Results are given from a search to form adinkra-like equations based on topologies that are not hypercubes. An alternate class of zonohedra topologies are used to construct adinkra-like graphs. In particular, the rhombic dodecahedron and rhombic icosahedron are studied in detail. Using these topological skeletons, equations similar to those of a supersymmetric system are found. But these fail to have the interpretation of an off-shell supersymmetric system of equations.