3D model and faceting diagram · 49 facets · 7.71 x 7.71 mm
The radiant on a square outline: cropped corners with a brilliant facet plan beneath.
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The radiant on a square outline: cropped corners with a brilliant facet plan beneath.
More forgiving at the corners than a princess, with a similar sparkle.
Measured from the delivered model, not quoted from a standard.
The same geometry behaves differently in every material. Light that meets a pavilion facet at less than the stone's critical angle passes straight out of the back instead of reflecting, which shows face-up as a window. For each stone we measured how much of this model's pavilion, as seen face-down, is steeper than that angle, and what the model weighs at its reference size. The pavilion mains of this design sit at 34.6°. As a rule of thumb a round design needs about 43.5° in amethyst for head-on light to reflect twice before it leaves the crown, so the mains are worth steepening for diamond, moissanite, cubic zirconia, ruby, sapphire, emerald, amethyst.
| Stone | Refractive index | Critical angle | Pavilion reflecting head-on light | Weight at this size | Verdict |
|---|---|---|---|---|---|
| Diamond | 2.417 | 24.4° | 100% | 1.52 ct | Holds head-on light |
| Moissanite | 2.648 to 2.691 | 22.2° | 100% | 1.39 ct | Holds head-on light |
| Cubic Zirconia | 2.15 to 2.18 | 27.7° | 100% | 2.50 ct | Holds head-on light |
| Ruby | 1.762 to 1.770 | 34.6° | 100% | 1.73 ct | Holds head-on light |
| Sapphire | 1.762 to 1.770 | 34.6° | 100% | 1.73 ct | Holds head-on light |
| Emerald | 1.577 to 1.583 | 39.4° | 97% | 1.17 ct | Minor windowing |
| Amethyst | 1.544 to 1.553 | 40.4° | 89% | 1.14 ct | Steepen the pavilion |
Head-on light, first reflection. A full light-return census is part of the Brilliani Labs engine and will come to this page.
Six formats: STEP (the exact faceted solid for CAD), 3DM for Rhino, STL and OBJ meshes, FBX for Blender, 3ds Max, Maya, Cinema 4D, Unity and Unreal, and GLB for the web and AR. All are in millimetres at real-world scale, with 49 planar facets.
Yes. The cutting files contain a GemCad .asc design (41 + 8 girdles = 49 facets, 96 index, 4-fold symmetry), a tier table with angles, indices and cutting order in CSV, and a printable faceting diagram.
We measured the pavilion of this model against the critical angle of each stone. In Diamond, Moissanite, Cubic Zirconia, Ruby, Sapphire, the whole pavilion reflects head-on light; in Amethyst, part of the pavilion lets light out of the back, so a steeper pavilion is advised. The pavilion mains of this design sit at 34.6°. As a rule of thumb a round design needs about 43.5° in amethyst for head-on light to reflect twice before it leaves the crown, so the mains are worth steepening for diamond, moissanite, cubic zirconia, ruby, sapphire, emerald, amethyst.
We check it facet by facet against the 3D model it was written from. Every crown and pavilion facet within 0.186° of the 3D model (average 0.137°); girdle facets within 0.226°. The angles are the ones you set on the machine; the 3D model is the same stone you render or set.
The model measures 7.71 x 7.71 x 4.64 mm, which is 2.00 ct in diamond. The same size weighs 1.39 ct in moissanite, 2.50 ct in cubic zirconia, 1.73 ct in ruby, 1.73 ct in sapphire, 1.17 ct in emerald, 1.14 ct in amethyst. Scale it uniformly to any size: weight follows the cube of the size.
Yes. The mesh is watertight and manifold, with outward normals and no duplicate vertices, so it prints and casts without repair. Use the STEP file when you need the exact faceted solid in CAD.
The Radiant Square Cut as exact geometry: 49 planar facets, real-world scale, ready for CAD, rendering, printing and casting.
The Radiant Square Cut as a faceting design: 41 + 8 girdles = 49 facets, 96 index, 4-fold symmetry, ready for the machine.
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