Abstract: A tensegrity structure is formed from a plurality of interconnected tensegrity modules. Each module includes several column-like compression members and tension elements run between ends of the compression members to define a polyhedron. The tension elements form the edges of the polyhedron and intersect at the vertices of the polyhedron. The interconnected modules are joined to each other with triangular faces abutting but with the edges and faces of the abutting triangular surfaces of the respective modules rotated 180.degree. away from superposition and with the vertices joined to tension element edges, being joined at a point located one-half or one-third of the way along the length of such edge.