The only cut in the registry that gives up nothing to the 1919 ideal on any of the eight axes.
Global score against T57, Tolkowsky’s 1919 ideal, measured the same way in the same material.
Diamondn = 2.417+3.97Ahead
Moissaniten = 2.65+0.89Ahead
Cubic zirconian = 2.16+3.28Ahead
−6T57 = 0+6
The short version
Rafaello is cut to survive movement. It holds 96.9 under a 20° tilt in diamond and 97.8 in moissanite, the two highest tilt figures in the registry, which in absolute terms is 91.0% of its light still returned at 20° against the standard’s 83.4%, and tilt is worth +1.04 of its diamond margin, more than any other cut earns from that term.
It is also the only cut here with no deficit on any of the eight axes: six clear wins, symmetry level at the 100 ceiling, and spread level within a tenth of a point. In cubic zirconia it returns 99.7% of light usefully and loses 0.13%, the best pair of numbers in the whole registry. Its weakness is moissanite, where it leaks 12.46%.
The ledger
Where the points come from
Global is a weighted sum of six terms. Subtract the standard's figure from this cut's,
term by term, and the six differences add back up to the published gap. Nothing is hidden in the total,
so you can see exactly which part of the stone is doing the work.
In diamond n = 2.417
Ahead
92.57 against the standard's 88.61. Scintillation +2.42, then tilt at +1.04, the biggest tilt contribution in the registry. Brilliance and fire add +0.82 between them; leak hands −0.31 back.
TermThis cut / standardPoints
Brillianceweight 0.3493.992.3+0.54
Fireweight 0.2080.278.8+0.28
Tiltweight 0.1696.990.4+1.04
Scintillationweight 0.1096.071.8+2.42
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓4.941.88−0.31
Sum of the six terms+3.98
Published Global gap +3.97. The six terms reconstruct it to
0.01 of a point. The difference is rounding in the source figures, not a second method.
In moissanite n = 2.65
Ahead
90.71 against the standard's 89.82, the thinnest margin this cut posts. Scintillation's +2.42 is very nearly cancelled: fire −1.44, leak −0.47 at 12.46%, and brilliance falling to 84.2.
TermThis cut / standardPoints
Brillianceweight 0.3484.285.3−0.37
Fireweight 0.2090.397.5−1.44
Tiltweight 0.1697.893.2+0.74
Scintillationweight 0.1096.071.8+2.42
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓12.467.76−0.47
Sum of the six terms+0.87
Published Global gap +0.89. The six terms reconstruct it to
0.02 of a point. The difference is rounding in the source figures, not a second method.
In cubic zirconia n = 2.16
Ahead
95.05 against the standard's 91.77. 99.7% of light returned usefully and 0.13% lost, the best pair of numbers in the registry, with scintillation adding +2.42 on top.
TermThis cut / standardPoints
Brillianceweight 0.3499.798.0+0.58
Fireweight 0.2087.186.8+0.06
Tiltweight 0.1688.287.1+0.18
Scintillationweight 0.1096.071.8+2.42
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓0.130.51+0.04
Sum of the six terms+3.27
Published Global gap +3.28. The six terms reconstruct it to
0.01 of a point. The difference is rounding in the source figures, not a second method.
Against the control
How much of this is facet count
Global gives scintillation a tenth of its weight, and scintillation is a closed formula on facet count rather than a ray measurement. T57 carries 57 facets, fewer than anything else published here, so any finely cut stone banks that term before a single ray is traced. Take it out and Rafaello’s real claim turns out not to be the one the pavilion angle suggests.
The facet-count term
Of the +3.97 diamond margin, +2.42 is scintillation, a formula on 145 facets rather than a measurement. The optical margin, the part traced ray by ray, is +1.55.
Against BL-Vitruvio
Vitruvio carries Tolkowsky’s own angles at 185 facets, so it is the fair control for a finely cut modern stone. Rafaello finishes +0.92 above it on Global and +1.17 on the optical terms alone.
What the angles buy
Put Rafaello’s angles on a plain 57-facet pavilion, crown 32.5°, pavilion 41.5°, table 57.4%, and fire rises 5.5 points over the standard, but tilt falls 4.3 and leak rises 1.7. The angles are a fire recipe, and on their own they cost stability rather than buying it.
What the tiling buys
The 145-facet pavilion reverses that: tilt +10.8, brilliance +1.7, fire −4.2. Stability is the tiling, not the steeper pavilion, and the two halves of the cut pull against each other. What comes out is the steadiest stone here: 91.0% of its light still returned at 20° against the standard’s 83.4%.
Where it departs from 1919
It keeps his pavilion and rewrites his crown
Rafaello’s pavilion sits at 41.49°, three quarters of a degree off Tolkowsky’s. That is not a departure from his rule but from his facet count: sweep the pavilion on a 145-facet architecture and the plateau moves from 40.00°–40.75° to 41.00°–41.50°. Rafaello is sitting on its own. Its crown, at 32.47°, is two degrees off his, and that is the real departure.
Pavilion: +0.74°
On the plateau its own pavilion produces. The optimum is a property of the material and the layout: hold the index at 2.417 and take the pavilion from 57 facets to 145, and the best angle moves a full degree.
Crown: −2.04°
Re-aiming the crown to his 34.5° costs 2.14 of Global, twice what the pavilion is worth.
What the angles bought
Against the same 145-facet pavilion carrying 1919 angles: fire +5.4, and almost nothing given up, brilliance −0.3 and tilt +0.7. On a plain 57-facet pavilion those same angles would cost 4.3 of tilt. They do not cost it here, and that difference is the tiling.
Why that is allowed
The pavilion is pinned by the critical angle: on this engine Global holds its value across only 0.75° of pavilion, 40.00° to 40.75°. The crown holds across 2.5°, 33.0° to 35.5°. Tolkowsky derived the first rigorously from the refractive index and the second loosely from appearance. This cut leaves the pinned one alone and moves the loose one.
What it’s doing
A ring spends very little of its life dead-on to the eye. Rafaello is cut for the other angles: 6.5 points of tilt performance over the standard, worth +1.04, the largest tilt contribution anywhere in the registry and more than brilliance (+0.54) and fire (+0.28) manage together.
It is also the only cut here that gives up nothing on any of the eight axes. Six clear wins, symmetry level at the 100 ceiling, and spread level within a tenth of a point. It gives some tilt gain back in leak, 4.94% against 1.88%, at a cost of −0.31. The net is a stone that changes less than the standard does when the hand turns, which is the condition closest to how jewellery is actually seen.
Where it gives ground
Moissanite, and plainly. It leaks 12.46% there, the worst figure in the registry in any material, and its fire falls to 90.3 against 97.5, worth −1.44. Add a brilliance deficit and its scintillation advantage is very nearly cancelled: +0.89 is the thinnest margin this cut posts.
The tilt advantage survives at 97.8, still the best in the registry. It cannot cover a light budget that poor. Cut this one in diamond or cubic zirconia.
How to read this
The protocol
Monte-Carlo ray census on exact facet geometry: 3,200 rays face-up plus 2,200 at
20° tilt, cosine-weighted from a 7° near-vertical cone. Every cut is scored against Tolkowsky's 1919 ideal,
measured the same way in the same material.
These are engine estimates, ± 2 points, not lab-certified grades.
A lead of under half a point sits inside the engine's resolution, so we don't claim it as a win. A deficit is reported as a deficit, however small.
Scintillation
The one term that is not ray-traced. It is a closed formula on the cut’s active facet count, 100(1 − e−n/45), at a tenth of the weight. Planes buried inside the solid form no facet and are not counted. The standard has 57 facets, fewer than anything else here, so every finely cut stone banks this term before a ray is traced. Each cut page reports its margin with the term removed.
Tilt
A retention figure, the share of face-up return the cut still delivers at 20°, capped at 100. It is a ratio, so read it beside the absolute return rather than on its own: a dim cut has less to lose and keeps a higher share of it.
Symmetry
Reads 100 for every cut, because each is modelled from exact geometry rather than
a finished stone. It contributes nothing to any comparison here: it cancels, and we show the row anyway.