Here’s a rhombic triacontahedron, possibly the most well-known of the Catalan solids. It’s thirty faces are all golden rhombi (rhombi with their diagonals in the golden ratio).

Here’s what you get if you augment each face with another rhombic triacontahedron:

Coloring this cluster-polyhedron by face type has this result:

So what happens if each face of this cluster-polyhedron is augmented by another rhombic triacontahedron? This does:

Here’s another view of that, in “rainbow color mode”:

I made these virtual models with Stella 4d: Polyhedron Navigator. If you’d like to try this software for free, the website to visit is http://www.software3d.com/Stella.php.