This paper addresses the potential utility of tensegrity structures for use in large area-spanning shape-changing space “platforms.” Among many potential platforms, this paper addresses parabolic, RF mesh reflectors. Cylindrical tensegrities are arranged adjacently to construct a planar 2-D platform. Different arrangements and configurations using cylindrical triplex and quadruplex tensegrity units are considered, both for their ability to grid together effectively, as well as for their ability to assume shapes adjacent to the initial 2-D configuration. Since the large-scale structures of interest will not be launched as a single payload, tensegrity modules are identified and explored with a view toward initial deployment followed by in-space assembly. Methods are developed to assess the surface geometry of a tensegrity-based reflector relative to that of a prescribed paraboloid. A six-unit triplex module offers ease of assembly, effective hexagonal surface gridding, and the ability to achieve prescribed surface shapes accurately. A four-unit quadruplex module offers similarly promising prospects for efficient assembly, gridding and shape change. The results indicate promise for the continued development of a lightweight, efficient, stiff module which can be assembled in space to construct shape-changing platforms.