The Rectified 600-Cell
Here is a Zome System model built during the 2001 conference Bridges: Mathematical Connections in Art, Music, and Science, in Winfield, Kansas. I got a lot of help from Thomas Engdahl, another participant in the conference, but George Hart and Douglas Dunham also spent considerable time on it. It took us several hours and over 2000 pieces. George Hart provided most of the pieces. The diameter of the completed model was about 4 feet.
This models a projection of a 600-cell which has been truncated to its edge midpoints. It is comprised of 600 regular octahedra and 120 regular icosahedra. Two octahedra and one icosahedron meet at every edge. Five octahedra and two icosahedra meet at every vertex. There are 10 edges per vertex. It is an example of a convex uniform polychoron.
The edges of several uniform polyhedra are visible in this model. Specifically, one can see the edges of the regular icosahedron, the icosidodecahedron, the rhombicosidodecahedron, and the truncated dodecahedron. All of these edges are blue. After a little more work, one can find "squashed" versions of all of these also. Of course, having the model in front of you helps to see these other objects.
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