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 polyhedrons that includes the Platonic solids and isohedra (https://mathworld.wolfram.com/Isohedron.html). An earlier post is https://math.stackexchange.com/questions/3888486/what-are-the-known-convex-polyhedra-with-congruent-faces

**Questions:** Are there monohedrons with odd number of faces (it is known that isohedrons necessarily have even number of faces - as stated in https://mathworld.wolfram.com/Isohedron.html)? 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?