Polytope of Type {5,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,4}*1320a
if this polytope has a name.
Group : SmallGroup(1320,133)
Rank : 3
Schlafli Type : {5,4}
Number of vertices, edges, etc : 165, 330, 132
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing 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*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1> of order 3.
      44 facets:
         44 of {5}*10
      55 vertex figures:
         55 of {4}*8
   P/N, where N=<s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 11.
      12 facets:
         12 of {5}*10
      15 vertex figures:
         15 of {4}*8

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {5,4}

Twisty Puzzle