A non-planar surface support structure that is compatible with deployable thin shell reflector segments. The structure is composed of multiple four strut closed loops connected to compliant hinges at the nodes to create an effective surface. The deployed surface shape is determined by the strut lengths (L) and the node locations and the packaged compatibility constraint in which L1+L3−L2−L4 approximately equals zero. Each of the compliant hinges have degrees of freedom such that the compact configuration of the support structure is obtained by the translation of two opposite nodes of each loop upwards and the remaining two nodes downwards in a continuous process until all struts are approximately parallel and tightly bundled and the hinges lock out all degrees of freedom in the deployed configuration.