Pinwheel Patterns: From 2D to 3D Schemas

Abstract

Pinwheels are generic configurations in architectural layout planning. Planar pinwheels provide familiar schemes for layouts which present design ‘in the round’ with a cyclic symmetry. The paper examines the 3-D versions of 2-D pinwheels where a ‘locked’ joint with three rectangular volume elements aligned along orthogonal axes is a characteristic feature. Pairing handed versions of these locked joints yields a candidate for a 3-D pinwheel schema with six repeated volume elements and threefold cyclic symmetry. Shape rules, based on spatial relations between volumes, generate this and other examples of 3-D pinwheel schemas. These schemas are set in a wider analysis of the numbers and types of joints in 3-rectangulations in terms of maximal bounding planes. The bounding-plane views of the arrangements is set alongside more functional volume descriptions which enables the elements and relations in architectural form to be (re)generated and (re)interpreted both ‘in view’ and ‘in use’.