On counting architectural plans

Abstract. This paper demonstrates the one-to-one correspondence between trivalent 3-polytopes and fundamental architectural schemes. Enumeration results from the literature of combinatorics are given and are related to the problem of counting various classes of architectural plans and their adjacency structures. This work is related to recent architectural research by other authors: Mitchell et al (1976), Korf (1977), and Lynes (1977). The foundations are laid for a mathematical theory of architectural planning.