Potentials for multi-dimensional tessellations in architectural applications

Abstract

Computationally, there exist significant potentials to integrate periodic (repeating ) and aperiodic (non-repeating) tessellations in architectural applications. While exploration of two-dimensional and three-dimensional tessellations appear in historically significant works, today, higher-dimensional tessellations are capable of being generated computationally which may be useful in various architectural applications. This paper, a collaboration between an architect and mathematician, explores these processes and potentials. Insights will be offered in to this early stage exploration regarding the creation and use of higher-dimensional geometries for architectural applications-such as patterning, volumetric descriptions, and modular assemblages.