Resistor Networks based on Symmetrical Polytopes

This paper shows how a method developed by Van Steenwijk can be generalized to calculate theresistance between any two vertices of a symmetrical polytope all of whose edges are identicalresistors. The method is applied to a number of structures that have not been considered earliersuch as the Archimedean polyhedra and their duals in three dimensions, the regular polytopes infour dimensions and the hypercube in any number of dimensions.