Thinking through the shapes with all of the math working precisely, enters Kirby Urner, holding a diagram of the geometry, no, wait, an animated gif pushing the power of visualization.

Here we have a Cuboctahedron dual Rhombic Dodecahedron…
6-square-8 triangular-14-in-all-Cuboctahedron-dual-Rhombic-Dodecahedron-Yellow-and-Blue-respectively!

This is not only for geometry buffs. There are practical applications.