The octahedron family: a source of tensegrity structures

A tensegrity family is a group of tensegrity structures that share a common connectivity pattern. In the case that just two values of the force density or force:length ratio are adopted (one for cables and another for struts), the members of the octahedron family are: the octahedron, the expanded octahedron and the double-expanded octahedron. In this work a higher number of possible force:length ratio values have been considered in order to find new members of the family. The values of the force:length ratios which satisfy the super-stability conditions have been computed analytically. New super-stable tensegrity forms of the octahedron family have been obtained. Results show that all of them are members of the octahedron family having as folded forms all the lower members of the family. Finally, based on topological rules, it has been proved that the double-expanded octahedron can be defined from a truncated cube