The present paper work was sent to Engineering Structures on 23 April 2020 (it is currently under review).A new family of tensegrity structures is presented: the Z-octahedron family. A tensegrity family is a group of tensegrity structures that share a common connectivity pattern. The members of the Z-octahedron family have been obtained replacing the elementary rhombic cells of the members of the octahedron family with elementary Z-shaped cells. In addition, a higher number of possible force density or force:length ratio values have been considered. The values of the force:length ratio of the members of the family that lead to super-stable tensegrity forms have been computed analytically. Two members of the family have been obtained: the Z-expanded octahedron and the Z-double-expanded octahedron. Finally it has been proved that the Z-double-expanded octahedron obtained here from topological rules can also be defined from a truncated cube based on purely geometrical intuition
