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The octahedron family of tensegrity structures is presented in this research. The octahedron and the expanded octahedron (well-known tensegrities in the literature) are the first and second components of the family. A new tensegrity is presented: the double-expanded octahedron. This new tensegrity form was obtained following the connectivity pattern of the octahedron family presented in this work. The values of the force densities or force:length ratios that satisfy the minimum required rank deficiency of the force density matrix were computed analytically. Two types of solutions are obtained: full and folded forms. Results show that each lower member of the octahedron family is a folded form of a superior member of this family. Several examples are shown.

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