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Polytope of Type {6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*432d
Also Known As : {6,12}3if this polytope has another name.
Group : SmallGroup(432,523)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 18, 108, 36
Order of s0s1s2 : 3
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,12,2} of size 864
   {6,12,4} of size 1728
Vertex Figure Of :
   {2,6,12} of size 864
   {4,6,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,12}*144d
   4-fold quotients : {6,6}*108
   9-fold quotients : {6,4}*48b
   18-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,12}*864b
   3-fold covers : {6,36}*1296i, {6,36}*1296j, {6,36}*1296k, {18,12}*1296i, {18,12}*1296j, {6,12}*1296e, {18,12}*1296k, {6,12}*1296f
   4-fold covers : {6,24}*1728a, {12,12}*1728j, {6,12}*1728b, {6,24}*1728c, {6,24}*1728e, {12,12}*1728o, {12,12}*1728u
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)
(26,27)(29,33)(30,35)(31,34)(32,36);;
s1 := ( 3, 4)( 7, 8)(11,12)(13,33)(14,34)(15,36)(16,35)(17,25)(18,26)(19,28)
(20,27)(21,29)(22,30)(23,32)(24,31);;
s2 := ( 1,16)( 2,15)( 3,14)( 4,13)( 5,24)( 6,23)( 7,22)( 8,21)( 9,20)(10,19)
(11,18)(12,17)(25,28)(26,27)(29,36)(30,35)(31,34)(32,33);;
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, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*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(36)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)
(20,24)(26,27)(29,33)(30,35)(31,34)(32,36);
s1 := Sym(36)!( 3, 4)( 7, 8)(11,12)(13,33)(14,34)(15,36)(16,35)(17,25)(18,26)
(19,28)(20,27)(21,29)(22,30)(23,32)(24,31);
s2 := Sym(36)!( 1,16)( 2,15)( 3,14)( 4,13)( 5,24)( 6,23)( 7,22)( 8,21)( 9,20)
(10,19)(11,18)(12,17)(25,28)(26,27)(29,36)(30,35)(31,34)(32,33);
poly := sub<Sym(36)|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, s0*s1*s2*s0*s1*s2*s0*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*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.
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