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