Abstract: A jewel of a brilliant type cut is made with facet angles with respect to the girdle plane as follows:(1) A planar table at .phi.=0.degree. (parallel of the girdle plane);(2) a pair of angles for one or a plurality of bezel facet rings at .phi..sub.1 and a pavilion facet ring at .psi., the pair of angles being within an intransparency triangle. The intransparency triangle is defined in the Cartesian coordinate system y=.psi.=0.degree. to 90.degree. above x=.phi.=0.degree. to 90.degree. on one side by the straight line .phi.=0.degree., and on the other sides by the transcendental curves (a) .epsilon..sub.o =.phi.-.alpha.-.psi. and (b) .epsilon..sub.o =180.degree.-3.psi.-.phi.+.alpha. respectively whereby .epsilon..sub.o is the sharp boundary of total reflection;(3) another bezel facet ring at .phi..sub.2 with angles between 50.degree. and 90.degree.; and(4) the range of the pavilion facet angles .psi.=25.degree. to 51.degree..

Abstract: A mounting assembly for mounting precious stones such as gem blanks in a cutting and/or polishing machine comprising a self-clamping type chuck in an adjustable threaded engagement with a first inner detent ring provided with divisions for interstices and semi-interstices for defining a plurality of predetermined angular positions, the first detent ring being fitted into a second external detent ring likewise provided with a predetermined division and serving as a guide for the first inner detent ring. The chuck is mounted within a carrier having a bore for a shaft portion of the chuck. The angular position of the chuck is adjusted and locked by the detent ring assembly.