Enumerating the Configurations in the n-Dimensional Orthogonal Polytopes Through Pólya's Countings and A Concise Representation

This article will describe Polya's countings as a methodology for determining the number of configurations to be present in the nD orthogonal pseudo-polytopes. Banks et al have used this methodology for counting configurations, in 1D to 4D spaces, under the context of the dual problem. We will describe a concise and simple representation for the configurations that provides the elements to reach the 5D and 6D cases and therefore to obtain their corresponding countings