Abstract: This paper is concerned with the design of geometric model of 58-facet brilliant gemstone and its grinding method, presents the general principle of the construction of the gemstone polyhedron, and deduces some formulae for the geometric calculation by using the separate method and the discrete method of unknowns to solve the indeterminate equation. In the end of the paper, the grinding method of gemstone polyhedron is discussed and two simple clamps are proposed.

Key words: 宝石, 几何模型, 夹具设计