Polytope of Type {30,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30,8}*1920i
if this polytope has a name.
Group : SmallGroup(1920,240269)
Rank : 3
Schlafli Type : {30,8}
Number of vertices, edges, etc : 120, 480, 32
Order of s₀s₁s₂ : 30
Order of s₀s₁s₂s₁ : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
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, {30,4}*960c
   3-fold quotients : {10,8}*640b
   4-fold quotients : {15,4}*480
   6-fold quotients : {5,8}*320a, {10,4}*320a
   12-fold quotients : {5,4}*160
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 := (  1,673)(  2,674)(  3,704)(  4,703)(  5,684)(  6,683)(  7,693)(  8,694)
(  9,700)( 10,699)( 11,678)( 12,677)( 13,690)( 14,689)( 15,688)( 16,687)
( 17,686)( 18,685)( 19,691)( 20,692)( 21,679)( 22,680)( 23,698)( 24,697)
( 25,696)( 26,695)( 27,682)( 28,681)( 29,702)( 30,701)( 31,676)( 32,675)
( 33,641)( 34,642)( 35,672)( 36,671)( 37,652)( 38,651)( 39,661)( 40,662)
( 41,668)( 42,667)( 43,646)( 44,645)( 45,658)( 46,657)( 47,656)( 48,655)
( 49,654)( 50,653)( 51,659)( 52,660)( 53,647)( 54,648)( 55,666)( 56,665)
( 57,664)( 58,663)( 59,650)( 60,649)( 61,670)( 62,669)( 63,644)( 64,643)
( 65,769)( 66,770)( 67,800)( 68,799)( 69,780)( 70,779)( 71,789)( 72,790)
( 73,796)( 74,795)( 75,774)( 76,773)( 77,786)( 78,785)( 79,784)( 80,783)
( 81,782)( 82,781)( 83,787)( 84,788)( 85,775)( 86,776)( 87,794)( 88,793)
( 89,792)( 90,791)( 91,778)( 92,777)( 93,798)( 94,797)( 95,772)( 96,771)
( 97,737)( 98,738)( 99,768)(100,767)(101,748)(102,747)(103,757)(104,758)
(105,764)(106,763)(107,742)(108,741)(109,754)(110,753)(111,752)(112,751)
(113,750)(114,749)(115,755)(116,756)(117,743)(118,744)(119,762)(120,761)
(121,760)(122,759)(123,746)(124,745)(125,766)(126,765)(127,740)(128,739)
(129,705)(130,706)(131,736)(132,735)(133,716)(134,715)(135,725)(136,726)
(137,732)(138,731)(139,710)(140,709)(141,722)(142,721)(143,720)(144,719)
(145,718)(146,717)(147,723)(148,724)(149,711)(150,712)(151,730)(152,729)
(153,728)(154,727)(155,714)(156,713)(157,734)(158,733)(159,708)(160,707)
(161,513)(162,514)(163,544)(164,543)(165,524)(166,523)(167,533)(168,534)
(169,540)(170,539)(171,518)(172,517)(173,530)(174,529)(175,528)(176,527)
(177,526)(178,525)(179,531)(180,532)(181,519)(182,520)(183,538)(184,537)
(185,536)(186,535)(187,522)(188,521)(189,542)(190,541)(191,516)(192,515)
(193,481)(194,482)(195,512)(196,511)(197,492)(198,491)(199,501)(200,502)
(201,508)(202,507)(203,486)(204,485)(205,498)(206,497)(207,496)(208,495)
(209,494)(210,493)(211,499)(212,500)(213,487)(214,488)(215,506)(216,505)
(217,504)(218,503)(219,490)(220,489)(221,510)(222,509)(223,484)(224,483)
(225,609)(226,610)(227,640)(228,639)(229,620)(230,619)(231,629)(232,630)
(233,636)(234,635)(235,614)(236,613)(237,626)(238,625)(239,624)(240,623)
(241,622)(242,621)(243,627)(244,628)(245,615)(246,616)(247,634)(248,633)
(249,632)(250,631)(251,618)(252,617)(253,638)(254,637)(255,612)(256,611)
(257,577)(258,578)(259,608)(260,607)(261,588)(262,587)(263,597)(264,598)
(265,604)(266,603)(267,582)(268,581)(269,594)(270,593)(271,592)(272,591)
(273,590)(274,589)(275,595)(276,596)(277,583)(278,584)(279,602)(280,601)
(281,600)(282,599)(283,586)(284,585)(285,606)(286,605)(287,580)(288,579)
(289,545)(290,546)(291,576)(292,575)(293,556)(294,555)(295,565)(296,566)
(297,572)(298,571)(299,550)(300,549)(301,562)(302,561)(303,560)(304,559)
(305,558)(306,557)(307,563)(308,564)(309,551)(310,552)(311,570)(312,569)
(313,568)(314,567)(315,554)(316,553)(317,574)(318,573)(319,548)(320,547)
(321,833)(322,834)(323,864)(324,863)(325,844)(326,843)(327,853)(328,854)
(329,860)(330,859)(331,838)(332,837)(333,850)(334,849)(335,848)(336,847)
(337,846)(338,845)(339,851)(340,852)(341,839)(342,840)(343,858)(344,857)
(345,856)(346,855)(347,842)(348,841)(349,862)(350,861)(351,836)(352,835)
(353,801)(354,802)(355,832)(356,831)(357,812)(358,811)(359,821)(360,822)
(361,828)(362,827)(363,806)(364,805)(365,818)(366,817)(367,816)(368,815)
(369,814)(370,813)(371,819)(372,820)(373,807)(374,808)(375,826)(376,825)
(377,824)(378,823)(379,810)(380,809)(381,830)(382,829)(383,804)(384,803)
(385,929)(386,930)(387,960)(388,959)(389,940)(390,939)(391,949)(392,950)
(393,956)(394,955)(395,934)(396,933)(397,946)(398,945)(399,944)(400,943)
(401,942)(402,941)(403,947)(404,948)(405,935)(406,936)(407,954)(408,953)
(409,952)(410,951)(411,938)(412,937)(413,958)(414,957)(415,932)(416,931)
(417,897)(418,898)(419,928)(420,927)(421,908)(422,907)(423,917)(424,918)
(425,924)(426,923)(427,902)(428,901)(429,914)(430,913)(431,912)(432,911)
(433,910)(434,909)(435,915)(436,916)(437,903)(438,904)(439,922)(440,921)
(441,920)(442,919)(443,906)(444,905)(445,926)(446,925)(447,900)(448,899)
(449,865)(450,866)(451,896)(452,895)(453,876)(454,875)(455,885)(456,886)
(457,892)(458,891)(459,870)(460,869)(461,882)(462,881)(463,880)(464,879)
(465,878)(466,877)(467,883)(468,884)(469,871)(470,872)(471,890)(472,889)
(473,888)(474,887)(475,874)(476,873)(477,894)(478,893)(479,868)(480,867);;
s2 := (  1,  4)(  2,  3)(  5,  8)(  6,  7)(  9, 12)( 10, 11)( 13, 16)( 14, 15)
( 17, 20)( 18, 19)( 21, 24)( 22, 23)( 25, 28)( 26, 27)( 29, 32)( 30, 31)
( 33, 36)( 34, 35)( 37, 40)( 38, 39)( 41, 44)( 42, 43)( 45, 48)( 46, 47)
( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)
( 65, 68)( 66, 67)( 69, 72)( 70, 71)( 73, 76)( 74, 75)( 77, 80)( 78, 79)
( 81, 84)( 82, 83)( 85, 88)( 86, 87)( 89, 92)( 90, 91)( 93, 96)( 94, 95)
( 97,100)( 98, 99)(101,104)(102,103)(105,108)(106,107)(109,112)(110,111)
(113,116)(114,115)(117,120)(118,119)(121,124)(122,123)(125,128)(126,127)
(129,132)(130,131)(133,136)(134,135)(137,140)(138,139)(141,144)(142,143)
(145,148)(146,147)(149,152)(150,151)(153,156)(154,155)(157,160)(158,159)
(161,164)(162,163)(165,168)(166,167)(169,172)(170,171)(173,176)(174,175)
(177,180)(178,179)(181,184)(182,183)(185,188)(186,187)(189,192)(190,191)
(193,196)(194,195)(197,200)(198,199)(201,204)(202,203)(205,208)(206,207)
(209,212)(210,211)(213,216)(214,215)(217,220)(218,219)(221,224)(222,223)
(225,228)(226,227)(229,232)(230,231)(233,236)(234,235)(237,240)(238,239)
(241,244)(242,243)(245,248)(246,247)(249,252)(250,251)(253,256)(254,255)
(257,260)(258,259)(261,264)(262,263)(265,268)(266,267)(269,272)(270,271)
(273,276)(274,275)(277,280)(278,279)(281,284)(282,283)(285,288)(286,287)
(289,292)(290,291)(293,296)(294,295)(297,300)(298,299)(301,304)(302,303)
(305,308)(306,307)(309,312)(310,311)(313,316)(314,315)(317,320)(318,319)
(321,324)(322,323)(325,328)(326,327)(329,332)(330,331)(333,336)(334,335)
(337,340)(338,339)(341,344)(342,343)(345,348)(346,347)(349,352)(350,351)
(353,356)(354,355)(357,360)(358,359)(361,364)(362,363)(365,368)(366,367)
(369,372)(370,371)(373,376)(374,375)(377,380)(378,379)(381,384)(382,383)
(385,388)(386,387)(389,392)(390,391)(393,396)(394,395)(397,400)(398,399)
(401,404)(402,403)(405,408)(406,407)(409,412)(410,411)(413,416)(414,415)
(417,420)(418,419)(421,424)(422,423)(425,428)(426,427)(429,432)(430,431)
(433,436)(434,435)(437,440)(438,439)(441,444)(442,443)(445,448)(446,447)
(449,452)(450,451)(453,456)(454,455)(457,460)(458,459)(461,464)(462,463)
(465,468)(466,467)(469,472)(470,471)(473,476)(474,475)(477,480)(478,479)
(481,484)(482,483)(485,488)(486,487)(489,492)(490,491)(493,496)(494,495)
(497,500)(498,499)(501,504)(502,503)(505,508)(506,507)(509,512)(510,511)
(513,516)(514,515)(517,520)(518,519)(521,524)(522,523)(525,528)(526,527)
(529,532)(530,531)(533,536)(534,535)(537,540)(538,539)(541,544)(542,543)
(545,548)(546,547)(549,552)(550,551)(553,556)(554,555)(557,560)(558,559)
(561,564)(562,563)(565,568)(566,567)(569,572)(570,571)(573,576)(574,575)
(577,580)(578,579)(581,584)(582,583)(585,588)(586,587)(589,592)(590,591)
(593,596)(594,595)(597,600)(598,599)(601,604)(602,603)(605,608)(606,607)
(609,612)(610,611)(613,616)(614,615)(617,620)(618,619)(621,624)(622,623)
(625,628)(626,627)(629,632)(630,631)(633,636)(634,635)(637,640)(638,639)
(641,644)(642,643)(645,648)(646,647)(649,652)(650,651)(653,656)(654,655)
(657,660)(658,659)(661,664)(662,663)(665,668)(666,667)(669,672)(670,671)
(673,676)(674,675)(677,680)(678,679)(681,684)(682,683)(685,688)(686,687)
(689,692)(690,691)(693,696)(694,695)(697,700)(698,699)(701,704)(702,703)
(705,708)(706,707)(709,712)(710,711)(713,716)(714,715)(717,720)(718,719)
(721,724)(722,723)(725,728)(726,727)(729,732)(730,731)(733,736)(734,735)
(737,740)(738,739)(741,744)(742,743)(745,748)(746,747)(749,752)(750,751)
(753,756)(754,755)(757,760)(758,759)(761,764)(762,763)(765,768)(766,767)
(769,772)(770,771)(773,776)(774,775)(777,780)(778,779)(781,784)(782,783)
(785,788)(786,787)(789,792)(790,791)(793,796)(794,795)(797,800)(798,799)
(801,804)(802,803)(805,808)(806,807)(809,812)(810,811)(813,816)(814,815)
(817,820)(818,819)(821,824)(822,823)(825,828)(826,827)(829,832)(830,831)
(833,836)(834,835)(837,840)(838,839)(841,844)(842,843)(845,848)(846,847)
(849,852)(850,851)(853,856)(854,855)(857,860)(858,859)(861,864)(862,863)
(865,868)(866,867)(869,872)(870,871)(873,876)(874,875)(877,880)(878,879)
(881,884)(882,883)(885,888)(886,887)(889,892)(890,891)(893,896)(894,895)
(897,900)(898,899)(901,904)(902,903)(905,908)(906,907)(909,912)(910,911)
(913,916)(914,915)(917,920)(918,919)(921,924)(922,923)(925,928)(926,927)
(929,932)(930,931)(933,936)(934,935)(937,940)(938,939)(941,944)(942,943)
(945,948)(946,947)(949,952)(950,951)(953,956)(954,955)(957,960)(958,959);;
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, 
s1*s2*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope