The 1919 angles at 185 facets, and the cleanest demonstration in the registry of what facet count alone is worth.
Global score against T57, Tolkowsky’s 1919 ideal, measured the same way in the same material.
Diamondn = 2.417+3.04Ahead
Moissaniten = 2.65+3.04Ahead
Cubic zirconian = 2.16+2.82Ahead
−6T57 = 0+6
The short version
BL-Vitruvio is Marcel Tolkowsky’s 1919 proportions modelled at 185 facets rather than the 57 he specified. Same table, same crown, same pavilion. Only the facet pattern changes.
That makes it the control for the whole registry. It finishes 3.04 points above the standard in diamond, and 2.66 of those points, 87% of the margin, is scintillation. Everything else nets to +0.38. If you want to know what a facet count is worth on this scale and what it is not, this is the row to read.
The full account of what Tolkowsky calculated, and what each cut in the T-series changes about it, is on the 1919 ideal.
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
91.65 against the standard's 88.61. Of the +3.04, scintillation is +2.66. Brilliance moves +0.10, fire −0.02, tilt +0.34 and leak −0.03. The optics are the same stone; the sparkle density is not.
TermThis cut / standardPoints
Brillianceweight 0.3492.692.3+0.10
Fireweight 0.2078.778.8−0.02
Tiltweight 0.1692.590.4+0.34
Scintillationweight 0.1098.471.8+2.66
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓2.171.88−0.03
Sum of the six terms+3.05
Published Global gap +3.04. 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
92.86 against the standard's 89.82, an identical +3.04 at a different index, and again +2.66 of it is scintillation. Leak nearly matches the standard's at 7.46% against 7.76%.
TermThis cut / standardPoints
Brillianceweight 0.3486.185.3+0.27
Fireweight 0.2097.297.5−0.06
Tiltweight 0.1694.093.2+0.13
Scintillationweight 0.1098.471.8+2.66
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓7.467.76+0.03
Sum of the six terms+3.03
Published Global gap +3.04. The six terms reconstruct it to
0.01 of a point. The difference is rounding in the source figures, not a second method.
In cubic zirconia n = 2.16
Ahead
94.59 against the standard's 91.77. The pattern holds a third time: +2.66 of the +2.82 is scintillation, and tilt lands level to the decimal.
TermThis cut / standardPoints
Brillianceweight 0.3498.498.0+0.14
Fireweight 0.2087.086.8+0.04
Tiltweight 0.1687.187.1+0.00
Scintillationweight 0.1098.471.8+2.66
Symmetryweight 0.10100.0100.0+0.00
Leakweight 0.10 ↓0.580.51−0.01
Sum of the six terms+2.83
Published Global gap +2.82. 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
This page is the control the rest of the registry is measured against. Tolkowsky’s 1919 angles, cut as fine as the series goes, so whatever Vitruvio gains over T57 is what facet count alone is worth. That makes it the most useful cut here and the least impressive one.
The facet-count term
Of the +3.04 diamond margin, +2.66 is scintillation, a formula on 185 facets rather than a measurement. The optical margin, the part traced ray by ray, is +0.38.
The optics barely move
Brilliance +0.29 and fire −0.11 against the standard, both inside the engine’s resolution and neither claimable as a win. Tilt gains 2.1. On the terms that are actually traced, this is the 1919 stone.
Where the extra facets are
The 128 planes Vitruvio adds to T57 are a girdle band: a 2.7% girdle rendered as vertical facets carrying 2% of the surface. Crown and pavilion are inclination-identical to the 1919 stone. Nothing was steepened, nothing was re-aimed.
Why that is worth publishing
Because it sets the price of the facet-count term. Read BL-Miliano, BL-Rafaello and BL-Girandola against this page rather than against a 57-facet stone from 1919, and what is left is the part that was designed.
Where it departs from 1919
It does not
Vitruvio’s pavilion measures 40.74° against Tolkowsky’s 40.75°, and its crown 34.47° against his 34.51°. Within the resolution of the measurement, this is his stone at 185 facets.
Pavilion −0.01°, crown −0.04°
No angle was re-aimed. The facet families are inclination-identical to the 1919 stone, and the extra planes are a girdle band.
Which is exactly the point
Because it holds his angles, everything it gains over T57 prices the facet-count term, and everything the house cuts gain over it is the part that was designed. Those three stay within three quarters of a degree of his pavilion and depart on his crown by up to three degrees.
What it’s doing
The registry carries the same 1919 design three times: at 57 facets with the girdle left as a knife edge, at 73 with the girdle faceted, and at 185. Across those three the optical terms barely move: brilliance travels 0.6 points, fire 0.5, leak 0.3. Scintillation travels 26.6, from 71.8 to 98.4.
Of the 3.04-point gap between the standard and this stone, 2.66 points, 87% of it, is the scintillation term alone. Everything else nets to +0.38. This row is the price list for facet count, and every other margin in the registry should be read against it.
Where it gives ground
It is a diamond solution, and it shows outside diamond. At n = 2.65 the same pavilion leaks 7.46% and brilliance falls to 86.1, which is why BL-M5, drawn for that index, finishes 2.27 points above it there.
Tolkowsky solved for the material in front of him in 1919. Moissanite did not reach the jewellery trade until the late 1990s.
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.