The Octahedron family as a source of tensegrity families: the X-Octahedron family

Abstract

A tensegrity family is a group of tensegrity structures that share a common connectivity pattern. The three first members of the Octahedron family are the octahedron, the expanded octahedron and the double-expanded octahedron. In this work a new family is presented: the X-Octahedron family. If in the elementary rhombic cells of the Octahedron family a diagonal cable is introduced then X-rhombic cells are obtained, resulting in tensegrity forms that belongs to the new family. Three members of the family have been obtained: the X-octahedron, the X-expanded octahedron and the X-double-expanded octahedron. Several element groupings have been considered in order to find new equilibrium shapes of the members of the new family. The values of the force:length ratios which satisfy the super-stability conditions have been computed analytically.