Topaz has one property that governs how it can be used and one deposit that governs what the best of it looks like.
The property is perfect basal cleavage. Topaz splits cleanly along a single plane at right angles to the long axis of the crystal, and a sharp knock in the wrong direction will part a finished stone in two. Cutters orient the table slightly off the cleavage plane to reduce the risk, setters handle it carefully, and topaz is a poor choice for a ring that will be worn daily. That is a mineralogical fact with direct consequences for the objects that survive.
The deposit is Ouro Preto in Minas Gerais, Brazil, the source of the orange to reddish material sold as imperial topaz, which is the most valuable colour the species produces. The name is a trade term of the nineteenth century and is applied loosely; the atlas records it as such.
Topaz also holds a curious record. Because the mineral occurs in very large, clean, colourless crystals in pegmatites, some of the largest faceted gemstones in the world are topaz, running to thousands of carats. They are cut because the rough exists, not because anyone needed them.
Most blue topaz on the market is colourless topaz that has been irradiated and then heated. The treatment is stable, it is inexpensive, and it is the reason blue topaz went from rare to ubiquitous in the later twentieth century. Untreated natural blue topaz is pale and uncommon, and the intense blues in a shop window are not what the stone does on its own.