Truncate/Contract/Snub

Try to find your way to all the Archimedean and Platonic solids from the tetrahedron using just three operations:

• Truncating every vertex
• Picking a pair of face shapes and contracting every edge between those shapes down to a point
• Adding triangles between all the existing faces to make a "snub" polyhedron

This isn't the only possible set of operations that can reach all of these polyhedra, but it happens to be a set that can animate well in wireframe form with smooth transitions. (To make the maze more navigable, you can also reverse the snub operation and break the octahedron's symmetry; these aren't strictly necessary.)