Polytope of Type {12,6} with group SmallGroup(1728,46356)

Overview

Group: SmallGroup(1728,46356)
Rank: 3
Schläfli Type: {12,6}
Vertices, edges, …: 144, 432, 72
Order of s₀s₁s₂: 12
Order of s₀s₁s₂s₁: 12
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{12,6}*864c

3-fold

4-fold

{12,6}*432g

6-fold

8-fold

{6,6}*216d

9-fold

{4,6}*192b

12-fold

18-fold

{4,6}*96

24-fold

36-fold

48-fold

72-fold

108-fold

{4,2}*16

144-fold

216-fold

{2,2}*8

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 2

36 facets

36 of {12}*24

72 vertex figures

72 of {6}*12

P/N, where N=<s1*s0*(s2*s1)^2*s0*s1*s0*(s2*s1)^2> of order 2

36 facets

36 of {12}*24

72 vertex figures

72 of {6}*12

P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*s2*s1*s0> of order 2

36 facets

36 of {12}*24

84 vertex figures

60 of {6}*12
24 of {3}*6

P/N, where N=<(s0*s1)^6> of order 2

48 facets

24 of {6}*12
24 of {12}*24

72 vertex figures

72 of {6}*12

P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s2> of order 3

24 facets

24 of {12}*24

48 vertex figures

48 of {6}*12

P/N, where N=<(s0*s1)^4> of order 3

48 facets

36 of {4}*8
12 of {12}*24

48 vertex figures

48 of {6}*12

P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*s2*s1*s0*s1*s2*s1> of order 3

24 facets

24 of {12}*24

60 vertex figures

42 of {6}*12
18 of {2}*4

P/N, where N=<(s0*s1)^6, (s0*s1)^2*(s2*s1)^2*s0*s2*s1*s0> of order 4

24 facets

12 of {6}*12
12 of {12}*24

42 vertex figures

30 of {6}*12
12 of {3}*6

P/N, where N=<s0*s1*s2*s1*s0*(s2*s1)^2> of order 4

18 facets

18 of {12}*24

36 vertex figures

36 of {6}*12

P/N, where N=<s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2, s0*s2*(s1*s0)^5*s1*s2> of order 4

30 facets

6 of {12}*24
24 of {6}*12

36 vertex figures

36 of {6}*12

P/N, where N=<(s0*s1)^6, (s0*s1)^2*s2*s1*s0*s1*(s2*s1*s0)^2*s1*s2> of order 4

30 facets

6 of {6}*12
12 of {3}*6
12 of {12}*24

36 vertex figures

36 of {6}*12

P/N, where N=<(s0*s1)^2> of order 6

32 facets

12 of {2}*4
4 of {6}*12
4 of {12}*24
12 of {4}*8

24 vertex figures

24 of {6}*12

P/N, where N=<(s0*s1)^4, s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 6

24 facets

18 of {4}*8
6 of {12}*24

24 vertex figures

24 of {6}*12

P/N, where N=<(s0*s1)^4, (s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 6

24 facets

18 of {4}*8
6 of {12}*24

24 vertex figures

24 of {6}*12

P/N, where N=<(s0*s1)^4, (s2*s1*s0)^2*(s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 12

20 facets

3 of {4}*8
1 of {12}*24
4 of {6}*12
12 of {2}*4

12 vertex figures

12 of {6}*12

Representations

Permutation Representation (GAP)

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

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*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*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

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

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*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*s0*s1*s0*s1 >;

References

None.

to this polytope.

Overview

Special Properties

Related Polytopes

Quotients maximal quotients in bold

Covers minimal covers in bold

Irregular Quotients of which this is a minimal cover

Representations

References

Twisty Puzzle