Catalog

3D models and cutting files by gemstone

Seven stones · 37 cuts scored in each

Why the stone changes the cut

A faceting design is a set of angles, and the right angles depend on the material. When the refractive index of a stone is lower, its critical angle is larger. Then its pavilion must be steeper to keep light inside. A pavilion that is perfect in diamond can make an amethyst look washed out in the center. Each page below gives the numbers for one stone. It also ranks the top ten brilliants and the top ten jewelry cuts in that stone, by brilliance, fire and scintillation.

Why the stone changes the cutSeven stones side by side, diamond to amethyst. Each has one pavilion facet at its guide pavilion angle, head-on light that comes straight down onto it, and a gray wedge around the facet normal: light inside the wedge leaves the stone. The wedge gets wider as the refractive index drops: 24.4, 22.2, 27.7, 34.6, 34.6, 39.4, 40.4 degrees. In emerald and amethyst the light runs along the edge of the wedge, so their guide pavilion is the critical angle itself.Diamond24.4°38.9°Moissanite22.2°39.5°CubicZirconia27.7°38.1°Ruby34.6°36.4°Sapphire34.6°36.4°Emerald39.4°39.4°Amethyst40.4°40.4°Critical angleGuide pavilionDiamond to sapphire: the exit through the table sets the guide.
Why the stone changes the cutSeven stones side by side, diamond to amethyst. Each has one pavilion facet at its guide pavilion angle, head-on light that comes straight down onto it, and a gray wedge around the facet normal: light inside the wedge leaves the stone. The wedge gets wider as the refractive index drops: 24.4, 22.2, 27.7, 34.6, 34.6, 39.4, 40.4 degrees. In emerald and amethyst the light runs along the edge of the wedge, so their guide pavilion is the critical angle itself.DiamondCritical angle 24.4°Guide pavilion 38.9°MoissaniteCritical angle 22.2°Guide pavilion 39.5°Cubic ZirconiaCritical angle 27.7°Guide pavilion 38.1°RubyCritical angle 34.6°Guide pavilion 36.4°SapphireCritical angle 34.6°Guide pavilion 36.4°EmeraldCritical angle 39.4°Guide pavilion 39.4°AmethystCritical angle 40.4°Guide pavilion 40.4°Diamond to sapphire: the exit through the table sets the guide.
Head-on light (the arrow) reflects only outside the gray wedge, and the wedge gets wider as the refractive index drops.

One cut does not fit every stone

The clearest way to see it is with two rounds that look almost the same on paper. The T73 has the round brilliant proportions published in 1919, calculated for diamond. DG-Anteros keeps the same 73 facets and the same 53% table. But its crown and pavilion angles are re-solved for moissanite, which bends light more strongly. Put each cut in each stone and look.

DiamondRI 2.417
MoissaniteRI 2.648
T73
T73 in diamond: face-up Light Return map
T73 in diamond through a Hearts and Arrows viewer, face-up: the arrowsArrows, face-up T73 in diamond through a Hearts and Arrows viewer, face-down: the heartsHearts, face-down
T73 in diamond. Crisp arrows and crisp hearts: the proportions were worked out for diamond.
T73 in moissanite: face-up Light Return map
T73 in moissanite through a Hearts and Arrows viewer, face-up: the arrowsArrows, face-up T73 in moissanite through a Hearts and Arrows viewer, face-down: the heartsHearts, face-down
T73 in moissanite. Both patterns break up. The same angles bend moissanite's light too far.
DG-Anteros
DG-Anteros in diamond: face-up Light Return map
DG-Anteros in diamond through a Hearts and Arrows viewer, face-up: the arrowsArrows, face-up DG-Anteros in diamond through a Hearts and Arrows viewer, face-down: the heartsHearts, face-down
DG-Anteros in diamond. The arrows go dark and the hearts flood with white: wrong stone for this cut.
DG-Anteros in moissanite: face-up Light Return map
DG-Anteros in moissanite through a Hearts and Arrows viewer, face-up: the arrowsArrows, face-up DG-Anteros in moissanite through a Hearts and Arrows viewer, face-down: the heartsHearts, face-down
DG-Anteros in moissanite. Crisp arrows and eight clean hearts: the cut it was drawn for.

Direct Indirect Contrast Leak. Face-up, the way a light-return scope shows a stone.

White: light from the viewer's white disk, which draws the arrows and hearts. Red: light from the red reflector. Black: the lens port, or light that never comes back.

We compute all eight panels per instrument from the cut files themselves, with the same rules for every stone. The Hearts & Arrows viewer has a 2.5° lens hole, a white disk to 13.5° and a red reflector to 90°.