There are two strategies for opening up the complete photonic band gap. The first one is to increase the refractive index contrast for the band gap in each direction becomes wider and the second one is to make the Brillouin zone more similar to sphere. However, the former is limited by the available technologies and materials and the latter is restricted by the crystallographic restriction theorem. For this reason, the photonic crystals with a complete band gap demonstrated to date have face-centered cubic lattice with the most spherical Brillouin zone and made of high-refractive-index semiconductor materials. Another approach is to exploit quasicrystalline structures with no crystallography limits. A complete photonic bandgap was reported for low-index polymer quasicrystalline samples manufactured by 3D printing.