A monohedron is a convex polyhedron with all faces mutually congruent but with no other symmetry necessarily needed. So obviously, this is a wide class of polyhedra that includes the Platonic solids and isohedra. An earlier post is What are the known convex polyhedra with congruent faces?

**Questions:** Are there monohedroa with odd numbers of faces (it is known that isohedra necessarily have even numbers of faces — as stated in the MathWorld article Isohedron)? What are the values for the number of edges on a face for which monohedrons are possible? Will relaxing convexity (of the body, not of the faces) have an impact on the answers to these questions?