Mainstream approaches to design spatial architectural forms that are structurally relevant consist either in adapting well-known and catalogued conventional types or in searching for close-to-optimum solutions of well-defined problems. Few means exist to explore structural forms detached from these routines. The approach in this paper generates diverse non-triangulated structural topologies that do not result from optimization procedures. The process incrementally transforms interim networks of bars and forces by means of a parametric policy (–) that maintains the static equilibrium of the network at every single step, (–) that ensures growth of the network within specified (non-)convex geometric boundaries, and (–) whose high-level abstract description controls all design parameters. The successive policy application aims at decreasing the number of interim forces while increasing the number of nodes and bars in compression or tension. The entire process ends when no interim force exists anymore, which is always achievable thanks to the permanence of the static equilibrium condition. From a designer perspective, the approach opens up the generative design black box by providing geometrical and topological control and partial automation of the generation process, while not resorting to common topology patterns – e.g. triangulated bar networks. This paper describes the conceptualization and its implementation into a computational framework, named Policy-based Exploration of Equilibrium Representations (PEER). It illustrates the potential of the approach to unveil unprecedented, unexpected, but statically-valid, structural topologies. Opportunities for further development are eventually discussed.