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Stones are hard to tell in pictures, of course, but off the cuff, I'd say the carbuncle is either Sard or Coral. Sard is mined in the Middle East, while coral would be widely available in the far east. Also in favor of coral is that it is commonly shaped into carbuncles, while Sard, being harder, is often used to make carved gemstones (with raised figures and designs on them).That mirror is just beautiful!