When we looked at Compounds we saw how the Platonic Solids fall nicely into pairs of Duals: every vertex in one matches a face in the other, and every face matches a vertex. This gives us pretty compounds like a Cube and Octahedron, a Dodecahedron and Icosahedron, and the Stella Octangula:
The later polyhedra we looked at all have duals too, where faces map to vertices and vertices to faces: but these duals are rather different shapes. They’re not regular polyhedra, but they do form an amazinf array of shapes with a fascination all of their own.
Our first stop is to look at the Duals of the Archimedean Solids: the Catalan Solids.