Polytope of Type {9,12,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,12,2}*1728
if this polytope has a name.
Group : SmallGroup(1728,30184)
Rank : 4
Schlafli Type : {9,12,2}
Number of vertices, edges, etc : 36, 216, 48, 2
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 : {9,6,2}*864
3-fold quotients : {3,12,2}*576
6-fold quotients : {3,6,2}*288
8-fold quotients : {9,6,2}*216
9-fold quotients : {3,12,2}*192
18-fold quotients : {3,6,2}*96
24-fold quotients : {9,2,2}*72, {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)
( 9,665)( 10,666)( 11,670)( 12,669)( 13,668)( 14,667)( 15,672)( 16,671)
( 17,657)( 18,658)( 19,662)( 20,661)( 21,660)( 22,659)( 23,664)( 24,663)
( 25,713)( 26,714)( 27,718)( 28,717)( 29,716)( 30,715)( 31,720)( 32,719)
( 33,705)( 34,706)( 35,710)( 36,709)( 37,708)( 38,707)( 39,712)( 40,711)
( 41,697)( 42,698)( 43,702)( 44,701)( 45,700)( 46,699)( 47,704)( 48,703)
( 49,689)( 50,690)( 51,694)( 52,693)( 53,692)( 54,691)( 55,696)( 56,695)
( 57,681)( 58,682)( 59,686)( 60,685)( 61,684)( 62,683)( 63,688)( 64,687)
( 65,673)( 66,674)( 67,678)( 68,677)( 69,676)( 70,675)( 71,680)( 72,679)
( 73,793)( 74,794)( 75,798)( 76,797)( 77,796)( 78,795)( 79,800)( 80,799)
( 81,809)( 82,810)( 83,814)( 84,813)( 85,812)( 86,811)( 87,816)( 88,815)
( 89,801)( 90,802)( 91,806)( 92,805)( 93,804)( 94,803)( 95,808)( 96,807)
( 97,857)( 98,858)( 99,862)(100,861)(101,860)(102,859)(103,864)(104,863)
(105,849)(106,850)(107,854)(108,853)(109,852)(110,851)(111,856)(112,855)
(113,841)(114,842)(115,846)(116,845)(117,844)(118,843)(119,848)(120,847)
(121,833)(122,834)(123,838)(124,837)(125,836)(126,835)(127,840)(128,839)
(129,825)(130,826)(131,830)(132,829)(133,828)(134,827)(135,832)(136,831)
(137,817)(138,818)(139,822)(140,821)(141,820)(142,819)(143,824)(144,823)
(145,721)(146,722)(147,726)(148,725)(149,724)(150,723)(151,728)(152,727)
(153,737)(154,738)(155,742)(156,741)(157,740)(158,739)(159,744)(160,743)
(161,729)(162,730)(163,734)(164,733)(165,732)(166,731)(167,736)(168,735)
(169,785)(170,786)(171,790)(172,789)(173,788)(174,787)(175,792)(176,791)
(177,777)(178,778)(179,782)(180,781)(181,780)(182,779)(183,784)(184,783)
(185,769)(186,770)(187,774)(188,773)(189,772)(190,771)(191,776)(192,775)
(193,761)(194,762)(195,766)(196,765)(197,764)(198,763)(199,768)(200,767)
(201,753)(202,754)(203,758)(204,757)(205,756)(206,755)(207,760)(208,759)
(209,745)(210,746)(211,750)(212,749)(213,748)(214,747)(215,752)(216,751)
(217,434)(218,433)(219,437)(220,438)(221,435)(222,436)(223,439)(224,440)
(225,450)(226,449)(227,453)(228,454)(229,451)(230,452)(231,455)(232,456)
(233,442)(234,441)(235,445)(236,446)(237,443)(238,444)(239,447)(240,448)
(241,498)(242,497)(243,501)(244,502)(245,499)(246,500)(247,503)(248,504)
(249,490)(250,489)(251,493)(252,494)(253,491)(254,492)(255,495)(256,496)
(257,482)(258,481)(259,485)(260,486)(261,483)(262,484)(263,487)(264,488)
(265,474)(266,473)(267,477)(268,478)(269,475)(270,476)(271,479)(272,480)
(273,466)(274,465)(275,469)(276,470)(277,467)(278,468)(279,471)(280,472)
(281,458)(282,457)(283,461)(284,462)(285,459)(286,460)(287,463)(288,464)
(289,578)(290,577)(291,581)(292,582)(293,579)(294,580)(295,583)(296,584)
(297,594)(298,593)(299,597)(300,598)(301,595)(302,596)(303,599)(304,600)
(305,586)(306,585)(307,589)(308,590)(309,587)(310,588)(311,591)(312,592)
(313,642)(314,641)(315,645)(316,646)(317,643)(318,644)(319,647)(320,648)
(321,634)(322,633)(323,637)(324,638)(325,635)(326,636)(327,639)(328,640)
(329,626)(330,625)(331,629)(332,630)(333,627)(334,628)(335,631)(336,632)
(337,618)(338,617)(339,621)(340,622)(341,619)(342,620)(343,623)(344,624)
(345,610)(346,609)(347,613)(348,614)(349,611)(350,612)(351,615)(352,616)
(353,602)(354,601)(355,605)(356,606)(357,603)(358,604)(359,607)(360,608)
(361,506)(362,505)(363,509)(364,510)(365,507)(366,508)(367,511)(368,512)
(369,522)(370,521)(371,525)(372,526)(373,523)(374,524)(375,527)(376,528)
(377,514)(378,513)(379,517)(380,518)(381,515)(382,516)(383,519)(384,520)
(385,570)(386,569)(387,573)(388,574)(389,571)(390,572)(391,575)(392,576)
(393,562)(394,561)(395,565)(396,566)(397,563)(398,564)(399,567)(400,568)
(401,554)(402,553)(403,557)(404,558)(405,555)(406,556)(407,559)(408,560)
(409,546)(410,545)(411,549)(412,550)(413,547)(414,548)(415,551)(416,552)
(417,538)(418,537)(419,541)(420,542)(421,539)(422,540)(423,543)(424,544)
(425,530)(426,529)(427,533)(428,534)(429,531)(430,532)(431,535)(432,536);;
s1 := ( 1,745)( 2,746)( 3,748)( 4,747)( 5,751)( 6,752)( 7,749)( 8,750)
( 9,761)( 10,762)( 11,764)( 12,763)( 13,767)( 14,768)( 15,765)( 16,766)
( 17,753)( 18,754)( 19,756)( 20,755)( 21,759)( 22,760)( 23,757)( 24,758)
( 25,721)( 26,722)( 27,724)( 28,723)( 29,727)( 30,728)( 31,725)( 32,726)
( 33,737)( 34,738)( 35,740)( 36,739)( 37,743)( 38,744)( 39,741)( 40,742)
( 41,729)( 42,730)( 43,732)( 44,731)( 45,735)( 46,736)( 47,733)( 48,734)
( 49,785)( 50,786)( 51,788)( 52,787)( 53,791)( 54,792)( 55,789)( 56,790)
( 57,777)( 58,778)( 59,780)( 60,779)( 61,783)( 62,784)( 63,781)( 64,782)
( 65,769)( 66,770)( 67,772)( 68,771)( 69,775)( 70,776)( 71,773)( 72,774)
( 73,673)( 74,674)( 75,676)( 76,675)( 77,679)( 78,680)( 79,677)( 80,678)
( 81,689)( 82,690)( 83,692)( 84,691)( 85,695)( 86,696)( 87,693)( 88,694)
( 89,681)( 90,682)( 91,684)( 92,683)( 93,687)( 94,688)( 95,685)( 96,686)
( 97,649)( 98,650)( 99,652)(100,651)(101,655)(102,656)(103,653)(104,654)
(105,665)(106,666)(107,668)(108,667)(109,671)(110,672)(111,669)(112,670)
(113,657)(114,658)(115,660)(116,659)(117,663)(118,664)(119,661)(120,662)
(121,713)(122,714)(123,716)(124,715)(125,719)(126,720)(127,717)(128,718)
(129,705)(130,706)(131,708)(132,707)(133,711)(134,712)(135,709)(136,710)
(137,697)(138,698)(139,700)(140,699)(141,703)(142,704)(143,701)(144,702)
(145,817)(146,818)(147,820)(148,819)(149,823)(150,824)(151,821)(152,822)
(153,833)(154,834)(155,836)(156,835)(157,839)(158,840)(159,837)(160,838)
(161,825)(162,826)(163,828)(164,827)(165,831)(166,832)(167,829)(168,830)
(169,793)(170,794)(171,796)(172,795)(173,799)(174,800)(175,797)(176,798)
(177,809)(178,810)(179,812)(180,811)(181,815)(182,816)(183,813)(184,814)
(185,801)(186,802)(187,804)(188,803)(189,807)(190,808)(191,805)(192,806)
(193,857)(194,858)(195,860)(196,859)(197,863)(198,864)(199,861)(200,862)
(201,849)(202,850)(203,852)(204,851)(205,855)(206,856)(207,853)(208,854)
(209,841)(210,842)(211,844)(212,843)(213,847)(214,848)(215,845)(216,846)
(217,530)(218,529)(219,531)(220,532)(221,536)(222,535)(223,534)(224,533)
(225,546)(226,545)(227,547)(228,548)(229,552)(230,551)(231,550)(232,549)
(233,538)(234,537)(235,539)(236,540)(237,544)(238,543)(239,542)(240,541)
(241,506)(242,505)(243,507)(244,508)(245,512)(246,511)(247,510)(248,509)
(249,522)(250,521)(251,523)(252,524)(253,528)(254,527)(255,526)(256,525)
(257,514)(258,513)(259,515)(260,516)(261,520)(262,519)(263,518)(264,517)
(265,570)(266,569)(267,571)(268,572)(269,576)(270,575)(271,574)(272,573)
(273,562)(274,561)(275,563)(276,564)(277,568)(278,567)(279,566)(280,565)
(281,554)(282,553)(283,555)(284,556)(285,560)(286,559)(287,558)(288,557)
(289,458)(290,457)(291,459)(292,460)(293,464)(294,463)(295,462)(296,461)
(297,474)(298,473)(299,475)(300,476)(301,480)(302,479)(303,478)(304,477)
(305,466)(306,465)(307,467)(308,468)(309,472)(310,471)(311,470)(312,469)
(313,434)(314,433)(315,435)(316,436)(317,440)(318,439)(319,438)(320,437)
(321,450)(322,449)(323,451)(324,452)(325,456)(326,455)(327,454)(328,453)
(329,442)(330,441)(331,443)(332,444)(333,448)(334,447)(335,446)(336,445)
(337,498)(338,497)(339,499)(340,500)(341,504)(342,503)(343,502)(344,501)
(345,490)(346,489)(347,491)(348,492)(349,496)(350,495)(351,494)(352,493)
(353,482)(354,481)(355,483)(356,484)(357,488)(358,487)(359,486)(360,485)
(361,602)(362,601)(363,603)(364,604)(365,608)(366,607)(367,606)(368,605)
(369,618)(370,617)(371,619)(372,620)(373,624)(374,623)(375,622)(376,621)
(377,610)(378,609)(379,611)(380,612)(381,616)(382,615)(383,614)(384,613)
(385,578)(386,577)(387,579)(388,580)(389,584)(390,583)(391,582)(392,581)
(393,594)(394,593)(395,595)(396,596)(397,600)(398,599)(399,598)(400,597)
(401,586)(402,585)(403,587)(404,588)(405,592)(406,591)(407,590)(408,589)
(409,642)(410,641)(411,643)(412,644)(413,648)(414,647)(415,646)(416,645)
(417,634)(418,633)(419,635)(420,636)(421,640)(422,639)(423,638)(424,637)
(425,626)(426,625)(427,627)(428,628)(429,632)(430,631)(431,630)(432,629);;
s2 := ( 1,223)( 2,224)( 3,219)( 4,220)( 5,222)( 6,221)( 7,217)( 8,218)
( 9,231)( 10,232)( 11,227)( 12,228)( 13,230)( 14,229)( 15,225)( 16,226)
( 17,239)( 18,240)( 19,235)( 20,236)( 21,238)( 22,237)( 23,233)( 24,234)
( 25,247)( 26,248)( 27,243)( 28,244)( 29,246)( 30,245)( 31,241)( 32,242)
( 33,255)( 34,256)( 35,251)( 36,252)( 37,254)( 38,253)( 39,249)( 40,250)
( 41,263)( 42,264)( 43,259)( 44,260)( 45,262)( 46,261)( 47,257)( 48,258)
( 49,271)( 50,272)( 51,267)( 52,268)( 53,270)( 54,269)( 55,265)( 56,266)
( 57,279)( 58,280)( 59,275)( 60,276)( 61,278)( 62,277)( 63,273)( 64,274)
( 65,287)( 66,288)( 67,283)( 68,284)( 69,286)( 70,285)( 71,281)( 72,282)
( 73,367)( 74,368)( 75,363)( 76,364)( 77,366)( 78,365)( 79,361)( 80,362)
( 81,375)( 82,376)( 83,371)( 84,372)( 85,374)( 86,373)( 87,369)( 88,370)
( 89,383)( 90,384)( 91,379)( 92,380)( 93,382)( 94,381)( 95,377)( 96,378)
( 97,391)( 98,392)( 99,387)(100,388)(101,390)(102,389)(103,385)(104,386)
(105,399)(106,400)(107,395)(108,396)(109,398)(110,397)(111,393)(112,394)
(113,407)(114,408)(115,403)(116,404)(117,406)(118,405)(119,401)(120,402)
(121,415)(122,416)(123,411)(124,412)(125,414)(126,413)(127,409)(128,410)
(129,423)(130,424)(131,419)(132,420)(133,422)(134,421)(135,417)(136,418)
(137,431)(138,432)(139,427)(140,428)(141,430)(142,429)(143,425)(144,426)
(145,295)(146,296)(147,291)(148,292)(149,294)(150,293)(151,289)(152,290)
(153,303)(154,304)(155,299)(156,300)(157,302)(158,301)(159,297)(160,298)
(161,311)(162,312)(163,307)(164,308)(165,310)(166,309)(167,305)(168,306)
(169,319)(170,320)(171,315)(172,316)(173,318)(174,317)(175,313)(176,314)
(177,327)(178,328)(179,323)(180,324)(181,326)(182,325)(183,321)(184,322)
(185,335)(186,336)(187,331)(188,332)(189,334)(190,333)(191,329)(192,330)
(193,343)(194,344)(195,339)(196,340)(197,342)(198,341)(199,337)(200,338)
(201,351)(202,352)(203,347)(204,348)(205,350)(206,349)(207,345)(208,346)
(209,359)(210,360)(211,355)(212,356)(213,358)(214,357)(215,353)(216,354)
(433,655)(434,656)(435,651)(436,652)(437,654)(438,653)(439,649)(440,650)
(441,663)(442,664)(443,659)(444,660)(445,662)(446,661)(447,657)(448,658)
(449,671)(450,672)(451,667)(452,668)(453,670)(454,669)(455,665)(456,666)
(457,679)(458,680)(459,675)(460,676)(461,678)(462,677)(463,673)(464,674)
(465,687)(466,688)(467,683)(468,684)(469,686)(470,685)(471,681)(472,682)
(473,695)(474,696)(475,691)(476,692)(477,694)(478,693)(479,689)(480,690)
(481,703)(482,704)(483,699)(484,700)(485,702)(486,701)(487,697)(488,698)
(489,711)(490,712)(491,707)(492,708)(493,710)(494,709)(495,705)(496,706)
(497,719)(498,720)(499,715)(500,716)(501,718)(502,717)(503,713)(504,714)
(505,799)(506,800)(507,795)(508,796)(509,798)(510,797)(511,793)(512,794)
(513,807)(514,808)(515,803)(516,804)(517,806)(518,805)(519,801)(520,802)
(521,815)(522,816)(523,811)(524,812)(525,814)(526,813)(527,809)(528,810)
(529,823)(530,824)(531,819)(532,820)(533,822)(534,821)(535,817)(536,818)
(537,831)(538,832)(539,827)(540,828)(541,830)(542,829)(543,825)(544,826)
(545,839)(546,840)(547,835)(548,836)(549,838)(550,837)(551,833)(552,834)
(553,847)(554,848)(555,843)(556,844)(557,846)(558,845)(559,841)(560,842)
(561,855)(562,856)(563,851)(564,852)(565,854)(566,853)(567,849)(568,850)
(569,863)(570,864)(571,859)(572,860)(573,862)(574,861)(575,857)(576,858)
(577,727)(578,728)(579,723)(580,724)(581,726)(582,725)(583,721)(584,722)
(585,735)(586,736)(587,731)(588,732)(589,734)(590,733)(591,729)(592,730)
(593,743)(594,744)(595,739)(596,740)(597,742)(598,741)(599,737)(600,738)
(601,751)(602,752)(603,747)(604,748)(605,750)(606,749)(607,745)(608,746)
(609,759)(610,760)(611,755)(612,756)(613,758)(614,757)(615,753)(616,754)
(617,767)(618,768)(619,763)(620,764)(621,766)(622,765)(623,761)(624,762)
(625,775)(626,776)(627,771)(628,772)(629,774)(630,773)(631,769)(632,770)
(633,783)(634,784)(635,779)(636,780)(637,782)(638,781)(639,777)(640,778)
(641,791)(642,792)(643,787)(644,788)(645,790)(646,789)(647,785)(648,786);;
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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*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)( 9,665)( 10,666)( 11,670)( 12,669)( 13,668)( 14,667)( 15,672)
( 16,671)( 17,657)( 18,658)( 19,662)( 20,661)( 21,660)( 22,659)( 23,664)
( 24,663)( 25,713)( 26,714)( 27,718)( 28,717)( 29,716)( 30,715)( 31,720)
( 32,719)( 33,705)( 34,706)( 35,710)( 36,709)( 37,708)( 38,707)( 39,712)
( 40,711)( 41,697)( 42,698)( 43,702)( 44,701)( 45,700)( 46,699)( 47,704)
( 48,703)( 49,689)( 50,690)( 51,694)( 52,693)( 53,692)( 54,691)( 55,696)
( 56,695)( 57,681)( 58,682)( 59,686)( 60,685)( 61,684)( 62,683)( 63,688)
( 64,687)( 65,673)( 66,674)( 67,678)( 68,677)( 69,676)( 70,675)( 71,680)
( 72,679)( 73,793)( 74,794)( 75,798)( 76,797)( 77,796)( 78,795)( 79,800)
( 80,799)( 81,809)( 82,810)( 83,814)( 84,813)( 85,812)( 86,811)( 87,816)
( 88,815)( 89,801)( 90,802)( 91,806)( 92,805)( 93,804)( 94,803)( 95,808)
( 96,807)( 97,857)( 98,858)( 99,862)(100,861)(101,860)(102,859)(103,864)
(104,863)(105,849)(106,850)(107,854)(108,853)(109,852)(110,851)(111,856)
(112,855)(113,841)(114,842)(115,846)(116,845)(117,844)(118,843)(119,848)
(120,847)(121,833)(122,834)(123,838)(124,837)(125,836)(126,835)(127,840)
(128,839)(129,825)(130,826)(131,830)(132,829)(133,828)(134,827)(135,832)
(136,831)(137,817)(138,818)(139,822)(140,821)(141,820)(142,819)(143,824)
(144,823)(145,721)(146,722)(147,726)(148,725)(149,724)(150,723)(151,728)
(152,727)(153,737)(154,738)(155,742)(156,741)(157,740)(158,739)(159,744)
(160,743)(161,729)(162,730)(163,734)(164,733)(165,732)(166,731)(167,736)
(168,735)(169,785)(170,786)(171,790)(172,789)(173,788)(174,787)(175,792)
(176,791)(177,777)(178,778)(179,782)(180,781)(181,780)(182,779)(183,784)
(184,783)(185,769)(186,770)(187,774)(188,773)(189,772)(190,771)(191,776)
(192,775)(193,761)(194,762)(195,766)(196,765)(197,764)(198,763)(199,768)
(200,767)(201,753)(202,754)(203,758)(204,757)(205,756)(206,755)(207,760)
(208,759)(209,745)(210,746)(211,750)(212,749)(213,748)(214,747)(215,752)
(216,751)(217,434)(218,433)(219,437)(220,438)(221,435)(222,436)(223,439)
(224,440)(225,450)(226,449)(227,453)(228,454)(229,451)(230,452)(231,455)
(232,456)(233,442)(234,441)(235,445)(236,446)(237,443)(238,444)(239,447)
(240,448)(241,498)(242,497)(243,501)(244,502)(245,499)(246,500)(247,503)
(248,504)(249,490)(250,489)(251,493)(252,494)(253,491)(254,492)(255,495)
(256,496)(257,482)(258,481)(259,485)(260,486)(261,483)(262,484)(263,487)
(264,488)(265,474)(266,473)(267,477)(268,478)(269,475)(270,476)(271,479)
(272,480)(273,466)(274,465)(275,469)(276,470)(277,467)(278,468)(279,471)
(280,472)(281,458)(282,457)(283,461)(284,462)(285,459)(286,460)(287,463)
(288,464)(289,578)(290,577)(291,581)(292,582)(293,579)(294,580)(295,583)
(296,584)(297,594)(298,593)(299,597)(300,598)(301,595)(302,596)(303,599)
(304,600)(305,586)(306,585)(307,589)(308,590)(309,587)(310,588)(311,591)
(312,592)(313,642)(314,641)(315,645)(316,646)(317,643)(318,644)(319,647)
(320,648)(321,634)(322,633)(323,637)(324,638)(325,635)(326,636)(327,639)
(328,640)(329,626)(330,625)(331,629)(332,630)(333,627)(334,628)(335,631)
(336,632)(337,618)(338,617)(339,621)(340,622)(341,619)(342,620)(343,623)
(344,624)(345,610)(346,609)(347,613)(348,614)(349,611)(350,612)(351,615)
(352,616)(353,602)(354,601)(355,605)(356,606)(357,603)(358,604)(359,607)
(360,608)(361,506)(362,505)(363,509)(364,510)(365,507)(366,508)(367,511)
(368,512)(369,522)(370,521)(371,525)(372,526)(373,523)(374,524)(375,527)
(376,528)(377,514)(378,513)(379,517)(380,518)(381,515)(382,516)(383,519)
(384,520)(385,570)(386,569)(387,573)(388,574)(389,571)(390,572)(391,575)
(392,576)(393,562)(394,561)(395,565)(396,566)(397,563)(398,564)(399,567)
(400,568)(401,554)(402,553)(403,557)(404,558)(405,555)(406,556)(407,559)
(408,560)(409,546)(410,545)(411,549)(412,550)(413,547)(414,548)(415,551)
(416,552)(417,538)(418,537)(419,541)(420,542)(421,539)(422,540)(423,543)
(424,544)(425,530)(426,529)(427,533)(428,534)(429,531)(430,532)(431,535)
(432,536);
s1 := Sym(866)!( 1,745)( 2,746)( 3,748)( 4,747)( 5,751)( 6,752)( 7,749)
( 8,750)( 9,761)( 10,762)( 11,764)( 12,763)( 13,767)( 14,768)( 15,765)
( 16,766)( 17,753)( 18,754)( 19,756)( 20,755)( 21,759)( 22,760)( 23,757)
( 24,758)( 25,721)( 26,722)( 27,724)( 28,723)( 29,727)( 30,728)( 31,725)
( 32,726)( 33,737)( 34,738)( 35,740)( 36,739)( 37,743)( 38,744)( 39,741)
( 40,742)( 41,729)( 42,730)( 43,732)( 44,731)( 45,735)( 46,736)( 47,733)
( 48,734)( 49,785)( 50,786)( 51,788)( 52,787)( 53,791)( 54,792)( 55,789)
( 56,790)( 57,777)( 58,778)( 59,780)( 60,779)( 61,783)( 62,784)( 63,781)
( 64,782)( 65,769)( 66,770)( 67,772)( 68,771)( 69,775)( 70,776)( 71,773)
( 72,774)( 73,673)( 74,674)( 75,676)( 76,675)( 77,679)( 78,680)( 79,677)
( 80,678)( 81,689)( 82,690)( 83,692)( 84,691)( 85,695)( 86,696)( 87,693)
( 88,694)( 89,681)( 90,682)( 91,684)( 92,683)( 93,687)( 94,688)( 95,685)
( 96,686)( 97,649)( 98,650)( 99,652)(100,651)(101,655)(102,656)(103,653)
(104,654)(105,665)(106,666)(107,668)(108,667)(109,671)(110,672)(111,669)
(112,670)(113,657)(114,658)(115,660)(116,659)(117,663)(118,664)(119,661)
(120,662)(121,713)(122,714)(123,716)(124,715)(125,719)(126,720)(127,717)
(128,718)(129,705)(130,706)(131,708)(132,707)(133,711)(134,712)(135,709)
(136,710)(137,697)(138,698)(139,700)(140,699)(141,703)(142,704)(143,701)
(144,702)(145,817)(146,818)(147,820)(148,819)(149,823)(150,824)(151,821)
(152,822)(153,833)(154,834)(155,836)(156,835)(157,839)(158,840)(159,837)
(160,838)(161,825)(162,826)(163,828)(164,827)(165,831)(166,832)(167,829)
(168,830)(169,793)(170,794)(171,796)(172,795)(173,799)(174,800)(175,797)
(176,798)(177,809)(178,810)(179,812)(180,811)(181,815)(182,816)(183,813)
(184,814)(185,801)(186,802)(187,804)(188,803)(189,807)(190,808)(191,805)
(192,806)(193,857)(194,858)(195,860)(196,859)(197,863)(198,864)(199,861)
(200,862)(201,849)(202,850)(203,852)(204,851)(205,855)(206,856)(207,853)
(208,854)(209,841)(210,842)(211,844)(212,843)(213,847)(214,848)(215,845)
(216,846)(217,530)(218,529)(219,531)(220,532)(221,536)(222,535)(223,534)
(224,533)(225,546)(226,545)(227,547)(228,548)(229,552)(230,551)(231,550)
(232,549)(233,538)(234,537)(235,539)(236,540)(237,544)(238,543)(239,542)
(240,541)(241,506)(242,505)(243,507)(244,508)(245,512)(246,511)(247,510)
(248,509)(249,522)(250,521)(251,523)(252,524)(253,528)(254,527)(255,526)
(256,525)(257,514)(258,513)(259,515)(260,516)(261,520)(262,519)(263,518)
(264,517)(265,570)(266,569)(267,571)(268,572)(269,576)(270,575)(271,574)
(272,573)(273,562)(274,561)(275,563)(276,564)(277,568)(278,567)(279,566)
(280,565)(281,554)(282,553)(283,555)(284,556)(285,560)(286,559)(287,558)
(288,557)(289,458)(290,457)(291,459)(292,460)(293,464)(294,463)(295,462)
(296,461)(297,474)(298,473)(299,475)(300,476)(301,480)(302,479)(303,478)
(304,477)(305,466)(306,465)(307,467)(308,468)(309,472)(310,471)(311,470)
(312,469)(313,434)(314,433)(315,435)(316,436)(317,440)(318,439)(319,438)
(320,437)(321,450)(322,449)(323,451)(324,452)(325,456)(326,455)(327,454)
(328,453)(329,442)(330,441)(331,443)(332,444)(333,448)(334,447)(335,446)
(336,445)(337,498)(338,497)(339,499)(340,500)(341,504)(342,503)(343,502)
(344,501)(345,490)(346,489)(347,491)(348,492)(349,496)(350,495)(351,494)
(352,493)(353,482)(354,481)(355,483)(356,484)(357,488)(358,487)(359,486)
(360,485)(361,602)(362,601)(363,603)(364,604)(365,608)(366,607)(367,606)
(368,605)(369,618)(370,617)(371,619)(372,620)(373,624)(374,623)(375,622)
(376,621)(377,610)(378,609)(379,611)(380,612)(381,616)(382,615)(383,614)
(384,613)(385,578)(386,577)(387,579)(388,580)(389,584)(390,583)(391,582)
(392,581)(393,594)(394,593)(395,595)(396,596)(397,600)(398,599)(399,598)
(400,597)(401,586)(402,585)(403,587)(404,588)(405,592)(406,591)(407,590)
(408,589)(409,642)(410,641)(411,643)(412,644)(413,648)(414,647)(415,646)
(416,645)(417,634)(418,633)(419,635)(420,636)(421,640)(422,639)(423,638)
(424,637)(425,626)(426,625)(427,627)(428,628)(429,632)(430,631)(431,630)
(432,629);
s2 := Sym(866)!( 1,223)( 2,224)( 3,219)( 4,220)( 5,222)( 6,221)( 7,217)
( 8,218)( 9,231)( 10,232)( 11,227)( 12,228)( 13,230)( 14,229)( 15,225)
( 16,226)( 17,239)( 18,240)( 19,235)( 20,236)( 21,238)( 22,237)( 23,233)
( 24,234)( 25,247)( 26,248)( 27,243)( 28,244)( 29,246)( 30,245)( 31,241)
( 32,242)( 33,255)( 34,256)( 35,251)( 36,252)( 37,254)( 38,253)( 39,249)
( 40,250)( 41,263)( 42,264)( 43,259)( 44,260)( 45,262)( 46,261)( 47,257)
( 48,258)( 49,271)( 50,272)( 51,267)( 52,268)( 53,270)( 54,269)( 55,265)
( 56,266)( 57,279)( 58,280)( 59,275)( 60,276)( 61,278)( 62,277)( 63,273)
( 64,274)( 65,287)( 66,288)( 67,283)( 68,284)( 69,286)( 70,285)( 71,281)
( 72,282)( 73,367)( 74,368)( 75,363)( 76,364)( 77,366)( 78,365)( 79,361)
( 80,362)( 81,375)( 82,376)( 83,371)( 84,372)( 85,374)( 86,373)( 87,369)
( 88,370)( 89,383)( 90,384)( 91,379)( 92,380)( 93,382)( 94,381)( 95,377)
( 96,378)( 97,391)( 98,392)( 99,387)(100,388)(101,390)(102,389)(103,385)
(104,386)(105,399)(106,400)(107,395)(108,396)(109,398)(110,397)(111,393)
(112,394)(113,407)(114,408)(115,403)(116,404)(117,406)(118,405)(119,401)
(120,402)(121,415)(122,416)(123,411)(124,412)(125,414)(126,413)(127,409)
(128,410)(129,423)(130,424)(131,419)(132,420)(133,422)(134,421)(135,417)
(136,418)(137,431)(138,432)(139,427)(140,428)(141,430)(142,429)(143,425)
(144,426)(145,295)(146,296)(147,291)(148,292)(149,294)(150,293)(151,289)
(152,290)(153,303)(154,304)(155,299)(156,300)(157,302)(158,301)(159,297)
(160,298)(161,311)(162,312)(163,307)(164,308)(165,310)(166,309)(167,305)
(168,306)(169,319)(170,320)(171,315)(172,316)(173,318)(174,317)(175,313)
(176,314)(177,327)(178,328)(179,323)(180,324)(181,326)(182,325)(183,321)
(184,322)(185,335)(186,336)(187,331)(188,332)(189,334)(190,333)(191,329)
(192,330)(193,343)(194,344)(195,339)(196,340)(197,342)(198,341)(199,337)
(200,338)(201,351)(202,352)(203,347)(204,348)(205,350)(206,349)(207,345)
(208,346)(209,359)(210,360)(211,355)(212,356)(213,358)(214,357)(215,353)
(216,354)(433,655)(434,656)(435,651)(436,652)(437,654)(438,653)(439,649)
(440,650)(441,663)(442,664)(443,659)(444,660)(445,662)(446,661)(447,657)
(448,658)(449,671)(450,672)(451,667)(452,668)(453,670)(454,669)(455,665)
(456,666)(457,679)(458,680)(459,675)(460,676)(461,678)(462,677)(463,673)
(464,674)(465,687)(466,688)(467,683)(468,684)(469,686)(470,685)(471,681)
(472,682)(473,695)(474,696)(475,691)(476,692)(477,694)(478,693)(479,689)
(480,690)(481,703)(482,704)(483,699)(484,700)(485,702)(486,701)(487,697)
(488,698)(489,711)(490,712)(491,707)(492,708)(493,710)(494,709)(495,705)
(496,706)(497,719)(498,720)(499,715)(500,716)(501,718)(502,717)(503,713)
(504,714)(505,799)(506,800)(507,795)(508,796)(509,798)(510,797)(511,793)
(512,794)(513,807)(514,808)(515,803)(516,804)(517,806)(518,805)(519,801)
(520,802)(521,815)(522,816)(523,811)(524,812)(525,814)(526,813)(527,809)
(528,810)(529,823)(530,824)(531,819)(532,820)(533,822)(534,821)(535,817)
(536,818)(537,831)(538,832)(539,827)(540,828)(541,830)(542,829)(543,825)
(544,826)(545,839)(546,840)(547,835)(548,836)(549,838)(550,837)(551,833)
(552,834)(553,847)(554,848)(555,843)(556,844)(557,846)(558,845)(559,841)
(560,842)(561,855)(562,856)(563,851)(564,852)(565,854)(566,853)(567,849)
(568,850)(569,863)(570,864)(571,859)(572,860)(573,862)(574,861)(575,857)
(576,858)(577,727)(578,728)(579,723)(580,724)(581,726)(582,725)(583,721)
(584,722)(585,735)(586,736)(587,731)(588,732)(589,734)(590,733)(591,729)
(592,730)(593,743)(594,744)(595,739)(596,740)(597,742)(598,741)(599,737)
(600,738)(601,751)(602,752)(603,747)(604,748)(605,750)(606,749)(607,745)
(608,746)(609,759)(610,760)(611,755)(612,756)(613,758)(614,757)(615,753)
(616,754)(617,767)(618,768)(619,763)(620,764)(621,766)(622,765)(623,761)
(624,762)(625,775)(626,776)(627,771)(628,772)(629,774)(630,773)(631,769)
(632,770)(633,783)(634,784)(635,779)(636,780)(637,782)(638,781)(639,777)
(640,778)(641,791)(642,792)(643,787)(644,788)(645,790)(646,789)(647,785)
(648,786);
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*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1 >;
to this polytope