Mathematical tools for speeding up the determination of configurations of the n-dimensional orthogonal pseudo-polytopes

This article introduces some tools that could support us in the task of obtaining in a more direct way the configurations that can represent the n-dimensional orthogonal pseudo-polytopes. In order to speed up the determination of the topological equivalence between a pair of configurations, we describe a relation whose implementation compares any two configurations in a time which only depends of the number of hyper-octants in the space in which their hyper-boxes are embedded. We show that our relation is in fact an equivalence relation which is "wider" than equivalence relations based in geometrical transformations and therefore it provides an approximate solution to our problem.