We have designed, fabricated, and tested a three-dimensional photonic-band-gap structure. The structure is built by an orderly stacking of dielectric rods. A network analyzer is used to measure the transmission and dispersion relations of electromagnetic waves along several crystal directions. The experimental results are in good agreement with the theoretical calculations. The structure is different from that previously suggested, as it is already used to improve the midgap frequency by almost two orders of magnitude, and it offers a viable geometry to extend the photonic band gap to optical regimes.