Polytope of Type {4,5}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,5}*1320a
if this polytope has a name.
Group : SmallGroup(1320,133)
Rank : 3
Schlafli Type : {4,5}
Number of vertices, edges, etc : 132, 330, 165
Order of s₀s₁s₂ : 11
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
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*s2*s1*s2*s1*s0*s1*s2*s1> of order 3.
      55 facets:
         55 of {4}*8
      44 vertex figures:
         44 of {5}*10

Permutation Representation (GAP) :

s0 := ( 1, 2)( 3, 7)( 4,12)( 5, 6)( 8,10)( 9,11);;
s1 := ( 2, 5)( 3,11)( 4,10)( 7, 8)( 9,12);;
s2 := ( 1, 2)( 3,10)( 5, 9)( 6,11)( 7, 8);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(12)!( 1, 2)( 3, 7)( 4,12)( 5, 6)( 8,10)( 9,11);
s1 := Sym(12)!( 2, 5)( 3,11)( 4,10)( 7, 8)( 9,12);
s2 := Sym(12)!( 1, 2)( 3,10)( 5, 9)( 6,11)( 7, 8);
poly := sub<Sym(12)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;

References : None.
to this polytope

Polytope of Type {4,5}

Twisty Puzzle