Polytope of Type {6,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*1152h
if this polytope has a name.
Group : SmallGroup(1152,157478)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 48, 288, 96
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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) :
   2-fold quotients : {6,6}*576d
   32-fold quotients : {6,3}*36
   96-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1> of order 2.
      48 facets:
         48 of {6}*12
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2> of order 3.
      32 facets:
         32 of {6}*12
      20 vertex figures:
         14 of {12}*24
         6 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s2*s1*s0*s1*s0*s2*s1*s0*s1> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1> of order 4.
      24 facets:
         24 of {6}*12
      12 vertex figures:
         12 of {12}*24

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,12}

Twisty Puzzle