This research develops a three-dimensional extension of graphic statics, based on polyhedral form and force diagrams, for compression-only and tension-only spatial structures with externally applied loads. It illustrates and clarifies Rankine's original proposition about the equilibrium of spatial frames and Maxwell's procedures for geometrically constructing three-dimensional reciprocal diagrams in specific cases. An updated definition for polyhedral, reciprocal form and force diagrams that allows including external forces is established. The computational procedure for constructing the form diagram from a given force diagram is presented and described. With an implementation of the presented approach in a CAD environment, for example, branching structures, spatial frames, and cellular structures can be designed based on chosen force distributions.