Polytope of Type {12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*1944c
if this polytope has a name.
Group : SmallGroup(1944,2324)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 162, 486, 81
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   9-fold quotients : {12,6}*216c
   27-fold quotients : {4,6}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 7, 9)(10,19)(11,21)(12,20)(13,23)(14,22)(15,24)(16,27)
(17,26)(18,25);;
s1 := ( 1,10)( 2,17)( 3,15)( 4,16)( 5,14)( 6,12)( 7,13)( 8,11)( 9,18)(20,26)
(21,24)(22,25);;
s2 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(10,11)(13,17)(14,16)(15,18)(19,21)(22,27)
(23,26)(24,25);;
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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*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, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(27)!( 2, 3)( 4, 5)( 7, 9)(10,19)(11,21)(12,20)(13,23)(14,22)(15,24)
(16,27)(17,26)(18,25);
s1 := Sym(27)!( 1,10)( 2,17)( 3,15)( 4,16)( 5,14)( 6,12)( 7,13)( 8,11)( 9,18)
(20,26)(21,24)(22,25);
s2 := Sym(27)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(10,11)(13,17)(14,16)(15,18)(19,21)
(22,27)(23,26)(24,25);
poly := sub<Sym(27)|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*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*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, 
s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope