We’ve looked at the Rhombic Dodecahedron (12 faces); now we come to a much bigger challenge, the Rhombic Triacontahedron (30 faces). We met this shape briefly under Duals of the Archimedean Solids as the dual of the icosidodecahedron, but it’s well worth another look. Not surprisingly its stellation pattern is huge and there are lots of possible stellations, but two are particularly interesting because they’re each made up from 30 diamond or rhombic faces. This means they are in their own right Rhombic Triacontahedrons, to which we assign the names Medial and Great.
We begin with the ordinary Rhombic Triacontahedron itself, the dual of the Icosidodecahedron. Now that we know there are two others, we’ll rename it the Small Rhombic Triacontahedron:
There are many many stellations of the (Small) Rhombic Triacontahedron, but as we noted there are only two more which are in themselves Rhombic Triacontahedrons: i.e. their faces are Rhombuses. They are the Medial and the Great Rhombic Triacontahedrons, and for my money they’re two of the prettiest shapes in the whole collection:
The next one to consider, of course, is the Stellation to Infinity – which is truly gorgeous – but since I haven’t made one of them yet we’ll divert back to the very first of the Catalan solids – Stellations of the Triakis Tetrahedron.