Three Polyhedra

Peter’s Geometry homework this week was to build a polyhedron. He got a little carried away and created this family of three. Aren’t they pretty?

The one in the front is the cuboctahedron. The one on the right is the snub cube. The one on the left is the rhombicuboctahedron. They’re an interesting set, aren’t they? They are all made of the same two types of faces. Two of them have octahedral symmetry, but the snub cube adds a twist.

You can think of the snub cube as being in between the other two if you twisted the red faces around their centers. An interesting feature of the snub cube is that there are actually two of them with opposite chirality. Think of twisting the red faces of the cuboctahedron clockwise versus counterclockwise. Both directions would end at the rhombicuboctahedron, but they would pass through two different snub cubes.

We built these using the method that George Hart calls the no-tab, taping method.