Resistor Networks based on Symmetrical Polytopes

Jeremy Moody, P.K. Aravind
2015 Electronic Journal of Graph Theory and Applications  
This paper shows how a method developed by Van Steenwijk can be generalized to calculate the resistance between any two vertices of a symmetrical polytope all of whose edges are identical resistors. The method is applied to a number of structures that have not been considered earlier such as the Archimedean polyhedra and their duals in three dimensions, the regular polytopes in four dimensions and the hypercube in any number of dimensions.
doi:10.5614/ejgta.2015.3.1.7 fatcat:cfupmgwjznh7djb4vhvxpn3ika