The 24-Cell and its Snub

There appear to be three "natural" Zome models of the 24-cell. One is merely a rhombic dodecahedron with a few more blue and yellow edges thrown in. Another is closely related to the Zome model of the 600-cell. If you can, notice the presence of "false" vertices in the second model. The third model uses green lines, which I did not own at the time of these photos:

One may "snub" the 24-cell in a way similar to the way one constructs the snub cube or snub dodecahedron. One replaces each of the 24 octahedra with a regular icosahedron, and replaces each of the 24 vertices with a particular configuration of 5 tetrahedra. Each of these configurations is "tree-like" because one of these tetrahedra is surrounded by the remaining 4. In group-theoretic language, this means that there are two distinct orbits of tetrahedra under the symmetry group of this polytope. Remarkably, the resulting polytope is uniform:

This model is obtained from the Zome model of the 600-cell merely by omitting some particular balls and struts.

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