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Complex, three dimensional (3D) structures widely exist in biology (e.g. cytoskeletal webs, neural circuits, vasculature networks), where they form naturally to provide essential functions in even the most basic forms of life. Compelling opportunities exist for analogous 3D architectures in man-made devices, but their design and fabrication are constrained by existing capabilities in materials growth and assembly. Here we report deterministic routes to previously inaccessible classes of 3D architectures in advanced materials, including device-grade silicon.