)( 68,563)( 69,566)( 70,565)( 71,567)( 72,568)
( 73,569)( 74,570)( 75,572)( 76,571)( 77,574)( 78,573)( 79,575)( 80,576)
( 81,546)( 82,545)( 83,547)( 84,548)( 85,549)( 86,550)( 87,552)( 88,551)
( 89,554)( 90,553)( 91,555)( 92,556)( 93,557)( 94,558)( 95,560)( 96,559)
( 97,593)( 98,594)( 99,596)(100,595)(101,598)(102,597)(103,599)(104,600)
(105,601)(106,602)(107,604)(108,603)(109,606)(110,605)(111,607)(112,608)
(113,578)(114,577)(115,579)(116,580)(117,581)(118,582)(119,584)(120,583)
(121,586)(122,585)(123,587)(124,588)(125,589)(126,590)(127,592)(128,591)
(129,625)(130,626)(131,628)(132,627)(133,630)(134,629)(135,631)(136,632)
(137,633)(138,634)(139,636)(140,635)(141,638)(142,637)(143,639)(144,640)
(145,610)(146,609)(147,611)(148,612)(149,613)(150,614)(151,616)(152,615)
(153,618)(154,617)(155,619)(156,620)(157,621)(158,622)(159,624)(160,623)
(161,657)(162,658)(163,660)(164,659)(165,662)(166,661)(167,663)(168,664)
(169,665)(170,666)(171,668)(172,667)(173,670)(174,669)(175,671)(176,672)
(177,642)(178,641)(179,643)(180,644)(181,645)(182,646)(183,648)(184,647)
(185,650)(186,649)(187,651)(188,652)(189,653)(190,654)(191,656)(192,655)
(193,689)(194,690)(195,692)(196,691)(197,694)(198,693)(199,695)(200,696)
(201,697)(202,698)(203,700)(204,699)(205,702)(206,701)(207,703)(208,704)
(209,674)(210,673)(211,675)(212,676)(213,677)(214,678)(215,680)(216,679)
(217,682)(218,681)(219,683)(220,684)(221,685)(222,686)(223,688)(224,687)
(225,721)(226,722)(227,724)(228,723)(229,726)(230,725)(231,727)(232,728)
(233,729)(234,730)(235,732)(236,731)(237,734)(238,733)(239,735)(240,736)
(241,706)(242,705)(243,707)(244,708)(245,709)(246,710)(247,712)(248,711)
(249,714)(250,713)(251,715)(252,716)(253,717)(254,718)(255,720)(256,719)
(257,753)(258,754)(259,756)(260,755)(261,758)(262,757)(263,759)(264,760)
(265,761)(266,762)(267,764)(268,763)(269,766)(270,765)(271,767)(272,768)
(273,738)(274,737)(275,739)(276,740)(277,741)(278,742)(279,744)(280,743)
(281,746)(282,745)(283,747)(284,748)(285,749)(286,750)(287,752)(288,751)
(289,785)(290,786)(291,788)(292,787)(293,790)(294,789)(295,791)(296,792)
(297,793)(298,794)(299,796)(300,795)(301,798)(302,797)(303,799)(304,800)
(305,770)(306,769)(307,771)(308,772)(309,773)(310,774)(311,776)(312,775)
(313,778)(314,777)(315,779)(316,780)(317,781)(318,782)(319,784)(320,783)
(321,817)(322,818)(323,820)(324,819)(325,822)(326,821)(327,823)(328,824)
(329,825)(330,826)(331,828)(332,827)(333,830)(334,829)(335,831)(336,832)
(337,802)(338,801)(339,803)(340,804)(341,805)(342,806)(343,808)(344,807)
(345,810)(346,809)(347,811)(348,812)(349,813)(350,814)(351,816)(352,815)
(353,849)(354,850)(355,852)(356,851)(357,854)(358,853)(359,855)(360,856)
(361,857)(362,858)(363,860)(364,859)(365,862)(366,861)(367,863)(368,864)
(369,834)(370,833)(371,835)(372,836)(373,837)(374,838)(375,840)(376,839)
(377,842)(378,841)(379,843)(380,844)(381,845)(382,846)(383,848)(384,847)
(385,881)(386,882)(387,884)(388,883)(389,886)(390,885)(391,887)(392,888)
(393,889)(394,890)(395,892)(396,891)(397,894)(398,893)(399,895)(400,896)
(401,866)(402,865)(403,867)(404,868)(405,869)(406,870)(407,872)(408,871)
(409,874)(410,873)(411,875)(412,876)(413,877)(414,878)(415,880)(416,879)
(417,913)(418,914)(419,916)(420,915)(421,918)(422,917)(423,919)(424,920)
(425,921)(426,922)(427,924)(428,923)(429,926)(430,925)(431,927)(432,928)
(433,898)(434,897)(435,899)(436,900)(437,901)(438,902)(439,904)(440,903)
(441,906)(442,905)(443,907)(444,908)(445,909)(446,910)(447,912)(448,911)
(449,945)(450,946)(451,948)(452,947)(453,950)(454,949)(455,951)(456,952)
(457,953)(458,954)(459,956)(460,955)(461,958)(462,957)(463,959)(464,960)
(465,930)(466,929)(467,931)(468,932)(469,933)(470,934)(471,936)(472,935)
(473,938)(474,937)(475,939)(476,940)(477,941)(478,942)(479,944)(480,943);;
s1 := ( 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)(481,482)(483,484)
(485,487)(486,488)(493,496)(494,495)(497,507)(498,508)(499,505)(500,506)
(501,510)(502,509)(503,512)(504,511)(513,610)(514,609)(515,612)(516,611)
(517,615)(518,616)(519,613)(520,614)(521,617)(522,618)(523,619)(524,620)
(525,624)(526,623)(527,622)(528,621)(529,635)(530,636)(531,633)(532,634)
(533,638)(534,637)(535,640)(536,639)(537,627)(538,628)(539,625)(540,626)
(541,630)(542,629)(543,632)(544,631)(545,578)(546,577)(547,580)(548,579)
(549,583)(550,584)(551,581)(552,582)(553,585)(554,586)(555,587)(556,588)
(557,592)(558,591)(559,590)(560,589)(561,603)(562,604)(563,601)(564,602)
(565,606)(566,605)(567,608)(568,607)(569,595)(570,596)(571,593)(572,594)
(573,598)(574,597)(575,600)(576,599)(641,802)(642,801)(643,804)(644,803)
(645,807)(646,808)(647,805)(648,806)(649,809)(650,810)(651,811)(652,812)
(653,816)(654,815)(655,814)(656,813)(657,827)(658,828)(659,825)(660,826)
(661,830)(662,829)(663,832)(664,831)(665,819)(666,820)(667,817)(668,818)
(669,822)(670,821)(671,824)(672,823)(673,930)(674,929)(675,932)(676,931)
(677,935)(678,936)(679,933)(680,934)(681,937)(682,938)(683,939)(684,940)
(685,944)(686,943)(687,942)(688,941)(689,955)(690,956)(691,953)(692,954)
(693,958)(694,957)(695,960)(696,959)(697,947)(698,948)(699,945)(700,946)
(701,950)(702,949)(703,952)(704,951)(705,898)(706,897)(707,900)(708,899)
(709,903)(710,904)(711,901)(712,902)(713,905)(714,906)(715,907)(716,908)
(717,912)(718,911)(719,910)(720,909)(721,923)(722,924)(723,921)(724,922)
(725,926)(726,925)(727,928)(728,927)(729,915)(730,916)(731,913)(732,914)
(733,918)(734,917)(735,920)(736,919)(737,866)(738,865)(739,868)(740,867)
(741,871)(742,872)(743,869)(744,870)(745,873)(746,874)(747,875)(748,876)
(749,880)(750,879)(751,878)(752,877)(753,891)(754,892)(755,889)(756,890)
(757,894)(758,893)(759,896)(760,895)(761,883)(762,884)(763,881)(764,882)
(765,886)(766,885)(767,888)(768,887)(769,834)(770,833)(771,836)(772,835)
(773,839)(774,840)(775,837)(776,838)(777,841)(778,842)(779,843)(780,844)
(781,848)(782,847)(783,846)(784,845)(785,859)(786,860)(787,857)(788,858)
(789,862)(790,861)(791,864)(792,863)(793,851)(794,852)(795,849)(796,850)
(797,854)(798,853)(799,856)(800,855);;
s2 := ( 1,257)( 2,258)( 3,276)( 4,275)( 5,277)( 6,278)( 7,264)( 8,263)
( 9,271)( 10,272)( 11,286)( 12,285)( 13,284)( 14,283)( 15,265)( 16,266)
( 17,274)( 18,273)( 19,260)( 20,259)( 21,261)( 22,262)( 23,279)( 24,280)
( 25,288)( 26,287)( 27,270)( 28,269)( 29,268)( 30,267)( 31,282)( 32,281)
( 33,225)( 34,226)( 35,244)( 36,243)( 37,245)( 38,246)( 39,232)( 40,231)
( 41,239)( 42,240)( 43,254)( 44,253)( 45,252)( 46,251)( 47,233)( 48,234)
( 49,242)( 50,241)( 51,228)( 52,227)( 53,229)( 54,230)( 55,247)( 56,248)
( 57,256)( 58,255)( 59,238)( 60,237)( 61,236)( 62,235)( 63,250)( 64,249)
( 65,193)( 66,194)( 67,212)( 68,211)( 69,213)( 70,214)( 71,200)( 72,199)
( 73,207)( 74,208)( 75,222)( 76,221)( 77,220)( 78,219)( 79,201)( 80,202)
( 81,210)( 82,209)( 83,196)( 84,195)( 85,197)( 86,198)( 87,215)( 88,216)
( 89,224)( 90,223)( 91,206)( 92,205)( 93,204)( 94,203)( 95,218)( 96,217)
( 97,161)( 98,162)( 99,180)(100,179)(101,181)(102,182)(103,168)(104,167)
(105,175)(106,176)(107,190)(108,189)(109,188)(110,187)(111,169)(112,170)
(113,178)(114,177)(115,164)(116,163)(117,165)(118,166)(119,183)(120,184)
(121,192)(122,191)(123,174)(124,173)(125,172)(126,171)(127,186)(128,185)
(129,289)(130,290)(131,308)(132,307)(133,309)(134,310)(135,296)(136,295)
(137,303)(138,304)(139,318)(140,317)(141,316)(142,315)(143,297)(144,298)
(145,306)(146,305)(147,292)(148,291)(149,293)(150,294)(151,311)(152,312)
(153,320)(154,319)(155,302)(156,301)(157,300)(158,299)(159,314)(160,313)
(321,417)(322,418)(323,436)(324,435)(325,437)(326,438)(327,424)(328,423)
(329,431)(330,432)(331,446)(332,445)(333,444)(334,443)(335,425)(336,426)
(337,434)(338,433)(339,420)(340,419)(341,421)(342,422)(343,439)(344,440)
(345,448)(346,447)(347,430)(348,429)(349,428)(350,427)(351,442)(352,441)
(353,385)(354,386)(355,404)(356,403)(357,405)(358,406)(359,392)(360,391)
(361,399)(362,400)(363,414)(364,413)(365,412)(366,411)(367,393)(368,394)
(369,402)(370,401)(371,388)(372,387)(373,389)(374,390)(375,407)(376,408)
(377,416)(378,415)(379,398)(380,397)(381,396)(382,395)(383,410)(384,409)
(451,468)(452,467)(453,469)(454,470)(455,456)(457,463)(458,464)(459,478)
(460,477)(461,476)(462,475)(465,466)(473,480)(474,479)(481,738)(482,737)
(483,755)(484,756)(485,758)(486,757)(487,743)(488,744)(489,752)(490,751)
(491,765)(492,766)(493,763)(494,764)(495,746)(496,745)(497,753)(498,754)
(499,739)(500,740)(501,742)(502,741)(503,760)(504,759)(505,767)(506,768)
(507,749)(508,750)(509,747)(510,748)(511,761)(512,762)(513,706)(514,705)
(515,723)(516,724)(517,726)(518,725)(519,711)(520,712)(521,720)(522,719)
(523,733)(524,734)(525,731)(526,732)(527,714)(528,713)(529,721)(530,722)
(531,707)(532,708)(533,710)(534,709)(535,728)(536,727)(537,735)(538,736)
(539,717)(540,718)(541,715)(542,716)(543,729)(544,730)(545,674)(546,673)
(547,691)(548,692)(549,694)(550,693)(551,679)(552,680)(553,688)(554,687)
(555,701)(556,702)(557,699)(558,700)(559,682)(560,681)(561,689)(562,690)
(563,675)(564,676)(565,678)(566,677)(567,696)(568,695)(569,703)(570,704)
(571,685)(572,686)(573,683)(574,684)(575,697)(576,698)(577,642)(578,641)
(579,659)(580,660)(581,662)(582,661)(583,647)(584,648)(585,656)(586,655)
(587,669)(588,670)(589,667)(590,668)(591,650)(592,649)(593,657)(594,658)
(595,643)(596,644)(597,646)(598,645)(599,664)(600,663)(601,671)(602,672)
(603,653)(604,654)(605,651)(606,652)(607,665)(608,666)(609,770)(610,769)
(611,787)(612,788)(613,790)(614,789)(615,775)(616,776)(617,784)(618,783)
(619,797)(620,798)(621,795)(622,796)(623,778)(624,777)(625,785)(626,786)
(627,771)(628,772)(629,774)(630,773)(631,792)(632,791)(633,799)(634,800)
(635,781)(636,782)(637,779)(638,780)(639,793)(640,794)(801,898)(802,897)
(803,915)(804,916)(805,918)(806,917)(807,903)(808,904)(809,912)(810,911)
(811,925)(812,926)(813,923)(814,924)(815,906)(816,905)(817,913)(818,914)
(819,899)(820,900)(821,902)(822,901)(823,920)(824,919)(825,927)(826,928)
(827,909)(828,910)(829,907)(830,908)(831,921)(832,922)(833,866)(834,865)
(835,883)(836,884)(837,886)(838,885)(839,871)(840,872)(841,880)(842,879)
(843,893)(844,894)(845,891)(846,892)(847,874)(848,873)(849,881)(850,882)
(851,867)(852,868)(853,870)(854,869)(855,888)(856,887)(857,895)(858,896)
(859,877)(860,878)(861,875)(862,876)(863,889)(864,890)(929,930)(931,947)
(932,948)(933,950)(934,949)(937,944)(938,943)(939,957)(940,958)(941,955)
(942,956)(951,952)(953,959)(954,960);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(960)!( 1,497)( 2,498)( 3,500)( 4,499)( 5,502)( 6,501)( 7,503)
( 8,504)( 9,505)( 10,506)( 11,508)( 12,507)( 13,510)( 14,509)( 15,511)
( 16,512)( 17,482)( 18,481)( 19,483)( 20,484)( 21,485)( 22,486)( 23,488)
( 24,487)( 25,490)( 26,489)( 27,491)( 28,492)( 29,493)( 30,494)( 31,496)
( 32,495)( 33,529)( 34,530)( 35,532)( 36,531)( 37,534)( 38,533)( 39,535)
( 40,536)( 41,537)( 42,538)( 43,540)( 44,539)( 45,542)( 46,541)( 47,543)
( 48,544)( 49,514)( 50,513)( 51,515)( 52,516)( 53,517)( 54,518)( 55,520)
( 56,519)( 57,522)( 58,521)( 59,523)( 60,524)( 61,525)( 62,526)( 63,528)
( 64,527)( 65,561)( 66,562)( 67,564)( 68,563)( 69,566)( 70,565)( 71,567)
( 72,568)( 73,569)( 74,570)( 75,572)( 76,571)( 77,574)( 78,573)( 79,575)
( 80,576)( 81,546)( 82,545)( 83,547)( 84,548)( 85,549)( 86,550)( 87,552)
( 88,551)( 89,554)( 90,553)( 91,555)( 92,556)( 93,557)( 94,558)( 95,560)
( 96,559)( 97,593)( 98,594)( 99,596)(100,595)(101,598)(102,597)(103,599)
(104,600)(105,601)(106,602)(107,604)(108,603)(109,606)(110,605)(111,607)
(112,608)(113,578)(114,577)(115,579)(116,580)(117,581)(118,582)(119,584)
(120,583)(121,586)(122,585)(123,587)(124,588)(125,589)(126,590)(127,592)
(128,591)(129,625)(130,626)(131,628)(132,627)(133,630)(134,629)(135,631)
(136,632)(137,633)(138,634)(139,636)(140,635)(141,638)(142,637)(143,639)
(144,640)(145,610)(146,609)(147,611)(148,612)(149,613)(150,614)(151,616)
(152,615)(153,618)(154,617)(155,619)(156,620)(157,621)(158,622)(159,624)
(160,623)(161,657)(162,658)(163,660)(164,659)(165,662)(166,661)(167,663)
(168,664)(169,665)(170,666)(171,668)(172,667)(173,670)(174,669)(175,671)
(176,672)(177,642)(178,641)(179,643)(180,644)(181,645)(182,646)(183,648)
(184,647)(185,650)(186,649)(187,651)(188,652)(189,653)(190,654)(191,656)
(192,655)(193,689)(194,690)(195,692)(196,691)(197,694)(198,693)(199,695)
(200,696)(201,697)(202,698)(203,700)(204,699)(205,702)(206,701)(207,703)
(208,704)(209,674)(210,673)(211,675)(212,676)(213,677)(214,678)(215,680)
(216,679)(217,682)(218,681)(219,683)(220,684)(221,685)(222,686)(223,688)
(224,687)(225,721)(226,722)(227,724)(228,723)(229,726)(230,725)(231,727)
(232,728)(233,729)(234,730)(235,732)(236,731)(237,734)(238,733)(239,735)
(240,736)(241,706)(242,705)(243,707)(244,708)(245,709)(246,710)(247,712)
(248,711)(249,714)(250,713)(251,715)(252,716)(253,717)(254,718)(255,720)
(256,719)(257,753)(258,754)(259,756)(260,755)(261,758)(262,757)(263,759)
(264,760)(265,761)(266,762)(267,764)(268,763)(269,766)(270,765)(271,767)
(272,768)(273,738)(274,737)(275,739)(276,740)(277,741)(278,742)(279,744)
(280,743)(281,746)(282,745)(283,747)(284,748)(285,749)(286,750)(287,752)
(288,751)(289,785)(290,786)(291,788)(292,787)(293,790)(294,789)(295,791)
(296,792)(297,793)(298,794)(299,796)(300,795)(301,798)(302,797)(303,799)
(304,800)(305,770)(306,769)(307,771)(308,772)(309,773)(310,774)(311,776)
(312,775)(313,778)(314,777)(315,779)(316,780)(317,781)(318,782)(319,784)
(320,783)(321,817)(322,818)(323,820)(324,819)(325,822)(326,821)(327,823)
(328,824)(329,825)(330,826)(331,828)(332,827)(333,830)(334,829)(335,831)
(336,832)(337,802)(338,801)(339,803)(340,804)(341,805)(342,806)(343,808)
(344,807)(345,810)(346,809)(347,811)(348,812)(349,813)(350,814)(351,816)
(352,815)(353,849)(354,850)(355,852)(356,851)(357,854)(358,853)(359,855)
(360,856)(361,857)(362,858)(363,860)(364,859)(365,862)(366,861)(367,863)
(368,864)(369,834)(370,833)(371,835)(372,836)(373,837)(374,838)(375,840)
(376,839)(377,842)(378,841)(379,843)(380,844)(381,845)(382,846)(383,848)
(384,847)(385,881)(386,882)(387,884)(388,883)(389,886)(390,885)(391,887)
(392,888)(393,889)(394,890)(395,892)(396,891)(397,894)(398,893)(399,895)
(400,896)(401,866)(402,865)(403,867)(404,868)(405,869)(406,870)(407,872)
(408,871)(409,874)(410,873)(411,875)(412,876)(413,877)(414,878)(415,880)
(416,879)(417,913)(418,914)(419,916)(420,915)(421,918)(422,917)(423,919)
(424,920)(425,921)(426,922)(427,924)(428,923)(429,926)(430,925)(431,927)
(432,928)(433,898)(434,897)(435,899)(436,900)(437,901)(438,902)(439,904)
(440,903)(441,906)(442,905)(443,907)(444,908)(445,909)(446,910)(447,912)
(448,911)(449,945)(450,946)(451,948)(452,947)(453,950)(454,949)(455,951)
(456,952)(457,953)(458,954)(459,956)(460,955)(461,958)(462,957)(463,959)
(464,960)(465,930)(466,929)(467,931)(468,932)(469,933)(470,934)(471,936)
(472,935)(473,938)(474,937)(475,939)(476,940)(477,941)(478,942)(479,944)
(480,943);
s1 := 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)(481,482)
(483,484)(485,487)(486,488)(493,496)(494,495)(497,507)(498,508)(499,505)
(500,506)(501,510)(502,509)(503,512)(504,511)(513,610)(514,609)(515,612)
(516,611)(517,615)(518,616)(519,613)(520,614)(521,617)(522,618)(523,619)
(524,620)(525,624)(526,623)(527,622)(528,621)(529,635)(530,636)(531,633)
(532,634)(533,638)(534,637)(535,640)(536,639)(537,627)(538,628)(539,625)
(540,626)(541,630)(542,629)(543,632)(544,631)(545,578)(546,577)(547,580)
(548,579)(549,583)(550,584)(551,581)(552,582)(553,585)(554,586)(555,587)
(556,588)(557,592)(558,591)(559,590)(560,589)(561,603)(562,604)(563,601)
(564,602)(565,606)(566,605)(567,608)(568,607)(569,595)(570,596)(571,593)
(572,594)(573,598)(574,597)(575,600)(576,599)(641,802)(642,801)(643,804)
(644,803)(645,807)(646,808)(647,805)(648,806)(649,809)(650,810)(651,811)
(652,812)(653,816)(654,815)(655,814)(656,813)(657,827)(658,828)(659,825)
(660,826)(661,830)(662,829)(663,832)(664,831)(665,819)(666,820)(667,817)
(668,818)(669,822)(670,821)(671,824)(672,823)(673,930)(674,929)(675,932)
(676,931)(677,935)(678,936)(679,933)(680,934)(681,937)(682,938)(683,939)
(684,940)(685,944)(686,943)(687,942)(688,941)(689,955)(690,956)(691,953)
(692,954)(693,958)(694,957)(695,960)(696,959)(697,947)(698,948)(699,945)
(700,946)(701,950)(702,949)(703,952)(704,951)(705,898)(706,897)(707,900)
(708,899)(709,903)(710,904)(711,901)(712,902)(713,905)(714,906)(715,907)
(716,908)(717,912)(718,911)(719,910)(720,909)(721,923)(722,924)(723,921)
(724,922)(725,926)(726,925)(727,928)(728,927)(729,915)(730,916)(731,913)
(732,914)(733,918)(734,917)(735,920)(736,919)(737,866)(738,865)(739,868)
(740,867)(741,871)(742,872)(743,869)(744,870)(745,873)(746,874)(747,875)
(748,876)(749,880)(750,879)(751,878)(752,877)(753,891)(754,892)(755,889)
(756,890)(757,894)(758,893)(759,896)(760,895)(761,883)(762,884)(763,881)
(764,882)(765,886)(766,885)(767,888)(768,887)(769,834)(770,833)(771,836)
(772,835)(773,839)(774,840)(775,837)(776,838)(777,841)(778,842)(779,843)
(780,844)(781,848)(782,847)(783,846)(784,845)(785,859)(786,860)(787,857)
(788,858)(789,862)(790,861)(791,864)(792,863)(793,851)(794,852)(795,849)
(796,850)(797,854)(798,853)(799,856)(800,855);
s2 := Sym(960)!( 1,257)( 2,258)( 3,276)( 4,275)( 5,277)( 6,278)( 7,264)
( 8,263)( 9,271)( 10,272)( 11,286)( 12,285)( 13,284)( 14,283)( 15,265)
( 16,266)( 17,274)( 18,273)( 19,260)( 20,259)( 21,261)( 22,262)( 23,279)
( 24,280)( 25,288)( 26,287)( 27,270)( 28,269)( 29,268)( 30,267)( 31,282)
( 32,281)( 33,225)( 34,226)( 35,244)( 36,243)( 37,245)( 38,246)( 39,232)
( 40,231)( 41,239)( 42,240)( 43,254)( 44,253)( 45,252)( 46,251)( 47,233)
( 48,234)( 49,242)( 50,241)( 51,228)( 52,227)( 53,229)( 54,230)( 55,247)
( 56,248)( 57,256)( 58,255)( 59,238)( 60,237)( 61,236)( 62,235)( 63,250)
( 64,249)( 65,193)( 66,194)( 67,212)( 68,211)( 69,213)( 70,214)( 71,200)
( 72,199)( 73,207)( 74,208)( 75,222)( 76,221)( 77,220)( 78,219)( 79,201)
( 80,202)( 81,210)( 82,209)( 83,196)( 84,195)( 85,197)( 86,198)( 87,215)
( 88,216)( 89,224)( 90,223)( 91,206)( 92,205)( 93,204)( 94,203)( 95,218)
( 96,217)( 97,161)( 98,162)( 99,180)(100,179)(101,181)(102,182)(103,168)
(104,167)(105,175)(106,176)(107,190)(108,189)(109,188)(110,187)(111,169)
(112,170)(113,178)(114,177)(115,164)(116,163)(117,165)(118,166)(119,183)
(120,184)(121,192)(122,191)(123,174)(124,173)(125,172)(126,171)(127,186)
(128,185)(129,289)(130,290)(131,308)(132,307)(133,309)(134,310)(135,296)
(136,295)(137,303)(138,304)(139,318)(140,317)(141,316)(142,315)(143,297)
(144,298)(145,306)(146,305)(147,292)(148,291)(149,293)(150,294)(151,311)
(152,312)(153,320)(154,319)(155,302)(156,301)(157,300)(158,299)(159,314)
(160,313)(321,417)(322,418)(323,436)(324,435)(325,437)(326,438)(327,424)
(328,423)(329,431)(330,432)(331,446)(332,445)(333,444)(334,443)(335,425)
(336,426)(337,434)(338,433)(339,420)(340,419)(341,421)(342,422)(343,439)
(344,440)(345,448)(346,447)(347,430)(348,429)(349,428)(350,427)(351,442)
(352,441)(353,385)(354,386)(355,404)(356,403)(357,405)(358,406)(359,392)
(360,391)(361,399)(362,400)(363,414)(364,413)(365,412)(366,411)(367,393)
(368,394)(369,402)(370,401)(371,388)(372,387)(373,389)(374,390)(375,407)
(376,408)(377,416)(378,415)(379,398)(380,397)(381,396)(382,395)(383,410)
(384,409)(451,468)(452,467)(453,469)(454,470)(455,456)(457,463)(458,464)
(459,478)(460,477)(461,476)(462,475)(465,466)(473,480)(474,479)(481,738)
(482,737)(483,755)(484,756)(485,758)(486,757)(487,743)(488,744)(489,752)
(490,751)(491,765)(492,766)(493,763)(494,764)(495,746)(496,745)(497,753)
(498,754)(499,739)(500,740)(501,742)(502,741)(503,760)(504,759)(505,767)
(506,768)(507,749)(508,750)(509,747)(510,748)(511,761)(512,762)(513,706)
(514,705)(515,723)(516,724)(517,726)(518,725)(519,711)(520,712)(521,720)
(522,719)(523,733)(524,734)(525,731)(526,732)(527,714)(528,713)(529,721)
(530,722)(531,707)(532,708)(533,710)(534,709)(535,728)(536,727)(537,735)
(538,736)(539,717)(540,718)(541,715)(542,716)(543,729)(544,730)(545,674)
(546,673)(547,691)(548,692)(549,694)(550,693)(551,679)(552,680)(553,688)
(554,687)(555,701)(556,702)(557,699)(558,700)(559,682)(560,681)(561,689)
(562,690)(563,675)(564,676)(565,678)(566,677)(567,696)(568,695)(569,703)
(570,704)(571,685)(572,686)(573,683)(574,684)(575,697)(576,698)(577,642)
(578,641)(579,659)(580,660)(581,662)(582,661)(583,647)(584,648)(585,656)
(586,655)(587,669)(588,670)(589,667)(590,668)(591,650)(592,649)(593,657)
(594,658)(595,643)(596,644)(597,646)(598,645)(599,664)(600,663)(601,671)
(602,672)(603,653)(604,654)(605,651)(606,652)(607,665)(608,666)(609,770)
(610,769)(611,787)(612,788)(613,790)(614,789)(615,775)(616,776)(617,784)
(618,783)(619,797)(620,798)(621,795)(622,796)(623,778)(624,777)(625,785)
(626,786)(627,771)(628,772)(629,774)(630,773)(631,792)(632,791)(633,799)
(634,800)(635,781)(636,782)(637,779)(638,780)(639,793)(640,794)(801,898)
(802,897)(803,915)(804,916)(805,918)(806,917)(807,903)(808,904)(809,912)
(810,911)(811,925)(812,926)(813,923)(814,924)(815,906)(816,905)(817,913)
(818,914)(819,899)(820,900)(821,902)(822,901)(823,920)(824,919)(825,927)
(826,928)(827,909)(828,910)(829,907)(830,908)(831,921)(832,922)(833,866)
(834,865)(835,883)(836,884)(837,886)(838,885)(839,871)(840,872)(841,880)
(842,879)(843,893)(844,894)(845,891)(846,892)(847,874)(848,873)(849,881)
(850,882)(851,867)(852,868)(853,870)(854,869)(855,888)(856,887)(857,895)
(858,896)(859,877)(860,878)(861,875)(862,876)(863,889)(864,890)(929,930)
(931,947)(932,948)(933,950)(934,949)(937,944)(938,943)(939,957)(940,958)
(941,955)(942,956)(951,952)(953,959)(954,960);
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope