Questions?
See the FAQ
or other info.

Polytope of Type {12,3,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,3,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,30267)
Rank : 4
Schlafli Type : {12,3,2}
Number of vertices, edges, etc : 144, 216, 36, 2
Order of s0s1s2s3 : 24
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 : {6,3,2}*864
   3-fold quotients : {12,3,2}*576
   6-fold quotients : {6,3,2}*288
   8-fold quotients : {6,3,2}*216
   9-fold quotients : {12,3,2}*192
   18-fold quotients : {6,3,2}*96
   24-fold quotients : {6,3,2}*72
   36-fold quotients : {3,3,2}*48
   72-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,217)(  2,218)(  3,222)(  4,221)(  5,220)(  6,219)(  7,224)(  8,223)
(  9,233)( 10,234)( 11,238)( 12,237)( 13,236)( 14,235)( 15,240)( 16,239)
( 17,225)( 18,226)( 19,230)( 20,229)( 21,228)( 22,227)( 23,232)( 24,231)
( 25,241)( 26,242)( 27,246)( 28,245)( 29,244)( 30,243)( 31,248)( 32,247)
( 33,257)( 34,258)( 35,262)( 36,261)( 37,260)( 38,259)( 39,264)( 40,263)
( 41,249)( 42,250)( 43,254)( 44,253)( 45,252)( 46,251)( 47,256)( 48,255)
( 49,265)( 50,266)( 51,270)( 52,269)( 53,268)( 54,267)( 55,272)( 56,271)
( 57,281)( 58,282)( 59,286)( 60,285)( 61,284)( 62,283)( 63,288)( 64,287)
( 65,273)( 66,274)( 67,278)( 68,277)( 69,276)( 70,275)( 71,280)( 72,279)
( 73,361)( 74,362)( 75,366)( 76,365)( 77,364)( 78,363)( 79,368)( 80,367)
( 81,377)( 82,378)( 83,382)( 84,381)( 85,380)( 86,379)( 87,384)( 88,383)
( 89,369)( 90,370)( 91,374)( 92,373)( 93,372)( 94,371)( 95,376)( 96,375)
( 97,385)( 98,386)( 99,390)(100,389)(101,388)(102,387)(103,392)(104,391)
(105,401)(106,402)(107,406)(108,405)(109,404)(110,403)(111,408)(112,407)
(113,393)(114,394)(115,398)(116,397)(117,396)(118,395)(119,400)(120,399)
(121,409)(122,410)(123,414)(124,413)(125,412)(126,411)(127,416)(128,415)
(129,425)(130,426)(131,430)(132,429)(133,428)(134,427)(135,432)(136,431)
(137,417)(138,418)(139,422)(140,421)(141,420)(142,419)(143,424)(144,423)
(145,289)(146,290)(147,294)(148,293)(149,292)(150,291)(151,296)(152,295)
(153,305)(154,306)(155,310)(156,309)(157,308)(158,307)(159,312)(160,311)
(161,297)(162,298)(163,302)(164,301)(165,300)(166,299)(167,304)(168,303)
(169,313)(170,314)(171,318)(172,317)(173,316)(174,315)(175,320)(176,319)
(177,329)(178,330)(179,334)(180,333)(181,332)(182,331)(183,336)(184,335)
(185,321)(186,322)(187,326)(188,325)(189,324)(190,323)(191,328)(192,327)
(193,337)(194,338)(195,342)(196,341)(197,340)(198,339)(199,344)(200,343)
(201,353)(202,354)(203,358)(204,357)(205,356)(206,355)(207,360)(208,359)
(209,345)(210,346)(211,350)(212,349)(213,348)(214,347)(215,352)(216,351)
(433,649)(434,650)(435,654)(436,653)(437,652)(438,651)(439,656)(440,655)
(441,665)(442,666)(443,670)(444,669)(445,668)(446,667)(447,672)(448,671)
(449,657)(450,658)(451,662)(452,661)(453,660)(454,659)(455,664)(456,663)
(457,673)(458,674)(459,678)(460,677)(461,676)(462,675)(463,680)(464,679)
(465,689)(466,690)(467,694)(468,693)(469,692)(470,691)(471,696)(472,695)
(473,681)(474,682)(475,686)(476,685)(477,684)(478,683)(479,688)(480,687)
(481,697)(482,698)(483,702)(484,701)(485,700)(486,699)(487,704)(488,703)
(489,713)(490,714)(491,718)(492,717)(493,716)(494,715)(495,720)(496,719)
(497,705)(498,706)(499,710)(500,709)(501,708)(502,707)(503,712)(504,711)
(505,793)(506,794)(507,798)(508,797)(509,796)(510,795)(511,800)(512,799)
(513,809)(514,810)(515,814)(516,813)(517,812)(518,811)(519,816)(520,815)
(521,801)(522,802)(523,806)(524,805)(525,804)(526,803)(527,808)(528,807)
(529,817)(530,818)(531,822)(532,821)(533,820)(534,819)(535,824)(536,823)
(537,833)(538,834)(539,838)(540,837)(541,836)(542,835)(543,840)(544,839)
(545,825)(546,826)(547,830)(548,829)(549,828)(550,827)(551,832)(552,831)
(553,841)(554,842)(555,846)(556,845)(557,844)(558,843)(559,848)(560,847)
(561,857)(562,858)(563,862)(564,861)(565,860)(566,859)(567,864)(568,863)
(569,849)(570,850)(571,854)(572,853)(573,852)(574,851)(575,856)(576,855)
(577,721)(578,722)(579,726)(580,725)(581,724)(582,723)(583,728)(584,727)
(585,737)(586,738)(587,742)(588,741)(589,740)(590,739)(591,744)(592,743)
(593,729)(594,730)(595,734)(596,733)(597,732)(598,731)(599,736)(600,735)
(601,745)(602,746)(603,750)(604,749)(605,748)(606,747)(607,752)(608,751)
(609,761)(610,762)(611,766)(612,765)(613,764)(614,763)(615,768)(616,767)
(617,753)(618,754)(619,758)(620,757)(621,756)(622,755)(623,760)(624,759)
(625,769)(626,770)(627,774)(628,773)(629,772)(630,771)(631,776)(632,775)
(633,785)(634,786)(635,790)(636,789)(637,788)(638,787)(639,792)(640,791)
(641,777)(642,778)(643,782)(644,781)(645,780)(646,779)(647,784)(648,783);;
s1 := (  1,721)(  2,722)(  3,724)(  4,723)(  5,727)(  6,728)(  7,725)(  8,726)
(  9,729)( 10,730)( 11,732)( 12,731)( 13,735)( 14,736)( 15,733)( 16,734)
( 17,737)( 18,738)( 19,740)( 20,739)( 21,743)( 22,744)( 23,741)( 24,742)
( 25,785)( 26,786)( 27,788)( 28,787)( 29,791)( 30,792)( 31,789)( 32,790)
( 33,769)( 34,770)( 35,772)( 36,771)( 37,775)( 38,776)( 39,773)( 40,774)
( 41,777)( 42,778)( 43,780)( 44,779)( 45,783)( 46,784)( 47,781)( 48,782)
( 49,753)( 50,754)( 51,756)( 52,755)( 53,759)( 54,760)( 55,757)( 56,758)
( 57,761)( 58,762)( 59,764)( 60,763)( 61,767)( 62,768)( 63,765)( 64,766)
( 65,745)( 66,746)( 67,748)( 68,747)( 69,751)( 70,752)( 71,749)( 72,750)
( 73,649)( 74,650)( 75,652)( 76,651)( 77,655)( 78,656)( 79,653)( 80,654)
( 81,657)( 82,658)( 83,660)( 84,659)( 85,663)( 86,664)( 87,661)( 88,662)
( 89,665)( 90,666)( 91,668)( 92,667)( 93,671)( 94,672)( 95,669)( 96,670)
( 97,713)( 98,714)( 99,716)(100,715)(101,719)(102,720)(103,717)(104,718)
(105,697)(106,698)(107,700)(108,699)(109,703)(110,704)(111,701)(112,702)
(113,705)(114,706)(115,708)(116,707)(117,711)(118,712)(119,709)(120,710)
(121,681)(122,682)(123,684)(124,683)(125,687)(126,688)(127,685)(128,686)
(129,689)(130,690)(131,692)(132,691)(133,695)(134,696)(135,693)(136,694)
(137,673)(138,674)(139,676)(140,675)(141,679)(142,680)(143,677)(144,678)
(145,793)(146,794)(147,796)(148,795)(149,799)(150,800)(151,797)(152,798)
(153,801)(154,802)(155,804)(156,803)(157,807)(158,808)(159,805)(160,806)
(161,809)(162,810)(163,812)(164,811)(165,815)(166,816)(167,813)(168,814)
(169,857)(170,858)(171,860)(172,859)(173,863)(174,864)(175,861)(176,862)
(177,841)(178,842)(179,844)(180,843)(181,847)(182,848)(183,845)(184,846)
(185,849)(186,850)(187,852)(188,851)(189,855)(190,856)(191,853)(192,854)
(193,825)(194,826)(195,828)(196,827)(197,831)(198,832)(199,829)(200,830)
(201,833)(202,834)(203,836)(204,835)(205,839)(206,840)(207,837)(208,838)
(209,817)(210,818)(211,820)(212,819)(213,823)(214,824)(215,821)(216,822)
(217,506)(218,505)(219,507)(220,508)(221,512)(222,511)(223,510)(224,509)
(225,514)(226,513)(227,515)(228,516)(229,520)(230,519)(231,518)(232,517)
(233,522)(234,521)(235,523)(236,524)(237,528)(238,527)(239,526)(240,525)
(241,570)(242,569)(243,571)(244,572)(245,576)(246,575)(247,574)(248,573)
(249,554)(250,553)(251,555)(252,556)(253,560)(254,559)(255,558)(256,557)
(257,562)(258,561)(259,563)(260,564)(261,568)(262,567)(263,566)(264,565)
(265,538)(266,537)(267,539)(268,540)(269,544)(270,543)(271,542)(272,541)
(273,546)(274,545)(275,547)(276,548)(277,552)(278,551)(279,550)(280,549)
(281,530)(282,529)(283,531)(284,532)(285,536)(286,535)(287,534)(288,533)
(289,434)(290,433)(291,435)(292,436)(293,440)(294,439)(295,438)(296,437)
(297,442)(298,441)(299,443)(300,444)(301,448)(302,447)(303,446)(304,445)
(305,450)(306,449)(307,451)(308,452)(309,456)(310,455)(311,454)(312,453)
(313,498)(314,497)(315,499)(316,500)(317,504)(318,503)(319,502)(320,501)
(321,482)(322,481)(323,483)(324,484)(325,488)(326,487)(327,486)(328,485)
(329,490)(330,489)(331,491)(332,492)(333,496)(334,495)(335,494)(336,493)
(337,466)(338,465)(339,467)(340,468)(341,472)(342,471)(343,470)(344,469)
(345,474)(346,473)(347,475)(348,476)(349,480)(350,479)(351,478)(352,477)
(353,458)(354,457)(355,459)(356,460)(357,464)(358,463)(359,462)(360,461)
(361,578)(362,577)(363,579)(364,580)(365,584)(366,583)(367,582)(368,581)
(369,586)(370,585)(371,587)(372,588)(373,592)(374,591)(375,590)(376,589)
(377,594)(378,593)(379,595)(380,596)(381,600)(382,599)(383,598)(384,597)
(385,642)(386,641)(387,643)(388,644)(389,648)(390,647)(391,646)(392,645)
(393,626)(394,625)(395,627)(396,628)(397,632)(398,631)(399,630)(400,629)
(401,634)(402,633)(403,635)(404,636)(405,640)(406,639)(407,638)(408,637)
(409,610)(410,609)(411,611)(412,612)(413,616)(414,615)(415,614)(416,613)
(417,618)(418,617)(419,619)(420,620)(421,624)(422,623)(423,622)(424,621)
(425,602)(426,601)(427,603)(428,604)(429,608)(430,607)(431,606)(432,605);;
s2 := (  1,680)(  2,679)(  3,676)(  4,675)(  5,677)(  6,678)(  7,674)(  8,673)
(  9,688)( 10,687)( 11,684)( 12,683)( 13,685)( 14,686)( 15,682)( 16,681)
( 17,696)( 18,695)( 19,692)( 20,691)( 21,693)( 22,694)( 23,690)( 24,689)
( 25,656)( 26,655)( 27,652)( 28,651)( 29,653)( 30,654)( 31,650)( 32,649)
( 33,664)( 34,663)( 35,660)( 36,659)( 37,661)( 38,662)( 39,658)( 40,657)
( 41,672)( 42,671)( 43,668)( 44,667)( 45,669)( 46,670)( 47,666)( 48,665)
( 49,704)( 50,703)( 51,700)( 52,699)( 53,701)( 54,702)( 55,698)( 56,697)
( 57,712)( 58,711)( 59,708)( 60,707)( 61,709)( 62,710)( 63,706)( 64,705)
( 65,720)( 66,719)( 67,716)( 68,715)( 69,717)( 70,718)( 71,714)( 72,713)
( 73,824)( 74,823)( 75,820)( 76,819)( 77,821)( 78,822)( 79,818)( 80,817)
( 81,832)( 82,831)( 83,828)( 84,827)( 85,829)( 86,830)( 87,826)( 88,825)
( 89,840)( 90,839)( 91,836)( 92,835)( 93,837)( 94,838)( 95,834)( 96,833)
( 97,800)( 98,799)( 99,796)(100,795)(101,797)(102,798)(103,794)(104,793)
(105,808)(106,807)(107,804)(108,803)(109,805)(110,806)(111,802)(112,801)
(113,816)(114,815)(115,812)(116,811)(117,813)(118,814)(119,810)(120,809)
(121,848)(122,847)(123,844)(124,843)(125,845)(126,846)(127,842)(128,841)
(129,856)(130,855)(131,852)(132,851)(133,853)(134,854)(135,850)(136,849)
(137,864)(138,863)(139,860)(140,859)(141,861)(142,862)(143,858)(144,857)
(145,752)(146,751)(147,748)(148,747)(149,749)(150,750)(151,746)(152,745)
(153,760)(154,759)(155,756)(156,755)(157,757)(158,758)(159,754)(160,753)
(161,768)(162,767)(163,764)(164,763)(165,765)(166,766)(167,762)(168,761)
(169,728)(170,727)(171,724)(172,723)(173,725)(174,726)(175,722)(176,721)
(177,736)(178,735)(179,732)(180,731)(181,733)(182,734)(183,730)(184,729)
(185,744)(186,743)(187,740)(188,739)(189,741)(190,742)(191,738)(192,737)
(193,776)(194,775)(195,772)(196,771)(197,773)(198,774)(199,770)(200,769)
(201,784)(202,783)(203,780)(204,779)(205,781)(206,782)(207,778)(208,777)
(209,792)(210,791)(211,788)(212,787)(213,789)(214,790)(215,786)(216,785)
(217,463)(218,464)(219,459)(220,460)(221,462)(222,461)(223,457)(224,458)
(225,471)(226,472)(227,467)(228,468)(229,470)(230,469)(231,465)(232,466)
(233,479)(234,480)(235,475)(236,476)(237,478)(238,477)(239,473)(240,474)
(241,439)(242,440)(243,435)(244,436)(245,438)(246,437)(247,433)(248,434)
(249,447)(250,448)(251,443)(252,444)(253,446)(254,445)(255,441)(256,442)
(257,455)(258,456)(259,451)(260,452)(261,454)(262,453)(263,449)(264,450)
(265,487)(266,488)(267,483)(268,484)(269,486)(270,485)(271,481)(272,482)
(273,495)(274,496)(275,491)(276,492)(277,494)(278,493)(279,489)(280,490)
(281,503)(282,504)(283,499)(284,500)(285,502)(286,501)(287,497)(288,498)
(289,607)(290,608)(291,603)(292,604)(293,606)(294,605)(295,601)(296,602)
(297,615)(298,616)(299,611)(300,612)(301,614)(302,613)(303,609)(304,610)
(305,623)(306,624)(307,619)(308,620)(309,622)(310,621)(311,617)(312,618)
(313,583)(314,584)(315,579)(316,580)(317,582)(318,581)(319,577)(320,578)
(321,591)(322,592)(323,587)(324,588)(325,590)(326,589)(327,585)(328,586)
(329,599)(330,600)(331,595)(332,596)(333,598)(334,597)(335,593)(336,594)
(337,631)(338,632)(339,627)(340,628)(341,630)(342,629)(343,625)(344,626)
(345,639)(346,640)(347,635)(348,636)(349,638)(350,637)(351,633)(352,634)
(353,647)(354,648)(355,643)(356,644)(357,646)(358,645)(359,641)(360,642)
(361,535)(362,536)(363,531)(364,532)(365,534)(366,533)(367,529)(368,530)
(369,543)(370,544)(371,539)(372,540)(373,542)(374,541)(375,537)(376,538)
(377,551)(378,552)(379,547)(380,548)(381,550)(382,549)(383,545)(384,546)
(385,511)(386,512)(387,507)(388,508)(389,510)(390,509)(391,505)(392,506)
(393,519)(394,520)(395,515)(396,516)(397,518)(398,517)(399,513)(400,514)
(401,527)(402,528)(403,523)(404,524)(405,526)(406,525)(407,521)(408,522)
(409,559)(410,560)(411,555)(412,556)(413,558)(414,557)(415,553)(416,554)
(417,567)(418,568)(419,563)(420,564)(421,566)(422,565)(423,561)(424,562)
(425,575)(426,576)(427,571)(428,572)(429,574)(430,573)(431,569)(432,570);;
s3 := (865,866);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*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, 
s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(866)!(  1,217)(  2,218)(  3,222)(  4,221)(  5,220)(  6,219)(  7,224)
(  8,223)(  9,233)( 10,234)( 11,238)( 12,237)( 13,236)( 14,235)( 15,240)
( 16,239)( 17,225)( 18,226)( 19,230)( 20,229)( 21,228)( 22,227)( 23,232)
( 24,231)( 25,241)( 26,242)( 27,246)( 28,245)( 29,244)( 30,243)( 31,248)
( 32,247)( 33,257)( 34,258)( 35,262)( 36,261)( 37,260)( 38,259)( 39,264)
( 40,263)( 41,249)( 42,250)( 43,254)( 44,253)( 45,252)( 46,251)( 47,256)
( 48,255)( 49,265)( 50,266)( 51,270)( 52,269)( 53,268)( 54,267)( 55,272)
( 56,271)( 57,281)( 58,282)( 59,286)( 60,285)( 61,284)( 62,283)( 63,288)
( 64,287)( 65,273)( 66,274)( 67,278)( 68,277)( 69,276)( 70,275)( 71,280)
( 72,279)( 73,361)( 74,362)( 75,366)( 76,365)( 77,364)( 78,363)( 79,368)
( 80,367)( 81,377)( 82,378)( 83,382)( 84,381)( 85,380)( 86,379)( 87,384)
( 88,383)( 89,369)( 90,370)( 91,374)( 92,373)( 93,372)( 94,371)( 95,376)
( 96,375)( 97,385)( 98,386)( 99,390)(100,389)(101,388)(102,387)(103,392)
(104,391)(105,401)(106,402)(107,406)(108,405)(109,404)(110,403)(111,408)
(112,407)(113,393)(114,394)(115,398)(116,397)(117,396)(118,395)(119,400)
(120,399)(121,409)(122,410)(123,414)(124,413)(125,412)(126,411)(127,416)
(128,415)(129,425)(130,426)(131,430)(132,429)(133,428)(134,427)(135,432)
(136,431)(137,417)(138,418)(139,422)(140,421)(141,420)(142,419)(143,424)
(144,423)(145,289)(146,290)(147,294)(148,293)(149,292)(150,291)(151,296)
(152,295)(153,305)(154,306)(155,310)(156,309)(157,308)(158,307)(159,312)
(160,311)(161,297)(162,298)(163,302)(164,301)(165,300)(166,299)(167,304)
(168,303)(169,313)(170,314)(171,318)(172,317)(173,316)(174,315)(175,320)
(176,319)(177,329)(178,330)(179,334)(180,333)(181,332)(182,331)(183,336)
(184,335)(185,321)(186,322)(187,326)(188,325)(189,324)(190,323)(191,328)
(192,327)(193,337)(194,338)(195,342)(196,341)(197,340)(198,339)(199,344)
(200,343)(201,353)(202,354)(203,358)(204,357)(205,356)(206,355)(207,360)
(208,359)(209,345)(210,346)(211,350)(212,349)(213,348)(214,347)(215,352)
(216,351)(433,649)(434,650)(435,654)(436,653)(437,652)(438,651)(439,656)
(440,655)(441,665)(442,666)(443,670)(444,669)(445,668)(446,667)(447,672)
(448,671)(449,657)(450,658)(451,662)(452,661)(453,660)(454,659)(455,664)
(456,663)(457,673)(458,674)(459,678)(460,677)(461,676)(462,675)(463,680)
(464,679)(465,689)(466,690)(467,694)(468,693)(469,692)(470,691)(471,696)
(472,695)(473,681)(474,682)(475,686)(476,685)(477,684)(478,683)(479,688)
(480,687)(481,697)(482,698)(483,702)(484,701)(485,700)(486,699)(487,704)
(488,703)(489,713)(490,714)(491,718)(492,717)(493,716)(494,715)(495,720)
(496,719)(497,705)(498,706)(499,710)(500,709)(501,708)(502,707)(503,712)
(504,711)(505,793)(506,794)(507,798)(508,797)(509,796)(510,795)(511,800)
(512,799)(513,809)(514,810)(515,814)(516,813)(517,812)(518,811)(519,816)
(520,815)(521,801)(522,802)(523,806)(524,805)(525,804)(526,803)(527,808)
(528,807)(529,817)(530,818)(531,822)(532,821)(533,820)(534,819)(535,824)
(536,823)(537,833)(538,834)(539,838)(540,837)(541,836)(542,835)(543,840)
(544,839)(545,825)(546,826)(547,830)(548,829)(549,828)(550,827)(551,832)
(552,831)(553,841)(554,842)(555,846)(556,845)(557,844)(558,843)(559,848)
(560,847)(561,857)(562,858)(563,862)(564,861)(565,860)(566,859)(567,864)
(568,863)(569,849)(570,850)(571,854)(572,853)(573,852)(574,851)(575,856)
(576,855)(577,721)(578,722)(579,726)(580,725)(581,724)(582,723)(583,728)
(584,727)(585,737)(586,738)(587,742)(588,741)(589,740)(590,739)(591,744)
(592,743)(593,729)(594,730)(595,734)(596,733)(597,732)(598,731)(599,736)
(600,735)(601,745)(602,746)(603,750)(604,749)(605,748)(606,747)(607,752)
(608,751)(609,761)(610,762)(611,766)(612,765)(613,764)(614,763)(615,768)
(616,767)(617,753)(618,754)(619,758)(620,757)(621,756)(622,755)(623,760)
(624,759)(625,769)(626,770)(627,774)(628,773)(629,772)(630,771)(631,776)
(632,775)(633,785)(634,786)(635,790)(636,789)(637,788)(638,787)(639,792)
(640,791)(641,777)(642,778)(643,782)(644,781)(645,780)(646,779)(647,784)
(648,783);
s1 := Sym(866)!(  1,721)(  2,722)(  3,724)(  4,723)(  5,727)(  6,728)(  7,725)
(  8,726)(  9,729)( 10,730)( 11,732)( 12,731)( 13,735)( 14,736)( 15,733)
( 16,734)( 17,737)( 18,738)( 19,740)( 20,739)( 21,743)( 22,744)( 23,741)
( 24,742)( 25,785)( 26,786)( 27,788)( 28,787)( 29,791)( 30,792)( 31,789)
( 32,790)( 33,769)( 34,770)( 35,772)( 36,771)( 37,775)( 38,776)( 39,773)
( 40,774)( 41,777)( 42,778)( 43,780)( 44,779)( 45,783)( 46,784)( 47,781)
( 48,782)( 49,753)( 50,754)( 51,756)( 52,755)( 53,759)( 54,760)( 55,757)
( 56,758)( 57,761)( 58,762)( 59,764)( 60,763)( 61,767)( 62,768)( 63,765)
( 64,766)( 65,745)( 66,746)( 67,748)( 68,747)( 69,751)( 70,752)( 71,749)
( 72,750)( 73,649)( 74,650)( 75,652)( 76,651)( 77,655)( 78,656)( 79,653)
( 80,654)( 81,657)( 82,658)( 83,660)( 84,659)( 85,663)( 86,664)( 87,661)
( 88,662)( 89,665)( 90,666)( 91,668)( 92,667)( 93,671)( 94,672)( 95,669)
( 96,670)( 97,713)( 98,714)( 99,716)(100,715)(101,719)(102,720)(103,717)
(104,718)(105,697)(106,698)(107,700)(108,699)(109,703)(110,704)(111,701)
(112,702)(113,705)(114,706)(115,708)(116,707)(117,711)(118,712)(119,709)
(120,710)(121,681)(122,682)(123,684)(124,683)(125,687)(126,688)(127,685)
(128,686)(129,689)(130,690)(131,692)(132,691)(133,695)(134,696)(135,693)
(136,694)(137,673)(138,674)(139,676)(140,675)(141,679)(142,680)(143,677)
(144,678)(145,793)(146,794)(147,796)(148,795)(149,799)(150,800)(151,797)
(152,798)(153,801)(154,802)(155,804)(156,803)(157,807)(158,808)(159,805)
(160,806)(161,809)(162,810)(163,812)(164,811)(165,815)(166,816)(167,813)
(168,814)(169,857)(170,858)(171,860)(172,859)(173,863)(174,864)(175,861)
(176,862)(177,841)(178,842)(179,844)(180,843)(181,847)(182,848)(183,845)
(184,846)(185,849)(186,850)(187,852)(188,851)(189,855)(190,856)(191,853)
(192,854)(193,825)(194,826)(195,828)(196,827)(197,831)(198,832)(199,829)
(200,830)(201,833)(202,834)(203,836)(204,835)(205,839)(206,840)(207,837)
(208,838)(209,817)(210,818)(211,820)(212,819)(213,823)(214,824)(215,821)
(216,822)(217,506)(218,505)(219,507)(220,508)(221,512)(222,511)(223,510)
(224,509)(225,514)(226,513)(227,515)(228,516)(229,520)(230,519)(231,518)
(232,517)(233,522)(234,521)(235,523)(236,524)(237,528)(238,527)(239,526)
(240,525)(241,570)(242,569)(243,571)(244,572)(245,576)(246,575)(247,574)
(248,573)(249,554)(250,553)(251,555)(252,556)(253,560)(254,559)(255,558)
(256,557)(257,562)(258,561)(259,563)(260,564)(261,568)(262,567)(263,566)
(264,565)(265,538)(266,537)(267,539)(268,540)(269,544)(270,543)(271,542)
(272,541)(273,546)(274,545)(275,547)(276,548)(277,552)(278,551)(279,550)
(280,549)(281,530)(282,529)(283,531)(284,532)(285,536)(286,535)(287,534)
(288,533)(289,434)(290,433)(291,435)(292,436)(293,440)(294,439)(295,438)
(296,437)(297,442)(298,441)(299,443)(300,444)(301,448)(302,447)(303,446)
(304,445)(305,450)(306,449)(307,451)(308,452)(309,456)(310,455)(311,454)
(312,453)(313,498)(314,497)(315,499)(316,500)(317,504)(318,503)(319,502)
(320,501)(321,482)(322,481)(323,483)(324,484)(325,488)(326,487)(327,486)
(328,485)(329,490)(330,489)(331,491)(332,492)(333,496)(334,495)(335,494)
(336,493)(337,466)(338,465)(339,467)(340,468)(341,472)(342,471)(343,470)
(344,469)(345,474)(346,473)(347,475)(348,476)(349,480)(350,479)(351,478)
(352,477)(353,458)(354,457)(355,459)(356,460)(357,464)(358,463)(359,462)
(360,461)(361,578)(362,577)(363,579)(364,580)(365,584)(366,583)(367,582)
(368,581)(369,586)(370,585)(371,587)(372,588)(373,592)(374,591)(375,590)
(376,589)(377,594)(378,593)(379,595)(380,596)(381,600)(382,599)(383,598)
(384,597)(385,642)(386,641)(387,643)(388,644)(389,648)(390,647)(391,646)
(392,645)(393,626)(394,625)(395,627)(396,628)(397,632)(398,631)(399,630)
(400,629)(401,634)(402,633)(403,635)(404,636)(405,640)(406,639)(407,638)
(408,637)(409,610)(410,609)(411,611)(412,612)(413,616)(414,615)(415,614)
(416,613)(417,618)(418,617)(419,619)(420,620)(421,624)(422,623)(423,622)
(424,621)(425,602)(426,601)(427,603)(428,604)(429,608)(430,607)(431,606)
(432,605);
s2 := Sym(866)!(  1,680)(  2,679)(  3,676)(  4,675)(  5,677)(  6,678)(  7,674)
(  8,673)(  9,688)( 10,687)( 11,684)( 12,683)( 13,685)( 14,686)( 15,682)
( 16,681)( 17,696)( 18,695)( 19,692)( 20,691)( 21,693)( 22,694)( 23,690)
( 24,689)( 25,656)( 26,655)( 27,652)( 28,651)( 29,653)( 30,654)( 31,650)
( 32,649)( 33,664)( 34,663)( 35,660)( 36,659)( 37,661)( 38,662)( 39,658)
( 40,657)( 41,672)( 42,671)( 43,668)( 44,667)( 45,669)( 46,670)( 47,666)
( 48,665)( 49,704)( 50,703)( 51,700)( 52,699)( 53,701)( 54,702)( 55,698)
( 56,697)( 57,712)( 58,711)( 59,708)( 60,707)( 61,709)( 62,710)( 63,706)
( 64,705)( 65,720)( 66,719)( 67,716)( 68,715)( 69,717)( 70,718)( 71,714)
( 72,713)( 73,824)( 74,823)( 75,820)( 76,819)( 77,821)( 78,822)( 79,818)
( 80,817)( 81,832)( 82,831)( 83,828)( 84,827)( 85,829)( 86,830)( 87,826)
( 88,825)( 89,840)( 90,839)( 91,836)( 92,835)( 93,837)( 94,838)( 95,834)
( 96,833)( 97,800)( 98,799)( 99,796)(100,795)(101,797)(102,798)(103,794)
(104,793)(105,808)(106,807)(107,804)(108,803)(109,805)(110,806)(111,802)
(112,801)(113,816)(114,815)(115,812)(116,811)(117,813)(118,814)(119,810)
(120,809)(121,848)(122,847)(123,844)(124,843)(125,845)(126,846)(127,842)
(128,841)(129,856)(130,855)(131,852)(132,851)(133,853)(134,854)(135,850)
(136,849)(137,864)(138,863)(139,860)(140,859)(141,861)(142,862)(143,858)
(144,857)(145,752)(146,751)(147,748)(148,747)(149,749)(150,750)(151,746)
(152,745)(153,760)(154,759)(155,756)(156,755)(157,757)(158,758)(159,754)
(160,753)(161,768)(162,767)(163,764)(164,763)(165,765)(166,766)(167,762)
(168,761)(169,728)(170,727)(171,724)(172,723)(173,725)(174,726)(175,722)
(176,721)(177,736)(178,735)(179,732)(180,731)(181,733)(182,734)(183,730)
(184,729)(185,744)(186,743)(187,740)(188,739)(189,741)(190,742)(191,738)
(192,737)(193,776)(194,775)(195,772)(196,771)(197,773)(198,774)(199,770)
(200,769)(201,784)(202,783)(203,780)(204,779)(205,781)(206,782)(207,778)
(208,777)(209,792)(210,791)(211,788)(212,787)(213,789)(214,790)(215,786)
(216,785)(217,463)(218,464)(219,459)(220,460)(221,462)(222,461)(223,457)
(224,458)(225,471)(226,472)(227,467)(228,468)(229,470)(230,469)(231,465)
(232,466)(233,479)(234,480)(235,475)(236,476)(237,478)(238,477)(239,473)
(240,474)(241,439)(242,440)(243,435)(244,436)(245,438)(246,437)(247,433)
(248,434)(249,447)(250,448)(251,443)(252,444)(253,446)(254,445)(255,441)
(256,442)(257,455)(258,456)(259,451)(260,452)(261,454)(262,453)(263,449)
(264,450)(265,487)(266,488)(267,483)(268,484)(269,486)(270,485)(271,481)
(272,482)(273,495)(274,496)(275,491)(276,492)(277,494)(278,493)(279,489)
(280,490)(281,503)(282,504)(283,499)(284,500)(285,502)(286,501)(287,497)
(288,498)(289,607)(290,608)(291,603)(292,604)(293,606)(294,605)(295,601)
(296,602)(297,615)(298,616)(299,611)(300,612)(301,614)(302,613)(303,609)
(304,610)(305,623)(306,624)(307,619)(308,620)(309,622)(310,621)(311,617)
(312,618)(313,583)(314,584)(315,579)(316,580)(317,582)(318,581)(319,577)
(320,578)(321,591)(322,592)(323,587)(324,588)(325,590)(326,589)(327,585)
(328,586)(329,599)(330,600)(331,595)(332,596)(333,598)(334,597)(335,593)
(336,594)(337,631)(338,632)(339,627)(340,628)(341,630)(342,629)(343,625)
(344,626)(345,639)(346,640)(347,635)(348,636)(349,638)(350,637)(351,633)
(352,634)(353,647)(354,648)(355,643)(356,644)(357,646)(358,645)(359,641)
(360,642)(361,535)(362,536)(363,531)(364,532)(365,534)(366,533)(367,529)
(368,530)(369,543)(370,544)(371,539)(372,540)(373,542)(374,541)(375,537)
(376,538)(377,551)(378,552)(379,547)(380,548)(381,550)(382,549)(383,545)
(384,546)(385,511)(386,512)(387,507)(388,508)(389,510)(390,509)(391,505)
(392,506)(393,519)(394,520)(395,515)(396,516)(397,518)(398,517)(399,513)
(400,514)(401,527)(402,528)(403,523)(404,524)(405,526)(406,525)(407,521)
(408,522)(409,559)(410,560)(411,555)(412,556)(413,558)(414,557)(415,553)
(416,554)(417,567)(418,568)(419,563)(420,564)(421,566)(422,565)(423,561)
(424,562)(425,575)(426,576)(427,571)(428,572)(429,574)(430,573)(431,569)
(432,570);
s3 := Sym(866)!(865,866);
poly := sub<Sym(866)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*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, 
s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1 >; 
 

to this polytope