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