Is there a characterization of all Moore (?) state machines that can be implemented in the following fashion: Given a convex polyhedron P; it is "in the state" represented by the letter "A" iff the polyhedron is sitting stably (under normal gravity) on a face labeled with "A". The polyhedron switches state by rotating on the edge bounding the "A" face and the "B" face until it now sits on the "B" face. The label on the edge between the "A" face and the "B" face is associated with the "input" -- e.g., it might be input "b". Note that we might have to have several different faces labeled "A" in order to provide enough flexibility for a wider range of possible state machines. We can also have several different edges labeled "b". Clearly, we can "unroll" this polyhedron into an infinite 2-D network with the face labels and edge labels intact. So I guess I'm asking whether we could unroll any Moore state machine into a similar infinite network, and then re-roll it back into the form of a polyhedron.