The Correspondence Between Convex Polydedra and Tensegrity Systems: A Classification System

Abstract

Since tensegrity systems are often topologically and geometrically complex it is important to have a simple and effective method to describe and classify them in an orderly manner. This paper sets forth a system of relating any convex polyhedron to a tensegrity by defining a one-to-one correspondence between the elements of the polyhedron and the elements of the tensegrity.

This system, which was first introduced by the author in a 1978 booklet while working in Buckminster Fuller's Philadelphia office, is now extended to include agglomerations of convex polyhedra — both regular and irregular space-filling arrays.

In both the original system and its extension, the principle of geometric duality is clearly demonstrated. More importantly for engineers, the method will allow those familiar with space structures an easy and convenient way to relate any space frame or truss to a corresponding tensegrity structure.