Opals are crystals (fcc cubic) - but not of atoms but of small amorphous quartz spheres or glass beads with diameters around 200 nm; about 100 times smaller than the diameter of a hair. If you think that's so small that it doesn't matter relative to atoms, think again. A 200 nm sphere contains very roughly 300.000.000 atoms.
The lattice constant of opals thus corresponds to the wave length of visible light and that causes its spectacular optical properties. Nowadays we call structures like that of opals "photonic crystals". Synthetically made photonic crystals caused a great stir in the scientific community in the 90ties of the old century and are still pursued for various "high-tech" optics applications.
Nowadays some of us live in a democracy, and we don't discriminate against half-breeds (of the mineral variety) anymore. We just have gemstones or jewels now, including "stones" that aren't true crystals, for example pearls or amber, rather tricky and unusual crystals like opals, or all kinds of things not found in nature but made by man (e.g. zirconia).
Here I only distinguish between crystalline and non-crystalline jewels. As far as the crystalline stones are concerned, they come in a few basic structures that we will give a first quick look.