Polytope of Type {2,12,30}

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

to this polytope