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