A face vector representation for the construction of polyhedra

In this paper I will present a methodology for the stepwise construction of complex polyhedra from basic primitive polyhedra by using a vector representation as a generalization of the two-dimensional vector approach used for the construction of polygons. Starting with the concept of an atomic polyhedral cell, a voxel, I will construct configurations of polyhedra through the stepwise 'gluing' of equal and opposite faces. A vector approach for the representation of polyhedra, in which polyhedra are represented as a closed loop of polygonal faces which in turn are represented as a closed loop of edge vectors, is proposed. A rule is postulated for the joining of two polyhedra in face-to-face contact through the addition of equal and opposite faces where such faces are an extension of equal and opposite vectors. Examples of cubic constructions and octahedral-tetrahedral constructions are given.