Abstract: A space frame constructed from a plurality of identical struts using octahedron/tetrahedron ("octet") geometry wherein the struts, instead of being simple tubular members, are fabricated as space frame masts using octet geometry. A second aspect of the invention concerns a connector piece for orienting and joining the ends of struts to form octet structures. In one embodiment, the connector piece is in the shape of two interpenetrating tetrahedrons, allowing assembly and disassembly of individual struts without disturbing other struts. Retaining means are described which do not require tools for assembly.