Polytope of Type {2,30,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,30,12}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240162)
Rank : 4
Schlafli Type : {2,30,12}
Number of vertices, edges, etc : 2, 40, 240, 16
Order of s0s1s2s3 : 40
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
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 : {2,15,12}*960, {2,30,6}*960
   4-fold quotients : {2,15,6}*480
   5-fold quotients : {2,6,12}*384b
   10-fold quotients : {2,3,12}*192, {2,6,6}*192
   20-fold quotients : {2,3,6}*96, {2,6,3}*96
   24-fold quotients : {2,10,2}*80
   40-fold quotients : {2,3,3}*48
   48-fold quotients : {2,5,2}*40
   120-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) : 
s0 := (1,2);;
s1 := (  3,723)(  4,724)(  5,728)(  6,727)(  7,726)(  8,725)(  9,730)( 10,729)
( 11,755)( 12,756)( 13,760)( 14,759)( 15,758)( 16,757)( 17,762)( 18,761)
( 19,747)( 20,748)( 21,752)( 22,751)( 23,750)( 24,749)( 25,754)( 26,753)
( 27,739)( 28,740)( 29,744)( 30,743)( 31,742)( 32,741)( 33,746)( 34,745)
( 35,731)( 36,732)( 37,736)( 38,735)( 39,734)( 40,733)( 41,738)( 42,737)
( 43,803)( 44,804)( 45,808)( 46,807)( 47,806)( 48,805)( 49,810)( 50,809)
( 51,835)( 52,836)( 53,840)( 54,839)( 55,838)( 56,837)( 57,842)( 58,841)
( 59,827)( 60,828)( 61,832)( 62,831)( 63,830)( 64,829)( 65,834)( 66,833)
( 67,819)( 68,820)( 69,824)( 70,823)( 71,822)( 72,821)( 73,826)( 74,825)
( 75,811)( 76,812)( 77,816)( 78,815)( 79,814)( 80,813)( 81,818)( 82,817)
( 83,763)( 84,764)( 85,768)( 86,767)( 87,766)( 88,765)( 89,770)( 90,769)
( 91,795)( 92,796)( 93,800)( 94,799)( 95,798)( 96,797)( 97,802)( 98,801)
( 99,787)(100,788)(101,792)(102,791)(103,790)(104,789)(105,794)(106,793)
(107,779)(108,780)(109,784)(110,783)(111,782)(112,781)(113,786)(114,785)
(115,771)(116,772)(117,776)(118,775)(119,774)(120,773)(121,778)(122,777)
(123,843)(124,844)(125,848)(126,847)(127,846)(128,845)(129,850)(130,849)
(131,875)(132,876)(133,880)(134,879)(135,878)(136,877)(137,882)(138,881)
(139,867)(140,868)(141,872)(142,871)(143,870)(144,869)(145,874)(146,873)
(147,859)(148,860)(149,864)(150,863)(151,862)(152,861)(153,866)(154,865)
(155,851)(156,852)(157,856)(158,855)(159,854)(160,853)(161,858)(162,857)
(163,923)(164,924)(165,928)(166,927)(167,926)(168,925)(169,930)(170,929)
(171,955)(172,956)(173,960)(174,959)(175,958)(176,957)(177,962)(178,961)
(179,947)(180,948)(181,952)(182,951)(183,950)(184,949)(185,954)(186,953)
(187,939)(188,940)(189,944)(190,943)(191,942)(192,941)(193,946)(194,945)
(195,931)(196,932)(197,936)(198,935)(199,934)(200,933)(201,938)(202,937)
(203,883)(204,884)(205,888)(206,887)(207,886)(208,885)(209,890)(210,889)
(211,915)(212,916)(213,920)(214,919)(215,918)(216,917)(217,922)(218,921)
(219,907)(220,908)(221,912)(222,911)(223,910)(224,909)(225,914)(226,913)
(227,899)(228,900)(229,904)(230,903)(231,902)(232,901)(233,906)(234,905)
(235,891)(236,892)(237,896)(238,895)(239,894)(240,893)(241,898)(242,897)
(243,484)(244,483)(245,487)(246,488)(247,485)(248,486)(249,489)(250,490)
(251,516)(252,515)(253,519)(254,520)(255,517)(256,518)(257,521)(258,522)
(259,508)(260,507)(261,511)(262,512)(263,509)(264,510)(265,513)(266,514)
(267,500)(268,499)(269,503)(270,504)(271,501)(272,502)(273,505)(274,506)
(275,492)(276,491)(277,495)(278,496)(279,493)(280,494)(281,497)(282,498)
(283,564)(284,563)(285,567)(286,568)(287,565)(288,566)(289,569)(290,570)
(291,596)(292,595)(293,599)(294,600)(295,597)(296,598)(297,601)(298,602)
(299,588)(300,587)(301,591)(302,592)(303,589)(304,590)(305,593)(306,594)
(307,580)(308,579)(309,583)(310,584)(311,581)(312,582)(313,585)(314,586)
(315,572)(316,571)(317,575)(318,576)(319,573)(320,574)(321,577)(322,578)
(323,524)(324,523)(325,527)(326,528)(327,525)(328,526)(329,529)(330,530)
(331,556)(332,555)(333,559)(334,560)(335,557)(336,558)(337,561)(338,562)
(339,548)(340,547)(341,551)(342,552)(343,549)(344,550)(345,553)(346,554)
(347,540)(348,539)(349,543)(350,544)(351,541)(352,542)(353,545)(354,546)
(355,532)(356,531)(357,535)(358,536)(359,533)(360,534)(361,537)(362,538)
(363,604)(364,603)(365,607)(366,608)(367,605)(368,606)(369,609)(370,610)
(371,636)(372,635)(373,639)(374,640)(375,637)(376,638)(377,641)(378,642)
(379,628)(380,627)(381,631)(382,632)(383,629)(384,630)(385,633)(386,634)
(387,620)(388,619)(389,623)(390,624)(391,621)(392,622)(393,625)(394,626)
(395,612)(396,611)(397,615)(398,616)(399,613)(400,614)(401,617)(402,618)
(403,684)(404,683)(405,687)(406,688)(407,685)(408,686)(409,689)(410,690)
(411,716)(412,715)(413,719)(414,720)(415,717)(416,718)(417,721)(418,722)
(419,708)(420,707)(421,711)(422,712)(423,709)(424,710)(425,713)(426,714)
(427,700)(428,699)(429,703)(430,704)(431,701)(432,702)(433,705)(434,706)
(435,692)(436,691)(437,695)(438,696)(439,693)(440,694)(441,697)(442,698)
(443,644)(444,643)(445,647)(446,648)(447,645)(448,646)(449,649)(450,650)
(451,676)(452,675)(453,679)(454,680)(455,677)(456,678)(457,681)(458,682)
(459,668)(460,667)(461,671)(462,672)(463,669)(464,670)(465,673)(466,674)
(467,660)(468,659)(469,663)(470,664)(471,661)(472,662)(473,665)(474,666)
(475,652)(476,651)(477,655)(478,656)(479,653)(480,654)(481,657)(482,658);;
s2 := (  3,891)(  4,892)(  5,894)(  6,893)(  7,897)(  8,898)(  9,895)( 10,896)
( 11,883)( 12,884)( 13,886)( 14,885)( 15,889)( 16,890)( 17,887)( 18,888)
( 19,915)( 20,916)( 21,918)( 22,917)( 23,921)( 24,922)( 25,919)( 26,920)
( 27,907)( 28,908)( 29,910)( 30,909)( 31,913)( 32,914)( 33,911)( 34,912)
( 35,899)( 36,900)( 37,902)( 38,901)( 39,905)( 40,906)( 41,903)( 42,904)
( 43,851)( 44,852)( 45,854)( 46,853)( 47,857)( 48,858)( 49,855)( 50,856)
( 51,843)( 52,844)( 53,846)( 54,845)( 55,849)( 56,850)( 57,847)( 58,848)
( 59,875)( 60,876)( 61,878)( 62,877)( 63,881)( 64,882)( 65,879)( 66,880)
( 67,867)( 68,868)( 69,870)( 70,869)( 71,873)( 72,874)( 73,871)( 74,872)
( 75,859)( 76,860)( 77,862)( 78,861)( 79,865)( 80,866)( 81,863)( 82,864)
( 83,931)( 84,932)( 85,934)( 86,933)( 87,937)( 88,938)( 89,935)( 90,936)
( 91,923)( 92,924)( 93,926)( 94,925)( 95,929)( 96,930)( 97,927)( 98,928)
( 99,955)(100,956)(101,958)(102,957)(103,961)(104,962)(105,959)(106,960)
(107,947)(108,948)(109,950)(110,949)(111,953)(112,954)(113,951)(114,952)
(115,939)(116,940)(117,942)(118,941)(119,945)(120,946)(121,943)(122,944)
(123,771)(124,772)(125,774)(126,773)(127,777)(128,778)(129,775)(130,776)
(131,763)(132,764)(133,766)(134,765)(135,769)(136,770)(137,767)(138,768)
(139,795)(140,796)(141,798)(142,797)(143,801)(144,802)(145,799)(146,800)
(147,787)(148,788)(149,790)(150,789)(151,793)(152,794)(153,791)(154,792)
(155,779)(156,780)(157,782)(158,781)(159,785)(160,786)(161,783)(162,784)
(163,731)(164,732)(165,734)(166,733)(167,737)(168,738)(169,735)(170,736)
(171,723)(172,724)(173,726)(174,725)(175,729)(176,730)(177,727)(178,728)
(179,755)(180,756)(181,758)(182,757)(183,761)(184,762)(185,759)(186,760)
(187,747)(188,748)(189,750)(190,749)(191,753)(192,754)(193,751)(194,752)
(195,739)(196,740)(197,742)(198,741)(199,745)(200,746)(201,743)(202,744)
(203,811)(204,812)(205,814)(206,813)(207,817)(208,818)(209,815)(210,816)
(211,803)(212,804)(213,806)(214,805)(215,809)(216,810)(217,807)(218,808)
(219,835)(220,836)(221,838)(222,837)(223,841)(224,842)(225,839)(226,840)
(227,827)(228,828)(229,830)(230,829)(231,833)(232,834)(233,831)(234,832)
(235,819)(236,820)(237,822)(238,821)(239,825)(240,826)(241,823)(242,824)
(243,652)(244,651)(245,653)(246,654)(247,658)(248,657)(249,656)(250,655)
(251,644)(252,643)(253,645)(254,646)(255,650)(256,649)(257,648)(258,647)
(259,676)(260,675)(261,677)(262,678)(263,682)(264,681)(265,680)(266,679)
(267,668)(268,667)(269,669)(270,670)(271,674)(272,673)(273,672)(274,671)
(275,660)(276,659)(277,661)(278,662)(279,666)(280,665)(281,664)(282,663)
(283,612)(284,611)(285,613)(286,614)(287,618)(288,617)(289,616)(290,615)
(291,604)(292,603)(293,605)(294,606)(295,610)(296,609)(297,608)(298,607)
(299,636)(300,635)(301,637)(302,638)(303,642)(304,641)(305,640)(306,639)
(307,628)(308,627)(309,629)(310,630)(311,634)(312,633)(313,632)(314,631)
(315,620)(316,619)(317,621)(318,622)(319,626)(320,625)(321,624)(322,623)
(323,692)(324,691)(325,693)(326,694)(327,698)(328,697)(329,696)(330,695)
(331,684)(332,683)(333,685)(334,686)(335,690)(336,689)(337,688)(338,687)
(339,716)(340,715)(341,717)(342,718)(343,722)(344,721)(345,720)(346,719)
(347,708)(348,707)(349,709)(350,710)(351,714)(352,713)(353,712)(354,711)
(355,700)(356,699)(357,701)(358,702)(359,706)(360,705)(361,704)(362,703)
(363,532)(364,531)(365,533)(366,534)(367,538)(368,537)(369,536)(370,535)
(371,524)(372,523)(373,525)(374,526)(375,530)(376,529)(377,528)(378,527)
(379,556)(380,555)(381,557)(382,558)(383,562)(384,561)(385,560)(386,559)
(387,548)(388,547)(389,549)(390,550)(391,554)(392,553)(393,552)(394,551)
(395,540)(396,539)(397,541)(398,542)(399,546)(400,545)(401,544)(402,543)
(403,492)(404,491)(405,493)(406,494)(407,498)(408,497)(409,496)(410,495)
(411,484)(412,483)(413,485)(414,486)(415,490)(416,489)(417,488)(418,487)
(419,516)(420,515)(421,517)(422,518)(423,522)(424,521)(425,520)(426,519)
(427,508)(428,507)(429,509)(430,510)(431,514)(432,513)(433,512)(434,511)
(435,500)(436,499)(437,501)(438,502)(439,506)(440,505)(441,504)(442,503)
(443,572)(444,571)(445,573)(446,574)(447,578)(448,577)(449,576)(450,575)
(451,564)(452,563)(453,565)(454,566)(455,570)(456,569)(457,568)(458,567)
(459,596)(460,595)(461,597)(462,598)(463,602)(464,601)(465,600)(466,599)
(467,588)(468,587)(469,589)(470,590)(471,594)(472,593)(473,592)(474,591)
(475,580)(476,579)(477,581)(478,582)(479,586)(480,585)(481,584)(482,583);;
s3 := (  3,249)(  4,250)(  5,245)(  6,246)(  7,248)(  8,247)(  9,243)( 10,244)
( 11,257)( 12,258)( 13,253)( 14,254)( 15,256)( 16,255)( 17,251)( 18,252)
( 19,265)( 20,266)( 21,261)( 22,262)( 23,264)( 24,263)( 25,259)( 26,260)
( 27,273)( 28,274)( 29,269)( 30,270)( 31,272)( 32,271)( 33,267)( 34,268)
( 35,281)( 36,282)( 37,277)( 38,278)( 39,280)( 40,279)( 41,275)( 42,276)
( 43,329)( 44,330)( 45,325)( 46,326)( 47,328)( 48,327)( 49,323)( 50,324)
( 51,337)( 52,338)( 53,333)( 54,334)( 55,336)( 56,335)( 57,331)( 58,332)
( 59,345)( 60,346)( 61,341)( 62,342)( 63,344)( 64,343)( 65,339)( 66,340)
( 67,353)( 68,354)( 69,349)( 70,350)( 71,352)( 72,351)( 73,347)( 74,348)
( 75,361)( 76,362)( 77,357)( 78,358)( 79,360)( 80,359)( 81,355)( 82,356)
( 83,289)( 84,290)( 85,285)( 86,286)( 87,288)( 88,287)( 89,283)( 90,284)
( 91,297)( 92,298)( 93,293)( 94,294)( 95,296)( 96,295)( 97,291)( 98,292)
( 99,305)(100,306)(101,301)(102,302)(103,304)(104,303)(105,299)(106,300)
(107,313)(108,314)(109,309)(110,310)(111,312)(112,311)(113,307)(114,308)
(115,321)(116,322)(117,317)(118,318)(119,320)(120,319)(121,315)(122,316)
(123,369)(124,370)(125,365)(126,366)(127,368)(128,367)(129,363)(130,364)
(131,377)(132,378)(133,373)(134,374)(135,376)(136,375)(137,371)(138,372)
(139,385)(140,386)(141,381)(142,382)(143,384)(144,383)(145,379)(146,380)
(147,393)(148,394)(149,389)(150,390)(151,392)(152,391)(153,387)(154,388)
(155,401)(156,402)(157,397)(158,398)(159,400)(160,399)(161,395)(162,396)
(163,449)(164,450)(165,445)(166,446)(167,448)(168,447)(169,443)(170,444)
(171,457)(172,458)(173,453)(174,454)(175,456)(176,455)(177,451)(178,452)
(179,465)(180,466)(181,461)(182,462)(183,464)(184,463)(185,459)(186,460)
(187,473)(188,474)(189,469)(190,470)(191,472)(192,471)(193,467)(194,468)
(195,481)(196,482)(197,477)(198,478)(199,480)(200,479)(201,475)(202,476)
(203,409)(204,410)(205,405)(206,406)(207,408)(208,407)(209,403)(210,404)
(211,417)(212,418)(213,413)(214,414)(215,416)(216,415)(217,411)(218,412)
(219,425)(220,426)(221,421)(222,422)(223,424)(224,423)(225,419)(226,420)
(227,433)(228,434)(229,429)(230,430)(231,432)(232,431)(233,427)(234,428)
(235,441)(236,442)(237,437)(238,438)(239,440)(240,439)(241,435)(242,436)
(483,729)(484,730)(485,725)(486,726)(487,728)(488,727)(489,723)(490,724)
(491,737)(492,738)(493,733)(494,734)(495,736)(496,735)(497,731)(498,732)
(499,745)(500,746)(501,741)(502,742)(503,744)(504,743)(505,739)(506,740)
(507,753)(508,754)(509,749)(510,750)(511,752)(512,751)(513,747)(514,748)
(515,761)(516,762)(517,757)(518,758)(519,760)(520,759)(521,755)(522,756)
(523,809)(524,810)(525,805)(526,806)(527,808)(528,807)(529,803)(530,804)
(531,817)(532,818)(533,813)(534,814)(535,816)(536,815)(537,811)(538,812)
(539,825)(540,826)(541,821)(542,822)(543,824)(544,823)(545,819)(546,820)
(547,833)(548,834)(549,829)(550,830)(551,832)(552,831)(553,827)(554,828)
(555,841)(556,842)(557,837)(558,838)(559,840)(560,839)(561,835)(562,836)
(563,769)(564,770)(565,765)(566,766)(567,768)(568,767)(569,763)(570,764)
(571,777)(572,778)(573,773)(574,774)(575,776)(576,775)(577,771)(578,772)
(579,785)(580,786)(581,781)(582,782)(583,784)(584,783)(585,779)(586,780)
(587,793)(588,794)(589,789)(590,790)(591,792)(592,791)(593,787)(594,788)
(595,801)(596,802)(597,797)(598,798)(599,800)(600,799)(601,795)(602,796)
(603,849)(604,850)(605,845)(606,846)(607,848)(608,847)(609,843)(610,844)
(611,857)(612,858)(613,853)(614,854)(615,856)(616,855)(617,851)(618,852)
(619,865)(620,866)(621,861)(622,862)(623,864)(624,863)(625,859)(626,860)
(627,873)(628,874)(629,869)(630,870)(631,872)(632,871)(633,867)(634,868)
(635,881)(636,882)(637,877)(638,878)(639,880)(640,879)(641,875)(642,876)
(643,929)(644,930)(645,925)(646,926)(647,928)(648,927)(649,923)(650,924)
(651,937)(652,938)(653,933)(654,934)(655,936)(656,935)(657,931)(658,932)
(659,945)(660,946)(661,941)(662,942)(663,944)(664,943)(665,939)(666,940)
(667,953)(668,954)(669,949)(670,950)(671,952)(672,951)(673,947)(674,948)
(675,961)(676,962)(677,957)(678,958)(679,960)(680,959)(681,955)(682,956)
(683,889)(684,890)(685,885)(686,886)(687,888)(688,887)(689,883)(690,884)
(691,897)(692,898)(693,893)(694,894)(695,896)(696,895)(697,891)(698,892)
(699,905)(700,906)(701,901)(702,902)(703,904)(704,903)(705,899)(706,900)
(707,913)(708,914)(709,909)(710,910)(711,912)(712,911)(713,907)(714,908)
(715,921)(716,922)(717,917)(718,918)(719,920)(720,919)(721,915)(722,916);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(962)!(1,2);
s1 := Sym(962)!(  3,723)(  4,724)(  5,728)(  6,727)(  7,726)(  8,725)(  9,730)
( 10,729)( 11,755)( 12,756)( 13,760)( 14,759)( 15,758)( 16,757)( 17,762)
( 18,761)( 19,747)( 20,748)( 21,752)( 22,751)( 23,750)( 24,749)( 25,754)
( 26,753)( 27,739)( 28,740)( 29,744)( 30,743)( 31,742)( 32,741)( 33,746)
( 34,745)( 35,731)( 36,732)( 37,736)( 38,735)( 39,734)( 40,733)( 41,738)
( 42,737)( 43,803)( 44,804)( 45,808)( 46,807)( 47,806)( 48,805)( 49,810)
( 50,809)( 51,835)( 52,836)( 53,840)( 54,839)( 55,838)( 56,837)( 57,842)
( 58,841)( 59,827)( 60,828)( 61,832)( 62,831)( 63,830)( 64,829)( 65,834)
( 66,833)( 67,819)( 68,820)( 69,824)( 70,823)( 71,822)( 72,821)( 73,826)
( 74,825)( 75,811)( 76,812)( 77,816)( 78,815)( 79,814)( 80,813)( 81,818)
( 82,817)( 83,763)( 84,764)( 85,768)( 86,767)( 87,766)( 88,765)( 89,770)
( 90,769)( 91,795)( 92,796)( 93,800)( 94,799)( 95,798)( 96,797)( 97,802)
( 98,801)( 99,787)(100,788)(101,792)(102,791)(103,790)(104,789)(105,794)
(106,793)(107,779)(108,780)(109,784)(110,783)(111,782)(112,781)(113,786)
(114,785)(115,771)(116,772)(117,776)(118,775)(119,774)(120,773)(121,778)
(122,777)(123,843)(124,844)(125,848)(126,847)(127,846)(128,845)(129,850)
(130,849)(131,875)(132,876)(133,880)(134,879)(135,878)(136,877)(137,882)
(138,881)(139,867)(140,868)(141,872)(142,871)(143,870)(144,869)(145,874)
(146,873)(147,859)(148,860)(149,864)(150,863)(151,862)(152,861)(153,866)
(154,865)(155,851)(156,852)(157,856)(158,855)(159,854)(160,853)(161,858)
(162,857)(163,923)(164,924)(165,928)(166,927)(167,926)(168,925)(169,930)
(170,929)(171,955)(172,956)(173,960)(174,959)(175,958)(176,957)(177,962)
(178,961)(179,947)(180,948)(181,952)(182,951)(183,950)(184,949)(185,954)
(186,953)(187,939)(188,940)(189,944)(190,943)(191,942)(192,941)(193,946)
(194,945)(195,931)(196,932)(197,936)(198,935)(199,934)(200,933)(201,938)
(202,937)(203,883)(204,884)(205,888)(206,887)(207,886)(208,885)(209,890)
(210,889)(211,915)(212,916)(213,920)(214,919)(215,918)(216,917)(217,922)
(218,921)(219,907)(220,908)(221,912)(222,911)(223,910)(224,909)(225,914)
(226,913)(227,899)(228,900)(229,904)(230,903)(231,902)(232,901)(233,906)
(234,905)(235,891)(236,892)(237,896)(238,895)(239,894)(240,893)(241,898)
(242,897)(243,484)(244,483)(245,487)(246,488)(247,485)(248,486)(249,489)
(250,490)(251,516)(252,515)(253,519)(254,520)(255,517)(256,518)(257,521)
(258,522)(259,508)(260,507)(261,511)(262,512)(263,509)(264,510)(265,513)
(266,514)(267,500)(268,499)(269,503)(270,504)(271,501)(272,502)(273,505)
(274,506)(275,492)(276,491)(277,495)(278,496)(279,493)(280,494)(281,497)
(282,498)(283,564)(284,563)(285,567)(286,568)(287,565)(288,566)(289,569)
(290,570)(291,596)(292,595)(293,599)(294,600)(295,597)(296,598)(297,601)
(298,602)(299,588)(300,587)(301,591)(302,592)(303,589)(304,590)(305,593)
(306,594)(307,580)(308,579)(309,583)(310,584)(311,581)(312,582)(313,585)
(314,586)(315,572)(316,571)(317,575)(318,576)(319,573)(320,574)(321,577)
(322,578)(323,524)(324,523)(325,527)(326,528)(327,525)(328,526)(329,529)
(330,530)(331,556)(332,555)(333,559)(334,560)(335,557)(336,558)(337,561)
(338,562)(339,548)(340,547)(341,551)(342,552)(343,549)(344,550)(345,553)
(346,554)(347,540)(348,539)(349,543)(350,544)(351,541)(352,542)(353,545)
(354,546)(355,532)(356,531)(357,535)(358,536)(359,533)(360,534)(361,537)
(362,538)(363,604)(364,603)(365,607)(366,608)(367,605)(368,606)(369,609)
(370,610)(371,636)(372,635)(373,639)(374,640)(375,637)(376,638)(377,641)
(378,642)(379,628)(380,627)(381,631)(382,632)(383,629)(384,630)(385,633)
(386,634)(387,620)(388,619)(389,623)(390,624)(391,621)(392,622)(393,625)
(394,626)(395,612)(396,611)(397,615)(398,616)(399,613)(400,614)(401,617)
(402,618)(403,684)(404,683)(405,687)(406,688)(407,685)(408,686)(409,689)
(410,690)(411,716)(412,715)(413,719)(414,720)(415,717)(416,718)(417,721)
(418,722)(419,708)(420,707)(421,711)(422,712)(423,709)(424,710)(425,713)
(426,714)(427,700)(428,699)(429,703)(430,704)(431,701)(432,702)(433,705)
(434,706)(435,692)(436,691)(437,695)(438,696)(439,693)(440,694)(441,697)
(442,698)(443,644)(444,643)(445,647)(446,648)(447,645)(448,646)(449,649)
(450,650)(451,676)(452,675)(453,679)(454,680)(455,677)(456,678)(457,681)
(458,682)(459,668)(460,667)(461,671)(462,672)(463,669)(464,670)(465,673)
(466,674)(467,660)(468,659)(469,663)(470,664)(471,661)(472,662)(473,665)
(474,666)(475,652)(476,651)(477,655)(478,656)(479,653)(480,654)(481,657)
(482,658);
s2 := Sym(962)!(  3,891)(  4,892)(  5,894)(  6,893)(  7,897)(  8,898)(  9,895)
( 10,896)( 11,883)( 12,884)( 13,886)( 14,885)( 15,889)( 16,890)( 17,887)
( 18,888)( 19,915)( 20,916)( 21,918)( 22,917)( 23,921)( 24,922)( 25,919)
( 26,920)( 27,907)( 28,908)( 29,910)( 30,909)( 31,913)( 32,914)( 33,911)
( 34,912)( 35,899)( 36,900)( 37,902)( 38,901)( 39,905)( 40,906)( 41,903)
( 42,904)( 43,851)( 44,852)( 45,854)( 46,853)( 47,857)( 48,858)( 49,855)
( 50,856)( 51,843)( 52,844)( 53,846)( 54,845)( 55,849)( 56,850)( 57,847)
( 58,848)( 59,875)( 60,876)( 61,878)( 62,877)( 63,881)( 64,882)( 65,879)
( 66,880)( 67,867)( 68,868)( 69,870)( 70,869)( 71,873)( 72,874)( 73,871)
( 74,872)( 75,859)( 76,860)( 77,862)( 78,861)( 79,865)( 80,866)( 81,863)
( 82,864)( 83,931)( 84,932)( 85,934)( 86,933)( 87,937)( 88,938)( 89,935)
( 90,936)( 91,923)( 92,924)( 93,926)( 94,925)( 95,929)( 96,930)( 97,927)
( 98,928)( 99,955)(100,956)(101,958)(102,957)(103,961)(104,962)(105,959)
(106,960)(107,947)(108,948)(109,950)(110,949)(111,953)(112,954)(113,951)
(114,952)(115,939)(116,940)(117,942)(118,941)(119,945)(120,946)(121,943)
(122,944)(123,771)(124,772)(125,774)(126,773)(127,777)(128,778)(129,775)
(130,776)(131,763)(132,764)(133,766)(134,765)(135,769)(136,770)(137,767)
(138,768)(139,795)(140,796)(141,798)(142,797)(143,801)(144,802)(145,799)
(146,800)(147,787)(148,788)(149,790)(150,789)(151,793)(152,794)(153,791)
(154,792)(155,779)(156,780)(157,782)(158,781)(159,785)(160,786)(161,783)
(162,784)(163,731)(164,732)(165,734)(166,733)(167,737)(168,738)(169,735)
(170,736)(171,723)(172,724)(173,726)(174,725)(175,729)(176,730)(177,727)
(178,728)(179,755)(180,756)(181,758)(182,757)(183,761)(184,762)(185,759)
(186,760)(187,747)(188,748)(189,750)(190,749)(191,753)(192,754)(193,751)
(194,752)(195,739)(196,740)(197,742)(198,741)(199,745)(200,746)(201,743)
(202,744)(203,811)(204,812)(205,814)(206,813)(207,817)(208,818)(209,815)
(210,816)(211,803)(212,804)(213,806)(214,805)(215,809)(216,810)(217,807)
(218,808)(219,835)(220,836)(221,838)(222,837)(223,841)(224,842)(225,839)
(226,840)(227,827)(228,828)(229,830)(230,829)(231,833)(232,834)(233,831)
(234,832)(235,819)(236,820)(237,822)(238,821)(239,825)(240,826)(241,823)
(242,824)(243,652)(244,651)(245,653)(246,654)(247,658)(248,657)(249,656)
(250,655)(251,644)(252,643)(253,645)(254,646)(255,650)(256,649)(257,648)
(258,647)(259,676)(260,675)(261,677)(262,678)(263,682)(264,681)(265,680)
(266,679)(267,668)(268,667)(269,669)(270,670)(271,674)(272,673)(273,672)
(274,671)(275,660)(276,659)(277,661)(278,662)(279,666)(280,665)(281,664)
(282,663)(283,612)(284,611)(285,613)(286,614)(287,618)(288,617)(289,616)
(290,615)(291,604)(292,603)(293,605)(294,606)(295,610)(296,609)(297,608)
(298,607)(299,636)(300,635)(301,637)(302,638)(303,642)(304,641)(305,640)
(306,639)(307,628)(308,627)(309,629)(310,630)(311,634)(312,633)(313,632)
(314,631)(315,620)(316,619)(317,621)(318,622)(319,626)(320,625)(321,624)
(322,623)(323,692)(324,691)(325,693)(326,694)(327,698)(328,697)(329,696)
(330,695)(331,684)(332,683)(333,685)(334,686)(335,690)(336,689)(337,688)
(338,687)(339,716)(340,715)(341,717)(342,718)(343,722)(344,721)(345,720)
(346,719)(347,708)(348,707)(349,709)(350,710)(351,714)(352,713)(353,712)
(354,711)(355,700)(356,699)(357,701)(358,702)(359,706)(360,705)(361,704)
(362,703)(363,532)(364,531)(365,533)(366,534)(367,538)(368,537)(369,536)
(370,535)(371,524)(372,523)(373,525)(374,526)(375,530)(376,529)(377,528)
(378,527)(379,556)(380,555)(381,557)(382,558)(383,562)(384,561)(385,560)
(386,559)(387,548)(388,547)(389,549)(390,550)(391,554)(392,553)(393,552)
(394,551)(395,540)(396,539)(397,541)(398,542)(399,546)(400,545)(401,544)
(402,543)(403,492)(404,491)(405,493)(406,494)(407,498)(408,497)(409,496)
(410,495)(411,484)(412,483)(413,485)(414,486)(415,490)(416,489)(417,488)
(418,487)(419,516)(420,515)(421,517)(422,518)(423,522)(424,521)(425,520)
(426,519)(427,508)(428,507)(429,509)(430,510)(431,514)(432,513)(433,512)
(434,511)(435,500)(436,499)(437,501)(438,502)(439,506)(440,505)(441,504)
(442,503)(443,572)(444,571)(445,573)(446,574)(447,578)(448,577)(449,576)
(450,575)(451,564)(452,563)(453,565)(454,566)(455,570)(456,569)(457,568)
(458,567)(459,596)(460,595)(461,597)(462,598)(463,602)(464,601)(465,600)
(466,599)(467,588)(468,587)(469,589)(470,590)(471,594)(472,593)(473,592)
(474,591)(475,580)(476,579)(477,581)(478,582)(479,586)(480,585)(481,584)
(482,583);
s3 := Sym(962)!(  3,249)(  4,250)(  5,245)(  6,246)(  7,248)(  8,247)(  9,243)
( 10,244)( 11,257)( 12,258)( 13,253)( 14,254)( 15,256)( 16,255)( 17,251)
( 18,252)( 19,265)( 20,266)( 21,261)( 22,262)( 23,264)( 24,263)( 25,259)
( 26,260)( 27,273)( 28,274)( 29,269)( 30,270)( 31,272)( 32,271)( 33,267)
( 34,268)( 35,281)( 36,282)( 37,277)( 38,278)( 39,280)( 40,279)( 41,275)
( 42,276)( 43,329)( 44,330)( 45,325)( 46,326)( 47,328)( 48,327)( 49,323)
( 50,324)( 51,337)( 52,338)( 53,333)( 54,334)( 55,336)( 56,335)( 57,331)
( 58,332)( 59,345)( 60,346)( 61,341)( 62,342)( 63,344)( 64,343)( 65,339)
( 66,340)( 67,353)( 68,354)( 69,349)( 70,350)( 71,352)( 72,351)( 73,347)
( 74,348)( 75,361)( 76,362)( 77,357)( 78,358)( 79,360)( 80,359)( 81,355)
( 82,356)( 83,289)( 84,290)( 85,285)( 86,286)( 87,288)( 88,287)( 89,283)
( 90,284)( 91,297)( 92,298)( 93,293)( 94,294)( 95,296)( 96,295)( 97,291)
( 98,292)( 99,305)(100,306)(101,301)(102,302)(103,304)(104,303)(105,299)
(106,300)(107,313)(108,314)(109,309)(110,310)(111,312)(112,311)(113,307)
(114,308)(115,321)(116,322)(117,317)(118,318)(119,320)(120,319)(121,315)
(122,316)(123,369)(124,370)(125,365)(126,366)(127,368)(128,367)(129,363)
(130,364)(131,377)(132,378)(133,373)(134,374)(135,376)(136,375)(137,371)
(138,372)(139,385)(140,386)(141,381)(142,382)(143,384)(144,383)(145,379)
(146,380)(147,393)(148,394)(149,389)(150,390)(151,392)(152,391)(153,387)
(154,388)(155,401)(156,402)(157,397)(158,398)(159,400)(160,399)(161,395)
(162,396)(163,449)(164,450)(165,445)(166,446)(167,448)(168,447)(169,443)
(170,444)(171,457)(172,458)(173,453)(174,454)(175,456)(176,455)(177,451)
(178,452)(179,465)(180,466)(181,461)(182,462)(183,464)(184,463)(185,459)
(186,460)(187,473)(188,474)(189,469)(190,470)(191,472)(192,471)(193,467)
(194,468)(195,481)(196,482)(197,477)(198,478)(199,480)(200,479)(201,475)
(202,476)(203,409)(204,410)(205,405)(206,406)(207,408)(208,407)(209,403)
(210,404)(211,417)(212,418)(213,413)(214,414)(215,416)(216,415)(217,411)
(218,412)(219,425)(220,426)(221,421)(222,422)(223,424)(224,423)(225,419)
(226,420)(227,433)(228,434)(229,429)(230,430)(231,432)(232,431)(233,427)
(234,428)(235,441)(236,442)(237,437)(238,438)(239,440)(240,439)(241,435)
(242,436)(483,729)(484,730)(485,725)(486,726)(487,728)(488,727)(489,723)
(490,724)(491,737)(492,738)(493,733)(494,734)(495,736)(496,735)(497,731)
(498,732)(499,745)(500,746)(501,741)(502,742)(503,744)(504,743)(505,739)
(506,740)(507,753)(508,754)(509,749)(510,750)(511,752)(512,751)(513,747)
(514,748)(515,761)(516,762)(517,757)(518,758)(519,760)(520,759)(521,755)
(522,756)(523,809)(524,810)(525,805)(526,806)(527,808)(528,807)(529,803)
(530,804)(531,817)(532,818)(533,813)(534,814)(535,816)(536,815)(537,811)
(538,812)(539,825)(540,826)(541,821)(542,822)(543,824)(544,823)(545,819)
(546,820)(547,833)(548,834)(549,829)(550,830)(551,832)(552,831)(553,827)
(554,828)(555,841)(556,842)(557,837)(558,838)(559,840)(560,839)(561,835)
(562,836)(563,769)(564,770)(565,765)(566,766)(567,768)(568,767)(569,763)
(570,764)(571,777)(572,778)(573,773)(574,774)(575,776)(576,775)(577,771)
(578,772)(579,785)(580,786)(581,781)(582,782)(583,784)(584,783)(585,779)
(586,780)(587,793)(588,794)(589,789)(590,790)(591,792)(592,791)(593,787)
(594,788)(595,801)(596,802)(597,797)(598,798)(599,800)(600,799)(601,795)
(602,796)(603,849)(604,850)(605,845)(606,846)(607,848)(608,847)(609,843)
(610,844)(611,857)(612,858)(613,853)(614,854)(615,856)(616,855)(617,851)
(618,852)(619,865)(620,866)(621,861)(622,862)(623,864)(624,863)(625,859)
(626,860)(627,873)(628,874)(629,869)(630,870)(631,872)(632,871)(633,867)
(634,868)(635,881)(636,882)(637,877)(638,878)(639,880)(640,879)(641,875)
(642,876)(643,929)(644,930)(645,925)(646,926)(647,928)(648,927)(649,923)
(650,924)(651,937)(652,938)(653,933)(654,934)(655,936)(656,935)(657,931)
(658,932)(659,945)(660,946)(661,941)(662,942)(663,944)(664,943)(665,939)
(666,940)(667,953)(668,954)(669,949)(670,950)(671,952)(672,951)(673,947)
(674,948)(675,961)(676,962)(677,957)(678,958)(679,960)(680,959)(681,955)
(682,956)(683,889)(684,890)(685,885)(686,886)(687,888)(688,887)(689,883)
(690,884)(691,897)(692,898)(693,893)(694,894)(695,896)(696,895)(697,891)
(698,892)(699,905)(700,906)(701,901)(702,902)(703,904)(704,903)(705,899)
(706,900)(707,913)(708,914)(709,909)(710,910)(711,912)(712,911)(713,907)
(714,908)(715,921)(716,922)(717,917)(718,918)(719,920)(720,919)(721,915)
(722,916);
poly := sub<Sym(962)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >;

to this polytope