Periodic layer‐by‐layer dielectric structures with full three‐dimensional photonic band gaps have been designed and fabricated. In contrast to previous layer‐by‐layer structures the rods in each successive layer are at an angle of 70.5° to each other, achieved by etching both sides of a silicon wafer. Photonic band‐structure calculations are utilized to optimize the photonic band gap by varying the structural geometry. The structure has been fabricated by double etching Si wafers producing millimeter wavephotonic band gaps between 300 and 500 GHz, in excellent agreement with band calculations. Overetching this structure produces a multiply connected geometry and increases both the size and frequency of the photonic band gap, in very good agreement with experimental measurements. This new robust double‐etched structure doubles the frequency possible from a single Si wafer, and can be scaled to produced band gaps at higher frequencies. © 1996 American Institute of Physics