A space frame having a high torsional strength comprising a first square bipyramid and two planar structures extending outward from an apex of the first square bipyramid to form a "V" shape is disclosed. Some embodiments comprise a plurality of edge-sharing square bipyramids configured linearly, where the two planar structures contact apexes of all the square bipyramids. A plurality of bridging struts, apex struts, corner struts and optional internal bracing struts increase the strength and rigidity of the space frame. In an embodiment, the space frame supports a solar reflector, such as a parabolic solar reflector. Methods of fabricating and using the space frames are also disclosed.