Polytope of Type {4,30}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,30}*1920d
if this polytope has a name.
Group : SmallGroup(1920,240409)
Rank : 3
Schlafli Type : {4,30}
Number of vertices, edges, etc : 32, 480, 240
Order of s₀s₁s₂ : 30
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, {4,30}*960c, {4,30}*960d
   3-fold quotients : {4,10}*640b
   4-fold quotients : {4,15}*480
   6-fold quotients : {4,5}*320, {4,10}*320a, {4,10}*320b
   12-fold quotients : {4,5}*160
   16-fold quotients : {2,30}*120
   32-fold quotients : {2,15}*60
   48-fold quotients : {2,10}*40
   80-fold quotients : {2,6}*24
   96-fold quotients : {2,5}*20
   160-fold quotients : {2,3}*12
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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