Incidence and Symmetry in Design and Architecture
by Jenny A. Baglivo and Jack E. Graver
Cambridge Urban & Architectural Studies, Volume 7, published 1983,
reissued 2010; detailed information available here
The primary purpose of Incidence and Symmetry in Design and Architecture is to develop mathematical topics relevant to the study of the incidence and symmetry structures of geometrical objects. A secondary purpose is to expand the reader’s geometrical intuition. The two fundamental mathematical topics employed in this endeavor are graph theory, and the theory of transformation groups.
Part I, Incidence, starts with two chapters on the basics of graph theory. Chapter 3 contains a variety of specific applications of graph theory: routing a power line; measuring the “compactness” of an architectural arrangement; minimally bracing a rectangular grid; and classifying architectural plans. In Chapter 4, the text becomes more theoretical; here graph theory is used to study surfaces other than the plane and sphere.
Part II, Symmetry, starts with a chapter on rigid motions or symmetries of the plane. This is followed by a chapter devoted entirely to the classification of planar patterns. Chapter 7 contains an overview of symmetry in 3-dimensional space. Graph theory and group theory come together in the last chapter in a study of enumeration problems in geometry.
Additional information: The book was developed from teaching materials for a core mathematics course for students in the School of Architecture at Syracuse University, Syracuse, New York. The book received the 1983 Alpha Sigma Nu National Jesuit Book Award in Science, awarded by the Association of Jesuit Colleges and Universities.