1. Introduction. Let P be a polyhedron (i.e., a 3-dimensional polytope). A path in P is defined as a sequence of edges (x1, x2), …, (xi−1, xi), (xi, xi−1), …, (xn−1, xn) where (xi, xi+1) denotes the edge with endpoints Xi and Xi+1. Define the length |A| of a path A to be the number of edges of said path. The distance between any two vertices x and y of P is defined to be the least length of all paths of P between x and y. For the purposes of this paper, if x and y lie on a particular path A, the distance between x and y along A will be defined to be the length of the segment of A between x and y. The radius of P is defined to be the smallest integer r for which there exists a vertex v of P such that the distance from v to any other vertex of P is at most r.