
 Great Icosidodecahedron 
 Vertex description: 5/2.3.5/2.3
 Faces: 32
 Edges: 60
 Vertices: 30
 External facelets: 132
 Dual: Great rhombic triacontahedron
This uniform polyhedron's faces consist of 20 triangles and 12 pentagrams.
Can you spot them?
The polyhedron can be thought of as a halfway point between the
great stellated dodecahedron and its dual the
great icosahedron. It's relationship to those
regular polyhedra is the same as the
icosidodecahedron's relationship to the
dodecahedron and its dual the
icosahedron. In both cases the uniform
polyhedron can be found at the halfway point when
morphing by truncation in Small Stella, Great Stella, or Stella4D.
This is one of my favourite polyhedra!

After making about half of this model, using only the externally
visible parts, I noticed it was quite flexible. I printed out some
decagrams, matching in size to the decagram you get when you take a
crosssection right through the centre of the model.


A number of decagram parts can be glued inside to the existing internal
tabs. Finally I glued a whole decagram (with a hole in the middle to
get tweezers through) under the free tabs around the rim of the first
half of the model.



Rather than figure out how to put the last part in, I made two complete
halves of this model as described above. Then I just glued the two
halves together. It's hard to tell where the join is now. I'm a bit
surprised this worked so well!


You can see roughly how big the model is here.


Here is a very small version of the model made using SLA rapid
prototyping, along with a model of its dual.

