Cubic Symmetry of Platonic Solids

The Platonic Solids are to 3D what regular polygons are to 2D. They are made of identical, regular faces arranged with identical angles. Despite millions of possible regular polygons, there are only 5 Platonic solids: tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Anyone who has used polyhedral dice has seen these shapes!

In a fascinating turn, all five have cubic symmetry. This turns up strangely in minerology, where you can get wildly different forms within a single mineral species. Two of the five also have golden ratio symmetry. I put together these models to showcase these unexpected symmetries. Each of the four non-cube models is inscribed within a cube, and are symmetric in any orientation.

They require support, but are generally easy to clean up if you take your time. The face bars on the icosahedron are slightly delicate, so be cautious removing the support from behind them. 

Enjoy!