Platonic Body Resistance Networks

There are surprisingly few graphs which are both regular (same degree of incidence at each node) and have regular duals. Because these graphs all can be arranged to appear as regular geometric solids, they are known, specifically, as Platonic bodies. While direct application of graph theoretical methods can be used to discover all the graphs, this paper shows how topological and electrical restrictions also can be used to find the Platonic bodies through graphs of resultant resistance networks.