Polytope of Type {2,12,9}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,9}*1728
if this polytope has a name.
Group : SmallGroup(1728,30184)
Rank : 4
Schlafli Type : {2,12,9}
Number of vertices, edges, etc : 2, 48, 216, 36
Order of s0s1s2s3 : 72
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 : {2,6,9}*864
3-fold quotients : {2,12,3}*576
6-fold quotients : {2,6,3}*288
8-fold quotients : {2,6,9}*216
9-fold quotients : {2,12,3}*192
18-fold quotients : {2,6,3}*96
24-fold quotients : {2,2,9}*72, {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)
( 11,227)( 12,228)( 13,232)( 14,231)( 15,230)( 16,229)( 17,234)( 18,233)
( 19,235)( 20,236)( 21,240)( 22,239)( 23,238)( 24,237)( 25,242)( 26,241)
( 27,243)( 28,244)( 29,248)( 30,247)( 31,246)( 32,245)( 33,250)( 34,249)
( 35,251)( 36,252)( 37,256)( 38,255)( 39,254)( 40,253)( 41,258)( 42,257)
( 43,259)( 44,260)( 45,264)( 46,263)( 47,262)( 48,261)( 49,266)( 50,265)
( 51,267)( 52,268)( 53,272)( 54,271)( 55,270)( 56,269)( 57,274)( 58,273)
( 59,275)( 60,276)( 61,280)( 62,279)( 63,278)( 64,277)( 65,282)( 66,281)
( 67,283)( 68,284)( 69,288)( 70,287)( 71,286)( 72,285)( 73,290)( 74,289)
( 75,363)( 76,364)( 77,368)( 78,367)( 79,366)( 80,365)( 81,370)( 82,369)
( 83,371)( 84,372)( 85,376)( 86,375)( 87,374)( 88,373)( 89,378)( 90,377)
( 91,379)( 92,380)( 93,384)( 94,383)( 95,382)( 96,381)( 97,386)( 98,385)
( 99,387)(100,388)(101,392)(102,391)(103,390)(104,389)(105,394)(106,393)
(107,395)(108,396)(109,400)(110,399)(111,398)(112,397)(113,402)(114,401)
(115,403)(116,404)(117,408)(118,407)(119,406)(120,405)(121,410)(122,409)
(123,411)(124,412)(125,416)(126,415)(127,414)(128,413)(129,418)(130,417)
(131,419)(132,420)(133,424)(134,423)(135,422)(136,421)(137,426)(138,425)
(139,427)(140,428)(141,432)(142,431)(143,430)(144,429)(145,434)(146,433)
(147,291)(148,292)(149,296)(150,295)(151,294)(152,293)(153,298)(154,297)
(155,299)(156,300)(157,304)(158,303)(159,302)(160,301)(161,306)(162,305)
(163,307)(164,308)(165,312)(166,311)(167,310)(168,309)(169,314)(170,313)
(171,315)(172,316)(173,320)(174,319)(175,318)(176,317)(177,322)(178,321)
(179,323)(180,324)(181,328)(182,327)(183,326)(184,325)(185,330)(186,329)
(187,331)(188,332)(189,336)(190,335)(191,334)(192,333)(193,338)(194,337)
(195,339)(196,340)(197,344)(198,343)(199,342)(200,341)(201,346)(202,345)
(203,347)(204,348)(205,352)(206,351)(207,350)(208,349)(209,354)(210,353)
(211,355)(212,356)(213,360)(214,359)(215,358)(216,357)(217,362)(218,361)
(435,651)(436,652)(437,656)(438,655)(439,654)(440,653)(441,658)(442,657)
(443,659)(444,660)(445,664)(446,663)(447,662)(448,661)(449,666)(450,665)
(451,667)(452,668)(453,672)(454,671)(455,670)(456,669)(457,674)(458,673)
(459,675)(460,676)(461,680)(462,679)(463,678)(464,677)(465,682)(466,681)
(467,683)(468,684)(469,688)(470,687)(471,686)(472,685)(473,690)(474,689)
(475,691)(476,692)(477,696)(478,695)(479,694)(480,693)(481,698)(482,697)
(483,699)(484,700)(485,704)(486,703)(487,702)(488,701)(489,706)(490,705)
(491,707)(492,708)(493,712)(494,711)(495,710)(496,709)(497,714)(498,713)
(499,715)(500,716)(501,720)(502,719)(503,718)(504,717)(505,722)(506,721)
(507,795)(508,796)(509,800)(510,799)(511,798)(512,797)(513,802)(514,801)
(515,803)(516,804)(517,808)(518,807)(519,806)(520,805)(521,810)(522,809)
(523,811)(524,812)(525,816)(526,815)(527,814)(528,813)(529,818)(530,817)
(531,819)(532,820)(533,824)(534,823)(535,822)(536,821)(537,826)(538,825)
(539,827)(540,828)(541,832)(542,831)(543,830)(544,829)(545,834)(546,833)
(547,835)(548,836)(549,840)(550,839)(551,838)(552,837)(553,842)(554,841)
(555,843)(556,844)(557,848)(558,847)(559,846)(560,845)(561,850)(562,849)
(563,851)(564,852)(565,856)(566,855)(567,854)(568,853)(569,858)(570,857)
(571,859)(572,860)(573,864)(574,863)(575,862)(576,861)(577,866)(578,865)
(579,723)(580,724)(581,728)(582,727)(583,726)(584,725)(585,730)(586,729)
(587,731)(588,732)(589,736)(590,735)(591,734)(592,733)(593,738)(594,737)
(595,739)(596,740)(597,744)(598,743)(599,742)(600,741)(601,746)(602,745)
(603,747)(604,748)(605,752)(606,751)(607,750)(608,749)(609,754)(610,753)
(611,755)(612,756)(613,760)(614,759)(615,758)(616,757)(617,762)(618,761)
(619,763)(620,764)(621,768)(622,767)(623,766)(624,765)(625,770)(626,769)
(627,771)(628,772)(629,776)(630,775)(631,774)(632,773)(633,778)(634,777)
(635,779)(636,780)(637,784)(638,783)(639,782)(640,781)(641,786)(642,785)
(643,787)(644,788)(645,792)(646,791)(647,790)(648,789)(649,794)(650,793);;
s2 := ( 3,723)( 4,724)( 5,726)( 6,725)( 7,729)( 8,730)( 9,727)( 10,728)
( 11,739)( 12,740)( 13,742)( 14,741)( 15,745)( 16,746)( 17,743)( 18,744)
( 19,731)( 20,732)( 21,734)( 22,733)( 23,737)( 24,738)( 25,735)( 26,736)
( 27,787)( 28,788)( 29,790)( 30,789)( 31,793)( 32,794)( 33,791)( 34,792)
( 35,779)( 36,780)( 37,782)( 38,781)( 39,785)( 40,786)( 41,783)( 42,784)
( 43,771)( 44,772)( 45,774)( 46,773)( 47,777)( 48,778)( 49,775)( 50,776)
( 51,763)( 52,764)( 53,766)( 54,765)( 55,769)( 56,770)( 57,767)( 58,768)
( 59,755)( 60,756)( 61,758)( 62,757)( 63,761)( 64,762)( 65,759)( 66,760)
( 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)
( 83,667)( 84,668)( 85,670)( 86,669)( 87,673)( 88,674)( 89,671)( 90,672)
( 91,659)( 92,660)( 93,662)( 94,661)( 95,665)( 96,666)( 97,663)( 98,664)
( 99,715)(100,716)(101,718)(102,717)(103,721)(104,722)(105,719)(106,720)
(107,707)(108,708)(109,710)(110,709)(111,713)(112,714)(113,711)(114,712)
(115,699)(116,700)(117,702)(118,701)(119,705)(120,706)(121,703)(122,704)
(123,691)(124,692)(125,694)(126,693)(127,697)(128,698)(129,695)(130,696)
(131,683)(132,684)(133,686)(134,685)(135,689)(136,690)(137,687)(138,688)
(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)
(155,811)(156,812)(157,814)(158,813)(159,817)(160,818)(161,815)(162,816)
(163,803)(164,804)(165,806)(166,805)(167,809)(168,810)(169,807)(170,808)
(171,859)(172,860)(173,862)(174,861)(175,865)(176,866)(177,863)(178,864)
(179,851)(180,852)(181,854)(182,853)(183,857)(184,858)(185,855)(186,856)
(187,843)(188,844)(189,846)(190,845)(191,849)(192,850)(193,847)(194,848)
(195,835)(196,836)(197,838)(198,837)(199,841)(200,842)(201,839)(202,840)
(203,827)(204,828)(205,830)(206,829)(207,833)(208,834)(209,831)(210,832)
(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)
(227,524)(228,523)(229,525)(230,526)(231,530)(232,529)(233,528)(234,527)
(235,516)(236,515)(237,517)(238,518)(239,522)(240,521)(241,520)(242,519)
(243,572)(244,571)(245,573)(246,574)(247,578)(248,577)(249,576)(250,575)
(251,564)(252,563)(253,565)(254,566)(255,570)(256,569)(257,568)(258,567)
(259,556)(260,555)(261,557)(262,558)(263,562)(264,561)(265,560)(266,559)
(267,548)(268,547)(269,549)(270,550)(271,554)(272,553)(273,552)(274,551)
(275,540)(276,539)(277,541)(278,542)(279,546)(280,545)(281,544)(282,543)
(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)
(299,452)(300,451)(301,453)(302,454)(303,458)(304,457)(305,456)(306,455)
(307,444)(308,443)(309,445)(310,446)(311,450)(312,449)(313,448)(314,447)
(315,500)(316,499)(317,501)(318,502)(319,506)(320,505)(321,504)(322,503)
(323,492)(324,491)(325,493)(326,494)(327,498)(328,497)(329,496)(330,495)
(331,484)(332,483)(333,485)(334,486)(335,490)(336,489)(337,488)(338,487)
(339,476)(340,475)(341,477)(342,478)(343,482)(344,481)(345,480)(346,479)
(347,468)(348,467)(349,469)(350,470)(351,474)(352,473)(353,472)(354,471)
(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)
(371,596)(372,595)(373,597)(374,598)(375,602)(376,601)(377,600)(378,599)
(379,588)(380,587)(381,589)(382,590)(383,594)(384,593)(385,592)(386,591)
(387,644)(388,643)(389,645)(390,646)(391,650)(392,649)(393,648)(394,647)
(395,636)(396,635)(397,637)(398,638)(399,642)(400,641)(401,640)(402,639)
(403,628)(404,627)(405,629)(406,630)(407,634)(408,633)(409,632)(410,631)
(411,620)(412,619)(413,621)(414,622)(415,626)(416,625)(417,624)(418,623)
(419,612)(420,611)(421,613)(422,614)(423,618)(424,617)(425,616)(426,615)
(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)
( 11,698)( 12,697)( 13,694)( 14,693)( 15,695)( 16,696)( 17,692)( 18,691)
( 19,690)( 20,689)( 21,686)( 22,685)( 23,687)( 24,688)( 25,684)( 26,683)
( 27,658)( 28,657)( 29,654)( 30,653)( 31,655)( 32,656)( 33,652)( 34,651)
( 35,674)( 36,673)( 37,670)( 38,669)( 39,671)( 40,672)( 41,668)( 42,667)
( 43,666)( 44,665)( 45,662)( 46,661)( 47,663)( 48,664)( 49,660)( 50,659)
( 51,722)( 52,721)( 53,718)( 54,717)( 55,719)( 56,720)( 57,716)( 58,715)
( 59,714)( 60,713)( 61,710)( 62,709)( 63,711)( 64,712)( 65,708)( 66,707)
( 67,706)( 68,705)( 69,702)( 70,701)( 71,703)( 72,704)( 73,700)( 74,699)
( 75,826)( 76,825)( 77,822)( 78,821)( 79,823)( 80,824)( 81,820)( 82,819)
( 83,842)( 84,841)( 85,838)( 86,837)( 87,839)( 88,840)( 89,836)( 90,835)
( 91,834)( 92,833)( 93,830)( 94,829)( 95,831)( 96,832)( 97,828)( 98,827)
( 99,802)(100,801)(101,798)(102,797)(103,799)(104,800)(105,796)(106,795)
(107,818)(108,817)(109,814)(110,813)(111,815)(112,816)(113,812)(114,811)
(115,810)(116,809)(117,806)(118,805)(119,807)(120,808)(121,804)(122,803)
(123,866)(124,865)(125,862)(126,861)(127,863)(128,864)(129,860)(130,859)
(131,858)(132,857)(133,854)(134,853)(135,855)(136,856)(137,852)(138,851)
(139,850)(140,849)(141,846)(142,845)(143,847)(144,848)(145,844)(146,843)
(147,754)(148,753)(149,750)(150,749)(151,751)(152,752)(153,748)(154,747)
(155,770)(156,769)(157,766)(158,765)(159,767)(160,768)(161,764)(162,763)
(163,762)(164,761)(165,758)(166,757)(167,759)(168,760)(169,756)(170,755)
(171,730)(172,729)(173,726)(174,725)(175,727)(176,728)(177,724)(178,723)
(179,746)(180,745)(181,742)(182,741)(183,743)(184,744)(185,740)(186,739)
(187,738)(188,737)(189,734)(190,733)(191,735)(192,736)(193,732)(194,731)
(195,794)(196,793)(197,790)(198,789)(199,791)(200,792)(201,788)(202,787)
(203,786)(204,785)(205,782)(206,781)(207,783)(208,784)(209,780)(210,779)
(211,778)(212,777)(213,774)(214,773)(215,775)(216,776)(217,772)(218,771)
(219,465)(220,466)(221,461)(222,462)(223,464)(224,463)(225,459)(226,460)
(227,481)(228,482)(229,477)(230,478)(231,480)(232,479)(233,475)(234,476)
(235,473)(236,474)(237,469)(238,470)(239,472)(240,471)(241,467)(242,468)
(243,441)(244,442)(245,437)(246,438)(247,440)(248,439)(249,435)(250,436)
(251,457)(252,458)(253,453)(254,454)(255,456)(256,455)(257,451)(258,452)
(259,449)(260,450)(261,445)(262,446)(263,448)(264,447)(265,443)(266,444)
(267,505)(268,506)(269,501)(270,502)(271,504)(272,503)(273,499)(274,500)
(275,497)(276,498)(277,493)(278,494)(279,496)(280,495)(281,491)(282,492)
(283,489)(284,490)(285,485)(286,486)(287,488)(288,487)(289,483)(290,484)
(291,609)(292,610)(293,605)(294,606)(295,608)(296,607)(297,603)(298,604)
(299,625)(300,626)(301,621)(302,622)(303,624)(304,623)(305,619)(306,620)
(307,617)(308,618)(309,613)(310,614)(311,616)(312,615)(313,611)(314,612)
(315,585)(316,586)(317,581)(318,582)(319,584)(320,583)(321,579)(322,580)
(323,601)(324,602)(325,597)(326,598)(327,600)(328,599)(329,595)(330,596)
(331,593)(332,594)(333,589)(334,590)(335,592)(336,591)(337,587)(338,588)
(339,649)(340,650)(341,645)(342,646)(343,648)(344,647)(345,643)(346,644)
(347,641)(348,642)(349,637)(350,638)(351,640)(352,639)(353,635)(354,636)
(355,633)(356,634)(357,629)(358,630)(359,632)(360,631)(361,627)(362,628)
(363,537)(364,538)(365,533)(366,534)(367,536)(368,535)(369,531)(370,532)
(371,553)(372,554)(373,549)(374,550)(375,552)(376,551)(377,547)(378,548)
(379,545)(380,546)(381,541)(382,542)(383,544)(384,543)(385,539)(386,540)
(387,513)(388,514)(389,509)(390,510)(391,512)(392,511)(393,507)(394,508)
(395,529)(396,530)(397,525)(398,526)(399,528)(400,527)(401,523)(402,524)
(403,521)(404,522)(405,517)(406,518)(407,520)(408,519)(409,515)(410,516)
(411,577)(412,578)(413,573)(414,574)(415,576)(416,575)(417,571)(418,572)
(419,569)(420,570)(421,565)(422,566)(423,568)(424,567)(425,563)(426,564)
(427,561)(428,562)(429,557)(430,558)(431,560)(432,559)(433,555)(434,556);;
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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s3*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)( 11,227)( 12,228)( 13,232)( 14,231)( 15,230)( 16,229)( 17,234)
( 18,233)( 19,235)( 20,236)( 21,240)( 22,239)( 23,238)( 24,237)( 25,242)
( 26,241)( 27,243)( 28,244)( 29,248)( 30,247)( 31,246)( 32,245)( 33,250)
( 34,249)( 35,251)( 36,252)( 37,256)( 38,255)( 39,254)( 40,253)( 41,258)
( 42,257)( 43,259)( 44,260)( 45,264)( 46,263)( 47,262)( 48,261)( 49,266)
( 50,265)( 51,267)( 52,268)( 53,272)( 54,271)( 55,270)( 56,269)( 57,274)
( 58,273)( 59,275)( 60,276)( 61,280)( 62,279)( 63,278)( 64,277)( 65,282)
( 66,281)( 67,283)( 68,284)( 69,288)( 70,287)( 71,286)( 72,285)( 73,290)
( 74,289)( 75,363)( 76,364)( 77,368)( 78,367)( 79,366)( 80,365)( 81,370)
( 82,369)( 83,371)( 84,372)( 85,376)( 86,375)( 87,374)( 88,373)( 89,378)
( 90,377)( 91,379)( 92,380)( 93,384)( 94,383)( 95,382)( 96,381)( 97,386)
( 98,385)( 99,387)(100,388)(101,392)(102,391)(103,390)(104,389)(105,394)
(106,393)(107,395)(108,396)(109,400)(110,399)(111,398)(112,397)(113,402)
(114,401)(115,403)(116,404)(117,408)(118,407)(119,406)(120,405)(121,410)
(122,409)(123,411)(124,412)(125,416)(126,415)(127,414)(128,413)(129,418)
(130,417)(131,419)(132,420)(133,424)(134,423)(135,422)(136,421)(137,426)
(138,425)(139,427)(140,428)(141,432)(142,431)(143,430)(144,429)(145,434)
(146,433)(147,291)(148,292)(149,296)(150,295)(151,294)(152,293)(153,298)
(154,297)(155,299)(156,300)(157,304)(158,303)(159,302)(160,301)(161,306)
(162,305)(163,307)(164,308)(165,312)(166,311)(167,310)(168,309)(169,314)
(170,313)(171,315)(172,316)(173,320)(174,319)(175,318)(176,317)(177,322)
(178,321)(179,323)(180,324)(181,328)(182,327)(183,326)(184,325)(185,330)
(186,329)(187,331)(188,332)(189,336)(190,335)(191,334)(192,333)(193,338)
(194,337)(195,339)(196,340)(197,344)(198,343)(199,342)(200,341)(201,346)
(202,345)(203,347)(204,348)(205,352)(206,351)(207,350)(208,349)(209,354)
(210,353)(211,355)(212,356)(213,360)(214,359)(215,358)(216,357)(217,362)
(218,361)(435,651)(436,652)(437,656)(438,655)(439,654)(440,653)(441,658)
(442,657)(443,659)(444,660)(445,664)(446,663)(447,662)(448,661)(449,666)
(450,665)(451,667)(452,668)(453,672)(454,671)(455,670)(456,669)(457,674)
(458,673)(459,675)(460,676)(461,680)(462,679)(463,678)(464,677)(465,682)
(466,681)(467,683)(468,684)(469,688)(470,687)(471,686)(472,685)(473,690)
(474,689)(475,691)(476,692)(477,696)(478,695)(479,694)(480,693)(481,698)
(482,697)(483,699)(484,700)(485,704)(486,703)(487,702)(488,701)(489,706)
(490,705)(491,707)(492,708)(493,712)(494,711)(495,710)(496,709)(497,714)
(498,713)(499,715)(500,716)(501,720)(502,719)(503,718)(504,717)(505,722)
(506,721)(507,795)(508,796)(509,800)(510,799)(511,798)(512,797)(513,802)
(514,801)(515,803)(516,804)(517,808)(518,807)(519,806)(520,805)(521,810)
(522,809)(523,811)(524,812)(525,816)(526,815)(527,814)(528,813)(529,818)
(530,817)(531,819)(532,820)(533,824)(534,823)(535,822)(536,821)(537,826)
(538,825)(539,827)(540,828)(541,832)(542,831)(543,830)(544,829)(545,834)
(546,833)(547,835)(548,836)(549,840)(550,839)(551,838)(552,837)(553,842)
(554,841)(555,843)(556,844)(557,848)(558,847)(559,846)(560,845)(561,850)
(562,849)(563,851)(564,852)(565,856)(566,855)(567,854)(568,853)(569,858)
(570,857)(571,859)(572,860)(573,864)(574,863)(575,862)(576,861)(577,866)
(578,865)(579,723)(580,724)(581,728)(582,727)(583,726)(584,725)(585,730)
(586,729)(587,731)(588,732)(589,736)(590,735)(591,734)(592,733)(593,738)
(594,737)(595,739)(596,740)(597,744)(598,743)(599,742)(600,741)(601,746)
(602,745)(603,747)(604,748)(605,752)(606,751)(607,750)(608,749)(609,754)
(610,753)(611,755)(612,756)(613,760)(614,759)(615,758)(616,757)(617,762)
(618,761)(619,763)(620,764)(621,768)(622,767)(623,766)(624,765)(625,770)
(626,769)(627,771)(628,772)(629,776)(630,775)(631,774)(632,773)(633,778)
(634,777)(635,779)(636,780)(637,784)(638,783)(639,782)(640,781)(641,786)
(642,785)(643,787)(644,788)(645,792)(646,791)(647,790)(648,789)(649,794)
(650,793);
s2 := Sym(866)!( 3,723)( 4,724)( 5,726)( 6,725)( 7,729)( 8,730)( 9,727)
( 10,728)( 11,739)( 12,740)( 13,742)( 14,741)( 15,745)( 16,746)( 17,743)
( 18,744)( 19,731)( 20,732)( 21,734)( 22,733)( 23,737)( 24,738)( 25,735)
( 26,736)( 27,787)( 28,788)( 29,790)( 30,789)( 31,793)( 32,794)( 33,791)
( 34,792)( 35,779)( 36,780)( 37,782)( 38,781)( 39,785)( 40,786)( 41,783)
( 42,784)( 43,771)( 44,772)( 45,774)( 46,773)( 47,777)( 48,778)( 49,775)
( 50,776)( 51,763)( 52,764)( 53,766)( 54,765)( 55,769)( 56,770)( 57,767)
( 58,768)( 59,755)( 60,756)( 61,758)( 62,757)( 63,761)( 64,762)( 65,759)
( 66,760)( 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)( 83,667)( 84,668)( 85,670)( 86,669)( 87,673)( 88,674)( 89,671)
( 90,672)( 91,659)( 92,660)( 93,662)( 94,661)( 95,665)( 96,666)( 97,663)
( 98,664)( 99,715)(100,716)(101,718)(102,717)(103,721)(104,722)(105,719)
(106,720)(107,707)(108,708)(109,710)(110,709)(111,713)(112,714)(113,711)
(114,712)(115,699)(116,700)(117,702)(118,701)(119,705)(120,706)(121,703)
(122,704)(123,691)(124,692)(125,694)(126,693)(127,697)(128,698)(129,695)
(130,696)(131,683)(132,684)(133,686)(134,685)(135,689)(136,690)(137,687)
(138,688)(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)(155,811)(156,812)(157,814)(158,813)(159,817)(160,818)(161,815)
(162,816)(163,803)(164,804)(165,806)(166,805)(167,809)(168,810)(169,807)
(170,808)(171,859)(172,860)(173,862)(174,861)(175,865)(176,866)(177,863)
(178,864)(179,851)(180,852)(181,854)(182,853)(183,857)(184,858)(185,855)
(186,856)(187,843)(188,844)(189,846)(190,845)(191,849)(192,850)(193,847)
(194,848)(195,835)(196,836)(197,838)(198,837)(199,841)(200,842)(201,839)
(202,840)(203,827)(204,828)(205,830)(206,829)(207,833)(208,834)(209,831)
(210,832)(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)(227,524)(228,523)(229,525)(230,526)(231,530)(232,529)(233,528)
(234,527)(235,516)(236,515)(237,517)(238,518)(239,522)(240,521)(241,520)
(242,519)(243,572)(244,571)(245,573)(246,574)(247,578)(248,577)(249,576)
(250,575)(251,564)(252,563)(253,565)(254,566)(255,570)(256,569)(257,568)
(258,567)(259,556)(260,555)(261,557)(262,558)(263,562)(264,561)(265,560)
(266,559)(267,548)(268,547)(269,549)(270,550)(271,554)(272,553)(273,552)
(274,551)(275,540)(276,539)(277,541)(278,542)(279,546)(280,545)(281,544)
(282,543)(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)(299,452)(300,451)(301,453)(302,454)(303,458)(304,457)(305,456)
(306,455)(307,444)(308,443)(309,445)(310,446)(311,450)(312,449)(313,448)
(314,447)(315,500)(316,499)(317,501)(318,502)(319,506)(320,505)(321,504)
(322,503)(323,492)(324,491)(325,493)(326,494)(327,498)(328,497)(329,496)
(330,495)(331,484)(332,483)(333,485)(334,486)(335,490)(336,489)(337,488)
(338,487)(339,476)(340,475)(341,477)(342,478)(343,482)(344,481)(345,480)
(346,479)(347,468)(348,467)(349,469)(350,470)(351,474)(352,473)(353,472)
(354,471)(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)(371,596)(372,595)(373,597)(374,598)(375,602)(376,601)(377,600)
(378,599)(379,588)(380,587)(381,589)(382,590)(383,594)(384,593)(385,592)
(386,591)(387,644)(388,643)(389,645)(390,646)(391,650)(392,649)(393,648)
(394,647)(395,636)(396,635)(397,637)(398,638)(399,642)(400,641)(401,640)
(402,639)(403,628)(404,627)(405,629)(406,630)(407,634)(408,633)(409,632)
(410,631)(411,620)(412,619)(413,621)(414,622)(415,626)(416,625)(417,624)
(418,623)(419,612)(420,611)(421,613)(422,614)(423,618)(424,617)(425,616)
(426,615)(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)( 11,698)( 12,697)( 13,694)( 14,693)( 15,695)( 16,696)( 17,692)
( 18,691)( 19,690)( 20,689)( 21,686)( 22,685)( 23,687)( 24,688)( 25,684)
( 26,683)( 27,658)( 28,657)( 29,654)( 30,653)( 31,655)( 32,656)( 33,652)
( 34,651)( 35,674)( 36,673)( 37,670)( 38,669)( 39,671)( 40,672)( 41,668)
( 42,667)( 43,666)( 44,665)( 45,662)( 46,661)( 47,663)( 48,664)( 49,660)
( 50,659)( 51,722)( 52,721)( 53,718)( 54,717)( 55,719)( 56,720)( 57,716)
( 58,715)( 59,714)( 60,713)( 61,710)( 62,709)( 63,711)( 64,712)( 65,708)
( 66,707)( 67,706)( 68,705)( 69,702)( 70,701)( 71,703)( 72,704)( 73,700)
( 74,699)( 75,826)( 76,825)( 77,822)( 78,821)( 79,823)( 80,824)( 81,820)
( 82,819)( 83,842)( 84,841)( 85,838)( 86,837)( 87,839)( 88,840)( 89,836)
( 90,835)( 91,834)( 92,833)( 93,830)( 94,829)( 95,831)( 96,832)( 97,828)
( 98,827)( 99,802)(100,801)(101,798)(102,797)(103,799)(104,800)(105,796)
(106,795)(107,818)(108,817)(109,814)(110,813)(111,815)(112,816)(113,812)
(114,811)(115,810)(116,809)(117,806)(118,805)(119,807)(120,808)(121,804)
(122,803)(123,866)(124,865)(125,862)(126,861)(127,863)(128,864)(129,860)
(130,859)(131,858)(132,857)(133,854)(134,853)(135,855)(136,856)(137,852)
(138,851)(139,850)(140,849)(141,846)(142,845)(143,847)(144,848)(145,844)
(146,843)(147,754)(148,753)(149,750)(150,749)(151,751)(152,752)(153,748)
(154,747)(155,770)(156,769)(157,766)(158,765)(159,767)(160,768)(161,764)
(162,763)(163,762)(164,761)(165,758)(166,757)(167,759)(168,760)(169,756)
(170,755)(171,730)(172,729)(173,726)(174,725)(175,727)(176,728)(177,724)
(178,723)(179,746)(180,745)(181,742)(182,741)(183,743)(184,744)(185,740)
(186,739)(187,738)(188,737)(189,734)(190,733)(191,735)(192,736)(193,732)
(194,731)(195,794)(196,793)(197,790)(198,789)(199,791)(200,792)(201,788)
(202,787)(203,786)(204,785)(205,782)(206,781)(207,783)(208,784)(209,780)
(210,779)(211,778)(212,777)(213,774)(214,773)(215,775)(216,776)(217,772)
(218,771)(219,465)(220,466)(221,461)(222,462)(223,464)(224,463)(225,459)
(226,460)(227,481)(228,482)(229,477)(230,478)(231,480)(232,479)(233,475)
(234,476)(235,473)(236,474)(237,469)(238,470)(239,472)(240,471)(241,467)
(242,468)(243,441)(244,442)(245,437)(246,438)(247,440)(248,439)(249,435)
(250,436)(251,457)(252,458)(253,453)(254,454)(255,456)(256,455)(257,451)
(258,452)(259,449)(260,450)(261,445)(262,446)(263,448)(264,447)(265,443)
(266,444)(267,505)(268,506)(269,501)(270,502)(271,504)(272,503)(273,499)
(274,500)(275,497)(276,498)(277,493)(278,494)(279,496)(280,495)(281,491)
(282,492)(283,489)(284,490)(285,485)(286,486)(287,488)(288,487)(289,483)
(290,484)(291,609)(292,610)(293,605)(294,606)(295,608)(296,607)(297,603)
(298,604)(299,625)(300,626)(301,621)(302,622)(303,624)(304,623)(305,619)
(306,620)(307,617)(308,618)(309,613)(310,614)(311,616)(312,615)(313,611)
(314,612)(315,585)(316,586)(317,581)(318,582)(319,584)(320,583)(321,579)
(322,580)(323,601)(324,602)(325,597)(326,598)(327,600)(328,599)(329,595)
(330,596)(331,593)(332,594)(333,589)(334,590)(335,592)(336,591)(337,587)
(338,588)(339,649)(340,650)(341,645)(342,646)(343,648)(344,647)(345,643)
(346,644)(347,641)(348,642)(349,637)(350,638)(351,640)(352,639)(353,635)
(354,636)(355,633)(356,634)(357,629)(358,630)(359,632)(360,631)(361,627)
(362,628)(363,537)(364,538)(365,533)(366,534)(367,536)(368,535)(369,531)
(370,532)(371,553)(372,554)(373,549)(374,550)(375,552)(376,551)(377,547)
(378,548)(379,545)(380,546)(381,541)(382,542)(383,544)(384,543)(385,539)
(386,540)(387,513)(388,514)(389,509)(390,510)(391,512)(392,511)(393,507)
(394,508)(395,529)(396,530)(397,525)(398,526)(399,528)(400,527)(401,523)
(402,524)(403,521)(404,522)(405,517)(406,518)(407,520)(408,519)(409,515)
(410,516)(411,577)(412,578)(413,573)(414,574)(415,576)(416,575)(417,571)
(418,572)(419,569)(420,570)(421,565)(422,566)(423,568)(424,567)(425,563)
(426,564)(427,561)(428,562)(429,557)(430,558)(431,560)(432,559)(433,555)
(434,556);
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, s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s1*s3*s2*s1*s2*s3*s2*s1*s2*s1*s2 >;
to this polytope