Polytope of Type {6,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12,4}*1728j
if this polytope has a name.
Group : SmallGroup(1728,38778)
Rank : 4
Schlafli Type : {6,12,4}
Number of vertices, edges, etc : 18, 108, 72, 4
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,12,2}*864g, {6,6,4}*864h
3-fold quotients : {6,12,4}*576a, {6,12,4}*576b, {6,12,4}*576c
4-fold quotients : {6,6,2}*432d
6-fold quotients : {6,12,2}*288a, {6,12,2}*288b, {6,6,4}*288a, {6,6,4}*288b, {6,6,4}*288c, {6,12,2}*288c
9-fold quotients : {2,12,4}*192a, {6,4,4}*192
12-fold quotients : {3,6,4}*144, {6,6,2}*144a, {6,6,2}*144b, {6,6,2}*144c
18-fold quotients : {2,12,2}*96, {2,6,4}*96a, {6,2,4}*96, {6,4,2}*96a
24-fold quotients : {3,6,2}*72, {6,3,2}*72
27-fold quotients : {2,4,4}*64
36-fold quotients : {3,2,4}*48, {2,6,2}*48, {6,2,2}*48
54-fold quotients : {2,2,4}*32, {2,4,2}*32
72-fold quotients : {2,3,2}*24, {3,2,2}*24
108-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,649)( 2,651)( 3,650)( 4,652)( 5,654)( 6,653)( 7,655)( 8,657)
( 9,656)( 10,667)( 11,669)( 12,668)( 13,670)( 14,672)( 15,671)( 16,673)
( 17,675)( 18,674)( 19,658)( 20,660)( 21,659)( 22,661)( 23,663)( 24,662)
( 25,664)( 26,666)( 27,665)( 28,676)( 29,678)( 30,677)( 31,679)( 32,681)
( 33,680)( 34,682)( 35,684)( 36,683)( 37,694)( 38,696)( 39,695)( 40,697)
( 41,699)( 42,698)( 43,700)( 44,702)( 45,701)( 46,685)( 47,687)( 48,686)
( 49,688)( 50,690)( 51,689)( 52,691)( 53,693)( 54,692)( 55,703)( 56,705)
( 57,704)( 58,706)( 59,708)( 60,707)( 61,709)( 62,711)( 63,710)( 64,721)
( 65,723)( 66,722)( 67,724)( 68,726)( 69,725)( 70,727)( 71,729)( 72,728)
( 73,712)( 74,714)( 75,713)( 76,715)( 77,717)( 78,716)( 79,718)( 80,720)
( 81,719)( 82,730)( 83,732)( 84,731)( 85,733)( 86,735)( 87,734)( 88,736)
( 89,738)( 90,737)( 91,748)( 92,750)( 93,749)( 94,751)( 95,753)( 96,752)
( 97,754)( 98,756)( 99,755)(100,739)(101,741)(102,740)(103,742)(104,744)
(105,743)(106,745)(107,747)(108,746)(109,757)(110,759)(111,758)(112,760)
(113,762)(114,761)(115,763)(116,765)(117,764)(118,775)(119,777)(120,776)
(121,778)(122,780)(123,779)(124,781)(125,783)(126,782)(127,766)(128,768)
(129,767)(130,769)(131,771)(132,770)(133,772)(134,774)(135,773)(136,784)
(137,786)(138,785)(139,787)(140,789)(141,788)(142,790)(143,792)(144,791)
(145,802)(146,804)(147,803)(148,805)(149,807)(150,806)(151,808)(152,810)
(153,809)(154,793)(155,795)(156,794)(157,796)(158,798)(159,797)(160,799)
(161,801)(162,800)(163,811)(164,813)(165,812)(166,814)(167,816)(168,815)
(169,817)(170,819)(171,818)(172,829)(173,831)(174,830)(175,832)(176,834)
(177,833)(178,835)(179,837)(180,836)(181,820)(182,822)(183,821)(184,823)
(185,825)(186,824)(187,826)(188,828)(189,827)(190,838)(191,840)(192,839)
(193,841)(194,843)(195,842)(196,844)(197,846)(198,845)(199,856)(200,858)
(201,857)(202,859)(203,861)(204,860)(205,862)(206,864)(207,863)(208,847)
(209,849)(210,848)(211,850)(212,852)(213,851)(214,853)(215,855)(216,854)
(217,460)(218,462)(219,461)(220,463)(221,465)(222,464)(223,466)(224,468)
(225,467)(226,478)(227,480)(228,479)(229,481)(230,483)(231,482)(232,484)
(233,486)(234,485)(235,469)(236,471)(237,470)(238,472)(239,474)(240,473)
(241,475)(242,477)(243,476)(244,433)(245,435)(246,434)(247,436)(248,438)
(249,437)(250,439)(251,441)(252,440)(253,451)(254,453)(255,452)(256,454)
(257,456)(258,455)(259,457)(260,459)(261,458)(262,442)(263,444)(264,443)
(265,445)(266,447)(267,446)(268,448)(269,450)(270,449)(271,514)(272,516)
(273,515)(274,517)(275,519)(276,518)(277,520)(278,522)(279,521)(280,532)
(281,534)(282,533)(283,535)(284,537)(285,536)(286,538)(287,540)(288,539)
(289,523)(290,525)(291,524)(292,526)(293,528)(294,527)(295,529)(296,531)
(297,530)(298,487)(299,489)(300,488)(301,490)(302,492)(303,491)(304,493)
(305,495)(306,494)(307,505)(308,507)(309,506)(310,508)(311,510)(312,509)
(313,511)(314,513)(315,512)(316,496)(317,498)(318,497)(319,499)(320,501)
(321,500)(322,502)(323,504)(324,503)(325,568)(326,570)(327,569)(328,571)
(329,573)(330,572)(331,574)(332,576)(333,575)(334,586)(335,588)(336,587)
(337,589)(338,591)(339,590)(340,592)(341,594)(342,593)(343,577)(344,579)
(345,578)(346,580)(347,582)(348,581)(349,583)(350,585)(351,584)(352,541)
(353,543)(354,542)(355,544)(356,546)(357,545)(358,547)(359,549)(360,548)
(361,559)(362,561)(363,560)(364,562)(365,564)(366,563)(367,565)(368,567)
(369,566)(370,550)(371,552)(372,551)(373,553)(374,555)(375,554)(376,556)
(377,558)(378,557)(379,622)(380,624)(381,623)(382,625)(383,627)(384,626)
(385,628)(386,630)(387,629)(388,640)(389,642)(390,641)(391,643)(392,645)
(393,644)(394,646)(395,648)(396,647)(397,631)(398,633)(399,632)(400,634)
(401,636)(402,635)(403,637)(404,639)(405,638)(406,595)(407,597)(408,596)
(409,598)(410,600)(411,599)(412,601)(413,603)(414,602)(415,613)(416,615)
(417,614)(418,616)(419,618)(420,617)(421,619)(422,621)(423,620)(424,604)
(425,606)(426,605)(427,607)(428,609)(429,608)(430,610)(431,612)(432,611);;
s1 := ( 1,659)( 2,658)( 3,660)( 4,665)( 5,664)( 6,666)( 7,662)( 8,661)
( 9,663)( 10,650)( 11,649)( 12,651)( 13,656)( 14,655)( 15,657)( 16,653)
( 17,652)( 18,654)( 19,668)( 20,667)( 21,669)( 22,674)( 23,673)( 24,675)
( 25,671)( 26,670)( 27,672)( 28,686)( 29,685)( 30,687)( 31,692)( 32,691)
( 33,693)( 34,689)( 35,688)( 36,690)( 37,677)( 38,676)( 39,678)( 40,683)
( 41,682)( 42,684)( 43,680)( 44,679)( 45,681)( 46,695)( 47,694)( 48,696)
( 49,701)( 50,700)( 51,702)( 52,698)( 53,697)( 54,699)( 55,713)( 56,712)
( 57,714)( 58,719)( 59,718)( 60,720)( 61,716)( 62,715)( 63,717)( 64,704)
( 65,703)( 66,705)( 67,710)( 68,709)( 69,711)( 70,707)( 71,706)( 72,708)
( 73,722)( 74,721)( 75,723)( 76,728)( 77,727)( 78,729)( 79,725)( 80,724)
( 81,726)( 82,740)( 83,739)( 84,741)( 85,746)( 86,745)( 87,747)( 88,743)
( 89,742)( 90,744)( 91,731)( 92,730)( 93,732)( 94,737)( 95,736)( 96,738)
( 97,734)( 98,733)( 99,735)(100,749)(101,748)(102,750)(103,755)(104,754)
(105,756)(106,752)(107,751)(108,753)(109,767)(110,766)(111,768)(112,773)
(113,772)(114,774)(115,770)(116,769)(117,771)(118,758)(119,757)(120,759)
(121,764)(122,763)(123,765)(124,761)(125,760)(126,762)(127,776)(128,775)
(129,777)(130,782)(131,781)(132,783)(133,779)(134,778)(135,780)(136,794)
(137,793)(138,795)(139,800)(140,799)(141,801)(142,797)(143,796)(144,798)
(145,785)(146,784)(147,786)(148,791)(149,790)(150,792)(151,788)(152,787)
(153,789)(154,803)(155,802)(156,804)(157,809)(158,808)(159,810)(160,806)
(161,805)(162,807)(163,821)(164,820)(165,822)(166,827)(167,826)(168,828)
(169,824)(170,823)(171,825)(172,812)(173,811)(174,813)(175,818)(176,817)
(177,819)(178,815)(179,814)(180,816)(181,830)(182,829)(183,831)(184,836)
(185,835)(186,837)(187,833)(188,832)(189,834)(190,848)(191,847)(192,849)
(193,854)(194,853)(195,855)(196,851)(197,850)(198,852)(199,839)(200,838)
(201,840)(202,845)(203,844)(204,846)(205,842)(206,841)(207,843)(208,857)
(209,856)(210,858)(211,863)(212,862)(213,864)(214,860)(215,859)(216,861)
(217,443)(218,442)(219,444)(220,449)(221,448)(222,450)(223,446)(224,445)
(225,447)(226,434)(227,433)(228,435)(229,440)(230,439)(231,441)(232,437)
(233,436)(234,438)(235,452)(236,451)(237,453)(238,458)(239,457)(240,459)
(241,455)(242,454)(243,456)(244,470)(245,469)(246,471)(247,476)(248,475)
(249,477)(250,473)(251,472)(252,474)(253,461)(254,460)(255,462)(256,467)
(257,466)(258,468)(259,464)(260,463)(261,465)(262,479)(263,478)(264,480)
(265,485)(266,484)(267,486)(268,482)(269,481)(270,483)(271,497)(272,496)
(273,498)(274,503)(275,502)(276,504)(277,500)(278,499)(279,501)(280,488)
(281,487)(282,489)(283,494)(284,493)(285,495)(286,491)(287,490)(288,492)
(289,506)(290,505)(291,507)(292,512)(293,511)(294,513)(295,509)(296,508)
(297,510)(298,524)(299,523)(300,525)(301,530)(302,529)(303,531)(304,527)
(305,526)(306,528)(307,515)(308,514)(309,516)(310,521)(311,520)(312,522)
(313,518)(314,517)(315,519)(316,533)(317,532)(318,534)(319,539)(320,538)
(321,540)(322,536)(323,535)(324,537)(325,551)(326,550)(327,552)(328,557)
(329,556)(330,558)(331,554)(332,553)(333,555)(334,542)(335,541)(336,543)
(337,548)(338,547)(339,549)(340,545)(341,544)(342,546)(343,560)(344,559)
(345,561)(346,566)(347,565)(348,567)(349,563)(350,562)(351,564)(352,578)
(353,577)(354,579)(355,584)(356,583)(357,585)(358,581)(359,580)(360,582)
(361,569)(362,568)(363,570)(364,575)(365,574)(366,576)(367,572)(368,571)
(369,573)(370,587)(371,586)(372,588)(373,593)(374,592)(375,594)(376,590)
(377,589)(378,591)(379,605)(380,604)(381,606)(382,611)(383,610)(384,612)
(385,608)(386,607)(387,609)(388,596)(389,595)(390,597)(391,602)(392,601)
(393,603)(394,599)(395,598)(396,600)(397,614)(398,613)(399,615)(400,620)
(401,619)(402,621)(403,617)(404,616)(405,618)(406,632)(407,631)(408,633)
(409,638)(410,637)(411,639)(412,635)(413,634)(414,636)(415,623)(416,622)
(417,624)(418,629)(419,628)(420,630)(421,626)(422,625)(423,627)(424,641)
(425,640)(426,642)(427,647)(428,646)(429,648)(430,644)(431,643)(432,645);;
s2 := ( 1,436)( 2,437)( 3,438)( 4,433)( 5,434)( 6,435)( 7,439)( 8,440)
( 9,441)( 10,454)( 11,455)( 12,456)( 13,451)( 14,452)( 15,453)( 16,457)
( 17,458)( 18,459)( 19,445)( 20,446)( 21,447)( 22,442)( 23,443)( 24,444)
( 25,448)( 26,449)( 27,450)( 28,463)( 29,464)( 30,465)( 31,460)( 32,461)
( 33,462)( 34,466)( 35,467)( 36,468)( 37,481)( 38,482)( 39,483)( 40,478)
( 41,479)( 42,480)( 43,484)( 44,485)( 45,486)( 46,472)( 47,473)( 48,474)
( 49,469)( 50,470)( 51,471)( 52,475)( 53,476)( 54,477)( 55,490)( 56,491)
( 57,492)( 58,487)( 59,488)( 60,489)( 61,493)( 62,494)( 63,495)( 64,508)
( 65,509)( 66,510)( 67,505)( 68,506)( 69,507)( 70,511)( 71,512)( 72,513)
( 73,499)( 74,500)( 75,501)( 76,496)( 77,497)( 78,498)( 79,502)( 80,503)
( 81,504)( 82,517)( 83,518)( 84,519)( 85,514)( 86,515)( 87,516)( 88,520)
( 89,521)( 90,522)( 91,535)( 92,536)( 93,537)( 94,532)( 95,533)( 96,534)
( 97,538)( 98,539)( 99,540)(100,526)(101,527)(102,528)(103,523)(104,524)
(105,525)(106,529)(107,530)(108,531)(109,598)(110,599)(111,600)(112,595)
(113,596)(114,597)(115,601)(116,602)(117,603)(118,616)(119,617)(120,618)
(121,613)(122,614)(123,615)(124,619)(125,620)(126,621)(127,607)(128,608)
(129,609)(130,604)(131,605)(132,606)(133,610)(134,611)(135,612)(136,625)
(137,626)(138,627)(139,622)(140,623)(141,624)(142,628)(143,629)(144,630)
(145,643)(146,644)(147,645)(148,640)(149,641)(150,642)(151,646)(152,647)
(153,648)(154,634)(155,635)(156,636)(157,631)(158,632)(159,633)(160,637)
(161,638)(162,639)(163,544)(164,545)(165,546)(166,541)(167,542)(168,543)
(169,547)(170,548)(171,549)(172,562)(173,563)(174,564)(175,559)(176,560)
(177,561)(178,565)(179,566)(180,567)(181,553)(182,554)(183,555)(184,550)
(185,551)(186,552)(187,556)(188,557)(189,558)(190,571)(191,572)(192,573)
(193,568)(194,569)(195,570)(196,574)(197,575)(198,576)(199,589)(200,590)
(201,591)(202,586)(203,587)(204,588)(205,592)(206,593)(207,594)(208,580)
(209,581)(210,582)(211,577)(212,578)(213,579)(214,583)(215,584)(216,585)
(217,679)(218,680)(219,681)(220,676)(221,677)(222,678)(223,682)(224,683)
(225,684)(226,697)(227,698)(228,699)(229,694)(230,695)(231,696)(232,700)
(233,701)(234,702)(235,688)(236,689)(237,690)(238,685)(239,686)(240,687)
(241,691)(242,692)(243,693)(244,652)(245,653)(246,654)(247,649)(248,650)
(249,651)(250,655)(251,656)(252,657)(253,670)(254,671)(255,672)(256,667)
(257,668)(258,669)(259,673)(260,674)(261,675)(262,661)(263,662)(264,663)
(265,658)(266,659)(267,660)(268,664)(269,665)(270,666)(271,733)(272,734)
(273,735)(274,730)(275,731)(276,732)(277,736)(278,737)(279,738)(280,751)
(281,752)(282,753)(283,748)(284,749)(285,750)(286,754)(287,755)(288,756)
(289,742)(290,743)(291,744)(292,739)(293,740)(294,741)(295,745)(296,746)
(297,747)(298,706)(299,707)(300,708)(301,703)(302,704)(303,705)(304,709)
(305,710)(306,711)(307,724)(308,725)(309,726)(310,721)(311,722)(312,723)
(313,727)(314,728)(315,729)(316,715)(317,716)(318,717)(319,712)(320,713)
(321,714)(322,718)(323,719)(324,720)(325,841)(326,842)(327,843)(328,838)
(329,839)(330,840)(331,844)(332,845)(333,846)(334,859)(335,860)(336,861)
(337,856)(338,857)(339,858)(340,862)(341,863)(342,864)(343,850)(344,851)
(345,852)(346,847)(347,848)(348,849)(349,853)(350,854)(351,855)(352,814)
(353,815)(354,816)(355,811)(356,812)(357,813)(358,817)(359,818)(360,819)
(361,832)(362,833)(363,834)(364,829)(365,830)(366,831)(367,835)(368,836)
(369,837)(370,823)(371,824)(372,825)(373,820)(374,821)(375,822)(376,826)
(377,827)(378,828)(379,787)(380,788)(381,789)(382,784)(383,785)(384,786)
(385,790)(386,791)(387,792)(388,805)(389,806)(390,807)(391,802)(392,803)
(393,804)(394,808)(395,809)(396,810)(397,796)(398,797)(399,798)(400,793)
(401,794)(402,795)(403,799)(404,800)(405,801)(406,760)(407,761)(408,762)
(409,757)(410,758)(411,759)(412,763)(413,764)(414,765)(415,778)(416,779)
(417,780)(418,775)(419,776)(420,777)(421,781)(422,782)(423,783)(424,769)
(425,770)(426,771)(427,766)(428,767)(429,768)(430,772)(431,773)(432,774);;
s3 := ( 1,109)( 2,110)( 3,111)( 4,112)( 5,113)( 6,114)( 7,115)( 8,116)
( 9,117)( 10,118)( 11,119)( 12,120)( 13,121)( 14,122)( 15,123)( 16,124)
( 17,125)( 18,126)( 19,127)( 20,128)( 21,129)( 22,130)( 23,131)( 24,132)
( 25,133)( 26,134)( 27,135)( 28,136)( 29,137)( 30,138)( 31,139)( 32,140)
( 33,141)( 34,142)( 35,143)( 36,144)( 37,145)( 38,146)( 39,147)( 40,148)
( 41,149)( 42,150)( 43,151)( 44,152)( 45,153)( 46,154)( 47,155)( 48,156)
( 49,157)( 50,158)( 51,159)( 52,160)( 53,161)( 54,162)( 55,163)( 56,164)
( 57,165)( 58,166)( 59,167)( 60,168)( 61,169)( 62,170)( 63,171)( 64,172)
( 65,173)( 66,174)( 67,175)( 68,176)( 69,177)( 70,178)( 71,179)( 72,180)
( 73,181)( 74,182)( 75,183)( 76,184)( 77,185)( 78,186)( 79,187)( 80,188)
( 81,189)( 82,190)( 83,191)( 84,192)( 85,193)( 86,194)( 87,195)( 88,196)
( 89,197)( 90,198)( 91,199)( 92,200)( 93,201)( 94,202)( 95,203)( 96,204)
( 97,205)( 98,206)( 99,207)(100,208)(101,209)(102,210)(103,211)(104,212)
(105,213)(106,214)(107,215)(108,216)(217,325)(218,326)(219,327)(220,328)
(221,329)(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)(228,336)
(229,337)(230,338)(231,339)(232,340)(233,341)(234,342)(235,343)(236,344)
(237,345)(238,346)(239,347)(240,348)(241,349)(242,350)(243,351)(244,352)
(245,353)(246,354)(247,355)(248,356)(249,357)(250,358)(251,359)(252,360)
(253,361)(254,362)(255,363)(256,364)(257,365)(258,366)(259,367)(260,368)
(261,369)(262,370)(263,371)(264,372)(265,373)(266,374)(267,375)(268,376)
(269,377)(270,378)(271,379)(272,380)(273,381)(274,382)(275,383)(276,384)
(277,385)(278,386)(279,387)(280,388)(281,389)(282,390)(283,391)(284,392)
(285,393)(286,394)(287,395)(288,396)(289,397)(290,398)(291,399)(292,400)
(293,401)(294,402)(295,403)(296,404)(297,405)(298,406)(299,407)(300,408)
(301,409)(302,410)(303,411)(304,412)(305,413)(306,414)(307,415)(308,416)
(309,417)(310,418)(311,419)(312,420)(313,421)(314,422)(315,423)(316,424)
(317,425)(318,426)(319,427)(320,428)(321,429)(322,430)(323,431)(324,432)
(433,541)(434,542)(435,543)(436,544)(437,545)(438,546)(439,547)(440,548)
(441,549)(442,550)(443,551)(444,552)(445,553)(446,554)(447,555)(448,556)
(449,557)(450,558)(451,559)(452,560)(453,561)(454,562)(455,563)(456,564)
(457,565)(458,566)(459,567)(460,568)(461,569)(462,570)(463,571)(464,572)
(465,573)(466,574)(467,575)(468,576)(469,577)(470,578)(471,579)(472,580)
(473,581)(474,582)(475,583)(476,584)(477,585)(478,586)(479,587)(480,588)
(481,589)(482,590)(483,591)(484,592)(485,593)(486,594)(487,595)(488,596)
(489,597)(490,598)(491,599)(492,600)(493,601)(494,602)(495,603)(496,604)
(497,605)(498,606)(499,607)(500,608)(501,609)(502,610)(503,611)(504,612)
(505,613)(506,614)(507,615)(508,616)(509,617)(510,618)(511,619)(512,620)
(513,621)(514,622)(515,623)(516,624)(517,625)(518,626)(519,627)(520,628)
(521,629)(522,630)(523,631)(524,632)(525,633)(526,634)(527,635)(528,636)
(529,637)(530,638)(531,639)(532,640)(533,641)(534,642)(535,643)(536,644)
(537,645)(538,646)(539,647)(540,648)(649,757)(650,758)(651,759)(652,760)
(653,761)(654,762)(655,763)(656,764)(657,765)(658,766)(659,767)(660,768)
(661,769)(662,770)(663,771)(664,772)(665,773)(666,774)(667,775)(668,776)
(669,777)(670,778)(671,779)(672,780)(673,781)(674,782)(675,783)(676,784)
(677,785)(678,786)(679,787)(680,788)(681,789)(682,790)(683,791)(684,792)
(685,793)(686,794)(687,795)(688,796)(689,797)(690,798)(691,799)(692,800)
(693,801)(694,802)(695,803)(696,804)(697,805)(698,806)(699,807)(700,808)
(701,809)(702,810)(703,811)(704,812)(705,813)(706,814)(707,815)(708,816)
(709,817)(710,818)(711,819)(712,820)(713,821)(714,822)(715,823)(716,824)
(717,825)(718,826)(719,827)(720,828)(721,829)(722,830)(723,831)(724,832)
(725,833)(726,834)(727,835)(728,836)(729,837)(730,838)(731,839)(732,840)
(733,841)(734,842)(735,843)(736,844)(737,845)(738,846)(739,847)(740,848)
(741,849)(742,850)(743,851)(744,852)(745,853)(746,854)(747,855)(748,856)
(749,857)(750,858)(751,859)(752,860)(753,861)(754,862)(755,863)(756,864);;
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, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1,649)( 2,651)( 3,650)( 4,652)( 5,654)( 6,653)( 7,655)
( 8,657)( 9,656)( 10,667)( 11,669)( 12,668)( 13,670)( 14,672)( 15,671)
( 16,673)( 17,675)( 18,674)( 19,658)( 20,660)( 21,659)( 22,661)( 23,663)
( 24,662)( 25,664)( 26,666)( 27,665)( 28,676)( 29,678)( 30,677)( 31,679)
( 32,681)( 33,680)( 34,682)( 35,684)( 36,683)( 37,694)( 38,696)( 39,695)
( 40,697)( 41,699)( 42,698)( 43,700)( 44,702)( 45,701)( 46,685)( 47,687)
( 48,686)( 49,688)( 50,690)( 51,689)( 52,691)( 53,693)( 54,692)( 55,703)
( 56,705)( 57,704)( 58,706)( 59,708)( 60,707)( 61,709)( 62,711)( 63,710)
( 64,721)( 65,723)( 66,722)( 67,724)( 68,726)( 69,725)( 70,727)( 71,729)
( 72,728)( 73,712)( 74,714)( 75,713)( 76,715)( 77,717)( 78,716)( 79,718)
( 80,720)( 81,719)( 82,730)( 83,732)( 84,731)( 85,733)( 86,735)( 87,734)
( 88,736)( 89,738)( 90,737)( 91,748)( 92,750)( 93,749)( 94,751)( 95,753)
( 96,752)( 97,754)( 98,756)( 99,755)(100,739)(101,741)(102,740)(103,742)
(104,744)(105,743)(106,745)(107,747)(108,746)(109,757)(110,759)(111,758)
(112,760)(113,762)(114,761)(115,763)(116,765)(117,764)(118,775)(119,777)
(120,776)(121,778)(122,780)(123,779)(124,781)(125,783)(126,782)(127,766)
(128,768)(129,767)(130,769)(131,771)(132,770)(133,772)(134,774)(135,773)
(136,784)(137,786)(138,785)(139,787)(140,789)(141,788)(142,790)(143,792)
(144,791)(145,802)(146,804)(147,803)(148,805)(149,807)(150,806)(151,808)
(152,810)(153,809)(154,793)(155,795)(156,794)(157,796)(158,798)(159,797)
(160,799)(161,801)(162,800)(163,811)(164,813)(165,812)(166,814)(167,816)
(168,815)(169,817)(170,819)(171,818)(172,829)(173,831)(174,830)(175,832)
(176,834)(177,833)(178,835)(179,837)(180,836)(181,820)(182,822)(183,821)
(184,823)(185,825)(186,824)(187,826)(188,828)(189,827)(190,838)(191,840)
(192,839)(193,841)(194,843)(195,842)(196,844)(197,846)(198,845)(199,856)
(200,858)(201,857)(202,859)(203,861)(204,860)(205,862)(206,864)(207,863)
(208,847)(209,849)(210,848)(211,850)(212,852)(213,851)(214,853)(215,855)
(216,854)(217,460)(218,462)(219,461)(220,463)(221,465)(222,464)(223,466)
(224,468)(225,467)(226,478)(227,480)(228,479)(229,481)(230,483)(231,482)
(232,484)(233,486)(234,485)(235,469)(236,471)(237,470)(238,472)(239,474)
(240,473)(241,475)(242,477)(243,476)(244,433)(245,435)(246,434)(247,436)
(248,438)(249,437)(250,439)(251,441)(252,440)(253,451)(254,453)(255,452)
(256,454)(257,456)(258,455)(259,457)(260,459)(261,458)(262,442)(263,444)
(264,443)(265,445)(266,447)(267,446)(268,448)(269,450)(270,449)(271,514)
(272,516)(273,515)(274,517)(275,519)(276,518)(277,520)(278,522)(279,521)
(280,532)(281,534)(282,533)(283,535)(284,537)(285,536)(286,538)(287,540)
(288,539)(289,523)(290,525)(291,524)(292,526)(293,528)(294,527)(295,529)
(296,531)(297,530)(298,487)(299,489)(300,488)(301,490)(302,492)(303,491)
(304,493)(305,495)(306,494)(307,505)(308,507)(309,506)(310,508)(311,510)
(312,509)(313,511)(314,513)(315,512)(316,496)(317,498)(318,497)(319,499)
(320,501)(321,500)(322,502)(323,504)(324,503)(325,568)(326,570)(327,569)
(328,571)(329,573)(330,572)(331,574)(332,576)(333,575)(334,586)(335,588)
(336,587)(337,589)(338,591)(339,590)(340,592)(341,594)(342,593)(343,577)
(344,579)(345,578)(346,580)(347,582)(348,581)(349,583)(350,585)(351,584)
(352,541)(353,543)(354,542)(355,544)(356,546)(357,545)(358,547)(359,549)
(360,548)(361,559)(362,561)(363,560)(364,562)(365,564)(366,563)(367,565)
(368,567)(369,566)(370,550)(371,552)(372,551)(373,553)(374,555)(375,554)
(376,556)(377,558)(378,557)(379,622)(380,624)(381,623)(382,625)(383,627)
(384,626)(385,628)(386,630)(387,629)(388,640)(389,642)(390,641)(391,643)
(392,645)(393,644)(394,646)(395,648)(396,647)(397,631)(398,633)(399,632)
(400,634)(401,636)(402,635)(403,637)(404,639)(405,638)(406,595)(407,597)
(408,596)(409,598)(410,600)(411,599)(412,601)(413,603)(414,602)(415,613)
(416,615)(417,614)(418,616)(419,618)(420,617)(421,619)(422,621)(423,620)
(424,604)(425,606)(426,605)(427,607)(428,609)(429,608)(430,610)(431,612)
(432,611);
s1 := Sym(864)!( 1,659)( 2,658)( 3,660)( 4,665)( 5,664)( 6,666)( 7,662)
( 8,661)( 9,663)( 10,650)( 11,649)( 12,651)( 13,656)( 14,655)( 15,657)
( 16,653)( 17,652)( 18,654)( 19,668)( 20,667)( 21,669)( 22,674)( 23,673)
( 24,675)( 25,671)( 26,670)( 27,672)( 28,686)( 29,685)( 30,687)( 31,692)
( 32,691)( 33,693)( 34,689)( 35,688)( 36,690)( 37,677)( 38,676)( 39,678)
( 40,683)( 41,682)( 42,684)( 43,680)( 44,679)( 45,681)( 46,695)( 47,694)
( 48,696)( 49,701)( 50,700)( 51,702)( 52,698)( 53,697)( 54,699)( 55,713)
( 56,712)( 57,714)( 58,719)( 59,718)( 60,720)( 61,716)( 62,715)( 63,717)
( 64,704)( 65,703)( 66,705)( 67,710)( 68,709)( 69,711)( 70,707)( 71,706)
( 72,708)( 73,722)( 74,721)( 75,723)( 76,728)( 77,727)( 78,729)( 79,725)
( 80,724)( 81,726)( 82,740)( 83,739)( 84,741)( 85,746)( 86,745)( 87,747)
( 88,743)( 89,742)( 90,744)( 91,731)( 92,730)( 93,732)( 94,737)( 95,736)
( 96,738)( 97,734)( 98,733)( 99,735)(100,749)(101,748)(102,750)(103,755)
(104,754)(105,756)(106,752)(107,751)(108,753)(109,767)(110,766)(111,768)
(112,773)(113,772)(114,774)(115,770)(116,769)(117,771)(118,758)(119,757)
(120,759)(121,764)(122,763)(123,765)(124,761)(125,760)(126,762)(127,776)
(128,775)(129,777)(130,782)(131,781)(132,783)(133,779)(134,778)(135,780)
(136,794)(137,793)(138,795)(139,800)(140,799)(141,801)(142,797)(143,796)
(144,798)(145,785)(146,784)(147,786)(148,791)(149,790)(150,792)(151,788)
(152,787)(153,789)(154,803)(155,802)(156,804)(157,809)(158,808)(159,810)
(160,806)(161,805)(162,807)(163,821)(164,820)(165,822)(166,827)(167,826)
(168,828)(169,824)(170,823)(171,825)(172,812)(173,811)(174,813)(175,818)
(176,817)(177,819)(178,815)(179,814)(180,816)(181,830)(182,829)(183,831)
(184,836)(185,835)(186,837)(187,833)(188,832)(189,834)(190,848)(191,847)
(192,849)(193,854)(194,853)(195,855)(196,851)(197,850)(198,852)(199,839)
(200,838)(201,840)(202,845)(203,844)(204,846)(205,842)(206,841)(207,843)
(208,857)(209,856)(210,858)(211,863)(212,862)(213,864)(214,860)(215,859)
(216,861)(217,443)(218,442)(219,444)(220,449)(221,448)(222,450)(223,446)
(224,445)(225,447)(226,434)(227,433)(228,435)(229,440)(230,439)(231,441)
(232,437)(233,436)(234,438)(235,452)(236,451)(237,453)(238,458)(239,457)
(240,459)(241,455)(242,454)(243,456)(244,470)(245,469)(246,471)(247,476)
(248,475)(249,477)(250,473)(251,472)(252,474)(253,461)(254,460)(255,462)
(256,467)(257,466)(258,468)(259,464)(260,463)(261,465)(262,479)(263,478)
(264,480)(265,485)(266,484)(267,486)(268,482)(269,481)(270,483)(271,497)
(272,496)(273,498)(274,503)(275,502)(276,504)(277,500)(278,499)(279,501)
(280,488)(281,487)(282,489)(283,494)(284,493)(285,495)(286,491)(287,490)
(288,492)(289,506)(290,505)(291,507)(292,512)(293,511)(294,513)(295,509)
(296,508)(297,510)(298,524)(299,523)(300,525)(301,530)(302,529)(303,531)
(304,527)(305,526)(306,528)(307,515)(308,514)(309,516)(310,521)(311,520)
(312,522)(313,518)(314,517)(315,519)(316,533)(317,532)(318,534)(319,539)
(320,538)(321,540)(322,536)(323,535)(324,537)(325,551)(326,550)(327,552)
(328,557)(329,556)(330,558)(331,554)(332,553)(333,555)(334,542)(335,541)
(336,543)(337,548)(338,547)(339,549)(340,545)(341,544)(342,546)(343,560)
(344,559)(345,561)(346,566)(347,565)(348,567)(349,563)(350,562)(351,564)
(352,578)(353,577)(354,579)(355,584)(356,583)(357,585)(358,581)(359,580)
(360,582)(361,569)(362,568)(363,570)(364,575)(365,574)(366,576)(367,572)
(368,571)(369,573)(370,587)(371,586)(372,588)(373,593)(374,592)(375,594)
(376,590)(377,589)(378,591)(379,605)(380,604)(381,606)(382,611)(383,610)
(384,612)(385,608)(386,607)(387,609)(388,596)(389,595)(390,597)(391,602)
(392,601)(393,603)(394,599)(395,598)(396,600)(397,614)(398,613)(399,615)
(400,620)(401,619)(402,621)(403,617)(404,616)(405,618)(406,632)(407,631)
(408,633)(409,638)(410,637)(411,639)(412,635)(413,634)(414,636)(415,623)
(416,622)(417,624)(418,629)(419,628)(420,630)(421,626)(422,625)(423,627)
(424,641)(425,640)(426,642)(427,647)(428,646)(429,648)(430,644)(431,643)
(432,645);
s2 := Sym(864)!( 1,436)( 2,437)( 3,438)( 4,433)( 5,434)( 6,435)( 7,439)
( 8,440)( 9,441)( 10,454)( 11,455)( 12,456)( 13,451)( 14,452)( 15,453)
( 16,457)( 17,458)( 18,459)( 19,445)( 20,446)( 21,447)( 22,442)( 23,443)
( 24,444)( 25,448)( 26,449)( 27,450)( 28,463)( 29,464)( 30,465)( 31,460)
( 32,461)( 33,462)( 34,466)( 35,467)( 36,468)( 37,481)( 38,482)( 39,483)
( 40,478)( 41,479)( 42,480)( 43,484)( 44,485)( 45,486)( 46,472)( 47,473)
( 48,474)( 49,469)( 50,470)( 51,471)( 52,475)( 53,476)( 54,477)( 55,490)
( 56,491)( 57,492)( 58,487)( 59,488)( 60,489)( 61,493)( 62,494)( 63,495)
( 64,508)( 65,509)( 66,510)( 67,505)( 68,506)( 69,507)( 70,511)( 71,512)
( 72,513)( 73,499)( 74,500)( 75,501)( 76,496)( 77,497)( 78,498)( 79,502)
( 80,503)( 81,504)( 82,517)( 83,518)( 84,519)( 85,514)( 86,515)( 87,516)
( 88,520)( 89,521)( 90,522)( 91,535)( 92,536)( 93,537)( 94,532)( 95,533)
( 96,534)( 97,538)( 98,539)( 99,540)(100,526)(101,527)(102,528)(103,523)
(104,524)(105,525)(106,529)(107,530)(108,531)(109,598)(110,599)(111,600)
(112,595)(113,596)(114,597)(115,601)(116,602)(117,603)(118,616)(119,617)
(120,618)(121,613)(122,614)(123,615)(124,619)(125,620)(126,621)(127,607)
(128,608)(129,609)(130,604)(131,605)(132,606)(133,610)(134,611)(135,612)
(136,625)(137,626)(138,627)(139,622)(140,623)(141,624)(142,628)(143,629)
(144,630)(145,643)(146,644)(147,645)(148,640)(149,641)(150,642)(151,646)
(152,647)(153,648)(154,634)(155,635)(156,636)(157,631)(158,632)(159,633)
(160,637)(161,638)(162,639)(163,544)(164,545)(165,546)(166,541)(167,542)
(168,543)(169,547)(170,548)(171,549)(172,562)(173,563)(174,564)(175,559)
(176,560)(177,561)(178,565)(179,566)(180,567)(181,553)(182,554)(183,555)
(184,550)(185,551)(186,552)(187,556)(188,557)(189,558)(190,571)(191,572)
(192,573)(193,568)(194,569)(195,570)(196,574)(197,575)(198,576)(199,589)
(200,590)(201,591)(202,586)(203,587)(204,588)(205,592)(206,593)(207,594)
(208,580)(209,581)(210,582)(211,577)(212,578)(213,579)(214,583)(215,584)
(216,585)(217,679)(218,680)(219,681)(220,676)(221,677)(222,678)(223,682)
(224,683)(225,684)(226,697)(227,698)(228,699)(229,694)(230,695)(231,696)
(232,700)(233,701)(234,702)(235,688)(236,689)(237,690)(238,685)(239,686)
(240,687)(241,691)(242,692)(243,693)(244,652)(245,653)(246,654)(247,649)
(248,650)(249,651)(250,655)(251,656)(252,657)(253,670)(254,671)(255,672)
(256,667)(257,668)(258,669)(259,673)(260,674)(261,675)(262,661)(263,662)
(264,663)(265,658)(266,659)(267,660)(268,664)(269,665)(270,666)(271,733)
(272,734)(273,735)(274,730)(275,731)(276,732)(277,736)(278,737)(279,738)
(280,751)(281,752)(282,753)(283,748)(284,749)(285,750)(286,754)(287,755)
(288,756)(289,742)(290,743)(291,744)(292,739)(293,740)(294,741)(295,745)
(296,746)(297,747)(298,706)(299,707)(300,708)(301,703)(302,704)(303,705)
(304,709)(305,710)(306,711)(307,724)(308,725)(309,726)(310,721)(311,722)
(312,723)(313,727)(314,728)(315,729)(316,715)(317,716)(318,717)(319,712)
(320,713)(321,714)(322,718)(323,719)(324,720)(325,841)(326,842)(327,843)
(328,838)(329,839)(330,840)(331,844)(332,845)(333,846)(334,859)(335,860)
(336,861)(337,856)(338,857)(339,858)(340,862)(341,863)(342,864)(343,850)
(344,851)(345,852)(346,847)(347,848)(348,849)(349,853)(350,854)(351,855)
(352,814)(353,815)(354,816)(355,811)(356,812)(357,813)(358,817)(359,818)
(360,819)(361,832)(362,833)(363,834)(364,829)(365,830)(366,831)(367,835)
(368,836)(369,837)(370,823)(371,824)(372,825)(373,820)(374,821)(375,822)
(376,826)(377,827)(378,828)(379,787)(380,788)(381,789)(382,784)(383,785)
(384,786)(385,790)(386,791)(387,792)(388,805)(389,806)(390,807)(391,802)
(392,803)(393,804)(394,808)(395,809)(396,810)(397,796)(398,797)(399,798)
(400,793)(401,794)(402,795)(403,799)(404,800)(405,801)(406,760)(407,761)
(408,762)(409,757)(410,758)(411,759)(412,763)(413,764)(414,765)(415,778)
(416,779)(417,780)(418,775)(419,776)(420,777)(421,781)(422,782)(423,783)
(424,769)(425,770)(426,771)(427,766)(428,767)(429,768)(430,772)(431,773)
(432,774);
s3 := Sym(864)!( 1,109)( 2,110)( 3,111)( 4,112)( 5,113)( 6,114)( 7,115)
( 8,116)( 9,117)( 10,118)( 11,119)( 12,120)( 13,121)( 14,122)( 15,123)
( 16,124)( 17,125)( 18,126)( 19,127)( 20,128)( 21,129)( 22,130)( 23,131)
( 24,132)( 25,133)( 26,134)( 27,135)( 28,136)( 29,137)( 30,138)( 31,139)
( 32,140)( 33,141)( 34,142)( 35,143)( 36,144)( 37,145)( 38,146)( 39,147)
( 40,148)( 41,149)( 42,150)( 43,151)( 44,152)( 45,153)( 46,154)( 47,155)
( 48,156)( 49,157)( 50,158)( 51,159)( 52,160)( 53,161)( 54,162)( 55,163)
( 56,164)( 57,165)( 58,166)( 59,167)( 60,168)( 61,169)( 62,170)( 63,171)
( 64,172)( 65,173)( 66,174)( 67,175)( 68,176)( 69,177)( 70,178)( 71,179)
( 72,180)( 73,181)( 74,182)( 75,183)( 76,184)( 77,185)( 78,186)( 79,187)
( 80,188)( 81,189)( 82,190)( 83,191)( 84,192)( 85,193)( 86,194)( 87,195)
( 88,196)( 89,197)( 90,198)( 91,199)( 92,200)( 93,201)( 94,202)( 95,203)
( 96,204)( 97,205)( 98,206)( 99,207)(100,208)(101,209)(102,210)(103,211)
(104,212)(105,213)(106,214)(107,215)(108,216)(217,325)(218,326)(219,327)
(220,328)(221,329)(222,330)(223,331)(224,332)(225,333)(226,334)(227,335)
(228,336)(229,337)(230,338)(231,339)(232,340)(233,341)(234,342)(235,343)
(236,344)(237,345)(238,346)(239,347)(240,348)(241,349)(242,350)(243,351)
(244,352)(245,353)(246,354)(247,355)(248,356)(249,357)(250,358)(251,359)
(252,360)(253,361)(254,362)(255,363)(256,364)(257,365)(258,366)(259,367)
(260,368)(261,369)(262,370)(263,371)(264,372)(265,373)(266,374)(267,375)
(268,376)(269,377)(270,378)(271,379)(272,380)(273,381)(274,382)(275,383)
(276,384)(277,385)(278,386)(279,387)(280,388)(281,389)(282,390)(283,391)
(284,392)(285,393)(286,394)(287,395)(288,396)(289,397)(290,398)(291,399)
(292,400)(293,401)(294,402)(295,403)(296,404)(297,405)(298,406)(299,407)
(300,408)(301,409)(302,410)(303,411)(304,412)(305,413)(306,414)(307,415)
(308,416)(309,417)(310,418)(311,419)(312,420)(313,421)(314,422)(315,423)
(316,424)(317,425)(318,426)(319,427)(320,428)(321,429)(322,430)(323,431)
(324,432)(433,541)(434,542)(435,543)(436,544)(437,545)(438,546)(439,547)
(440,548)(441,549)(442,550)(443,551)(444,552)(445,553)(446,554)(447,555)
(448,556)(449,557)(450,558)(451,559)(452,560)(453,561)(454,562)(455,563)
(456,564)(457,565)(458,566)(459,567)(460,568)(461,569)(462,570)(463,571)
(464,572)(465,573)(466,574)(467,575)(468,576)(469,577)(470,578)(471,579)
(472,580)(473,581)(474,582)(475,583)(476,584)(477,585)(478,586)(479,587)
(480,588)(481,589)(482,590)(483,591)(484,592)(485,593)(486,594)(487,595)
(488,596)(489,597)(490,598)(491,599)(492,600)(493,601)(494,602)(495,603)
(496,604)(497,605)(498,606)(499,607)(500,608)(501,609)(502,610)(503,611)
(504,612)(505,613)(506,614)(507,615)(508,616)(509,617)(510,618)(511,619)
(512,620)(513,621)(514,622)(515,623)(516,624)(517,625)(518,626)(519,627)
(520,628)(521,629)(522,630)(523,631)(524,632)(525,633)(526,634)(527,635)
(528,636)(529,637)(530,638)(531,639)(532,640)(533,641)(534,642)(535,643)
(536,644)(537,645)(538,646)(539,647)(540,648)(649,757)(650,758)(651,759)
(652,760)(653,761)(654,762)(655,763)(656,764)(657,765)(658,766)(659,767)
(660,768)(661,769)(662,770)(663,771)(664,772)(665,773)(666,774)(667,775)
(668,776)(669,777)(670,778)(671,779)(672,780)(673,781)(674,782)(675,783)
(676,784)(677,785)(678,786)(679,787)(680,788)(681,789)(682,790)(683,791)
(684,792)(685,793)(686,794)(687,795)(688,796)(689,797)(690,798)(691,799)
(692,800)(693,801)(694,802)(695,803)(696,804)(697,805)(698,806)(699,807)
(700,808)(701,809)(702,810)(703,811)(704,812)(705,813)(706,814)(707,815)
(708,816)(709,817)(710,818)(711,819)(712,820)(713,821)(714,822)(715,823)
(716,824)(717,825)(718,826)(719,827)(720,828)(721,829)(722,830)(723,831)
(724,832)(725,833)(726,834)(727,835)(728,836)(729,837)(730,838)(731,839)
(732,840)(733,841)(734,842)(735,843)(736,844)(737,845)(738,846)(739,847)
(740,848)(741,849)(742,850)(743,851)(744,852)(745,853)(746,854)(747,855)
(748,856)(749,857)(750,858)(751,859)(752,860)(753,861)(754,862)(755,863)
(756,864);
poly := sub<Sym(864)|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,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope