Experienced gemcutters, or lapidaries, know how to get the most from an uncut gem. The perfect shape and the number and size of the facets all contribute to the price of the finished stone. In the cutting and polishing processes, however, between 66 and 70 per cent of the raw gem is lost, leaving less than one-third for the finished product.To increase the percentage left behind, scientists at Fraunhofer Institute for Industrial Mathemat-ics (ITWM) have created a fully automated grinding machine that uses a moiré projection system from Breuckmann GmbH of Meersburg to map the surface of the stone. The system employs mathematical optimization to determine the style and size of the finished product. The algorithms guide a computer numerical control grinding machine with 17 axes, ensuring that any desired angle can be accessed.The computer system uses the uncut stone’s measurements to determine which cut will use the most of its volume. Courtesy of Fraunhofer ITWM.The system currently is being used by Paul Wild GmbH of Kirschweiler. It takes an average of 20 min to cut the gem — with less time given to polishing — and uses an average of 15 per cent more of the original stone’s volume than a lapidary would. In addition, the machine is more accurate, with the facets being within 10 μm of perfection, while hand-polishing techniques result in an accuracy of ∼100 μm.