Polytope of Type {4,30}

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

References : None.
to this polytope