Analytical definitions of connectivity, incidence and node matrices for t-struts tensegrity prisms

Abstract

Regular tensegrity prism modules are widely used by researchers. Numerous research articles combine them to form grids and towers under various assembly strategies. Most of them define connectivity and node matrices that satisfy their structures as a whole, but a general definition for the basic modules has not been formally reported. This paper formalizes sets of definitions for the connectivity, incidence, and node matrices that are valid for any tensegrity prism formed by four struts or more. The definitions are based on geometry and provide simple and general formulations by applying floor and ceiling operators. Both clockwise and counterclockwise rotated modules are covered.