This paper introduces a new face-centered-cubic (fcc) photonic crystal structure that solves two major challenges in photonic band structure: achieving a full photonic band gap and enabling microfabrication on the scale of optical wavelengths. The structure is created by drilling three sets of holes at 35.26° off vertical into the top surface of a solid slab or wafer. The atoms in this structure are nonspherical, which lifts the degeneracy at the W point of the Brillouin zone and allows for a full photonic band gap rather than a pseudogap. The structure is based on the Wigner-Seitz unit cell of the fcc lattice, which is a rhombic dodecahedron. The structure is created by drilling cylindrical holes through the top three facets of the rhombic dodecahedron and exiting through the bottom three facets, resulting in atoms that are roughly cylindrical with a preferred axis in the vertical direction. The paper discusses the analogy between electron waves in a crystal and light waves in a three-dimensionally periodic dielectric structure, and the application of band theory to optical waves. It also discusses the challenges in creating a full photonic band gap and the importance of microfabrication. The paper presents experimental results showing that the structure has a 3D forbidden photonic band gap width of approximately 20% of its center frequency at a refractive index of n ~ 3.6. The structure is fabricated using reactive ion etching and can be scaled down for optical wavelengths. The paper also discusses the experimental results showing the dispersion relations for the structure, including the photonic band gap and the forbidden gaps for s and p polarizations. The paper concludes that the structure has potential applications in semiconductor physics, optical physics, and atomic physics.This paper introduces a new face-centered-cubic (fcc) photonic crystal structure that solves two major challenges in photonic band structure: achieving a full photonic band gap and enabling microfabrication on the scale of optical wavelengths. The structure is created by drilling three sets of holes at 35.26° off vertical into the top surface of a solid slab or wafer. The atoms in this structure are nonspherical, which lifts the degeneracy at the W point of the Brillouin zone and allows for a full photonic band gap rather than a pseudogap. The structure is based on the Wigner-Seitz unit cell of the fcc lattice, which is a rhombic dodecahedron. The structure is created by drilling cylindrical holes through the top three facets of the rhombic dodecahedron and exiting through the bottom three facets, resulting in atoms that are roughly cylindrical with a preferred axis in the vertical direction. The paper discusses the analogy between electron waves in a crystal and light waves in a three-dimensionally periodic dielectric structure, and the application of band theory to optical waves. It also discusses the challenges in creating a full photonic band gap and the importance of microfabrication. The paper presents experimental results showing that the structure has a 3D forbidden photonic band gap width of approximately 20% of its center frequency at a refractive index of n ~ 3.6. The structure is fabricated using reactive ion etching and can be scaled down for optical wavelengths. The paper also discusses the experimental results showing the dispersion relations for the structure, including the photonic band gap and the forbidden gaps for s and p polarizations. The paper concludes that the structure has potential applications in semiconductor physics, optical physics, and atomic physics.