Radiant Square Cut Pyrope: what our light census measures
Brilliance 75 · Fire 32 · Scintillation 66 · in our census, where the T73 scores 94 · 50 · 80 in pyrope
How the Radiant Square Cut handles light in pyrope, measured: brilliance 75, fire 32 and 21% leakage, set against the T73 in the same stone and against the same cut in diamond.
Light Return map of the Radiant Square Cut in pyrope, face-up, from our own tracer at refractive index 1.73. Red, green and blue return light to the eye; gray leaks.
Radiant Square Cut Pyrope
Pyrope has a refractive index of 1.730 to 1.766 and a dispersion of 0.022. Its critical angle, from the low end of that range, is 35.3°, so a round design needs a pavilion of at least 36.2° for head-on light to reflect off both sides of the pavilion and leave through the table. We trace it with one index, 1.748, the midpoint of the published range, and a fire spread of 0.019, 0.86 of the published dispersion. Every picture here is our Light Return tracer at 1.730, and every figure is from the same light census that scores the other gemstones; the 3D Gemstone Simulator shows the Radiant Square Cut in pyrope live.
The Radiant Square Cut has 49 facets and a total depth of 72.8% of its width; its pavilion mains sit at 34.6°. In pyrope, the census returns 75 of 100 for brilliance and 32 for fire, against 94 and 50 for the T73, our benchmark, in the same stone; the same Radiant Square Cut in diamond reads 72 and 62.
Is pyrope good in a Radiant Square? Pros and cons, measured
Compared with the T73 Round Brilliant in pyrope and with the Radiant Square Cut in diamond.
A difference counts from 3 points (Brilliance, Fire, Tilt, Leakage), 5 (Scintillation,
Symmetry), 4% (face-up size per carat) or 5% (weight); Tilt counts as a pro only for a stone within
5 points of the brilliance it is compared with. How we measure.
All eight scores against the T73
At a glance: the Radiant Square Cut in pyrope (white) against the T73 Round Brilliant in pyrope (dashed): solid white where
it reaches further, hatched where it falls short. Each pro and con is explained, with pictures, below.
Against the T73 Round Brilliant in pyrope: ahead on 2, level on 1, behind on 5.
Global70, the comparison 81, difference −11
Brilliance75, the comparison 94, difference −19
Fire32, the comparison 50, difference −18
Scintillation66, the comparison 80, difference −14
Spread101, the comparison 100, difference +1
Symmetry100, the comparison 100, difference 0
Shape-norm87, the comparison 102, difference −15
Tilt87, the comparison 75, difference +12
Face-up light census, a different measure from the Cut Grading Tool; Spread and Shape-norm above 100 sit on the ring. Spread is the census's estimate from depth alone; the face-up size in the pros and cons is measured from each model's outline. Open it in the Cut Performance Wheel; these are the same census figures as our Cut Performance Index.
What the Radiant Square Cut gains in pyrope
Against the T73 in pyrope and the same cut in diamond, no figure of the Radiant Square Cut is ahead by the thresholds above. Its figures are in the wheel and the FAQ; Pyrope ranks every cut we score in pyrope.
What the Radiant Square Cut gives up in pyrope
Less fire in pyrope than in diamond
Fire 32 against 62 for the Radiant Square Cut in diamond: 30 points lower
Fire is the share of the returned light that splits into color at the exit facet: the census traces each exit again at the refractive index minus and plus the fire spread (0.019 in pyrope) and counts a ray as fire when the two directions differ by more than 0.6°. The Radiant Square Cut reads 32 against 62 for the same cut in diamond. The figure is the census's; the 3D Gemstone Simulator renders pyrope's fire live.
The fire figure is the census's, traced at the refractive index minus and plus the fire spread. See the fire in the 3D Gemstone Simulator: the Radiant Square Cut in pyrope under the sunny-day lighting.
What helps:the DG-Elongated Hexagon reads 85 for fire in pyrope, the best of the cuts we score there.
Brilliance 75 against 94 for the T73 Round Brilliant in pyrope: 19 points lower
Brilliance is the share of the 3,200 census rays that enter the stone and come back out of the crown towards the viewer. In pyrope, whose critical angle is 35.3°, the Radiant Square Cut returns 75 of 100 and the T73 94. The Radiant Square Cut's pavilion mains sit at 34.6°, the T73's at 40.8°. The maps below show where each stone's light returns from and where it leaks.
Radiant Square Cut in pyrope · Brilliance 75
T73 Round Brilliant in pyrope · Brilliance 94
Red, green and blue = light returning to the eye; gray = leakage, light that leaves heading down or stays inside. This is the head-on view; the Brilliance score averages a wider cone of light, so the score can differ from what one picture shows.
What helps:the DG-M5 reads 100 for brilliance in pyrope, the best of the cuts we score there.
Leakage 21 against 5 for the T73 Round Brilliant in pyrope: 16 points higher
Leakage is the share of the census rays that enter the stone and leave through the pavilion, or through the crown heading down. The Radiant Square Cut leaks 21% in pyrope against 5% for the T73 in pyrope. Grey in the maps below is leaking light; the share under each picture is that picture's own.
Radiant Square Cut in pyrope · Leakage 21
0° · 21% leak
10° · 25% leak
20° · 29% leak
30° · 40% leak
T73 Round Brilliant in pyrope · Leakage 5
0° · 0% leak
10° · 14% leak
20° · 28% leak
30° · 31% leak
Each frame is the Light Return map with the stone tilted away from you by the angle shown; gray is leakage. The share under each frame is that picture's own.
What helps:the DG-M5 reads 0% for leakage in pyrope, the best of the cuts we score there.
Scintillation 66 against 80 for the T73 Round Brilliant in pyrope: 14 points lower
Scintillation follows the number of facets the stone shows: 100 × (1 − e^(−facets / 45)). The Radiant Square Cut has 49 facets and the T73 73, so 66 against 80. It depends on the geometry alone, so it is the same in every stone.
Scintillation follows the number of facets: more facets, more and smaller flashes as the stone moves. Compare the facet counts under the drawings; each drawing shows only the crown. Drawn from each cut's own model.
What helps:the DG-Miliano reads 98 for scintillation in pyrope, the best of the cuts we score there.
Against the T73 in pyrope and the same cut in diamond, no figure of the Radiant Square Cut is ahead by our thresholds. The catch: it shows less fire than in diamond, returns less light than the T73, leaks more light than the T73 and has fewer facets to sparkle with.
If that catch matters more to you, the DG-Elongated Hexagon reads 85 for fire in pyrope, the best of the cuts we score there.
Every figure on this page is from our light census, traced at one refractive index: a simulation of the geometry, not a grading report. The 3D files and cutting files below are the same Radiant Square Cut model we traced.
Radiant Square Cut Pyrope: questions
Is the Radiant Square a good cut for pyrope?
In our census the Radiant Square Cut returns 75 of 100 for brilliance and 32 for fire in pyrope, against 94 and 50 for the T73 in the same stone. Against that round and against the same cut in diamond it has 0 pros and 4 cons by our thresholds; the summary above names them.
What pavilion angle does pyrope need?
At least 36.2° for a round design: pyrope's critical angle is 35.3°, from the low end of its refractive index range, and head-on light has to reflect off both sides of the pavilion and leave through the table. The Radiant Square Cut's pavilion mains sit at 34.6°.
How much does a Radiant Square weigh in pyrope?
At 6.5 mm across, 1.73 ct in pyrope, against 1.62 ct for the same cut in diamond (+7%): pyrope's specific gravity is 3.76, diamond's 3.52.
Can I see the Radiant Square in pyrope in 3D?
Yes: the 3D Gemstone Simulator renders it live, with pyrope's own refractive index and dispersion. Pyrope is traced by the same light census as the other gemstones, with its refractive index and fire spread derived from published values, so its scores are on the same scale; the pictures here are our Light Return tracer, and the Cut Performance Wheel sets it against any other cut and stone.
Get the Radiant Square Cut files
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Radiant Square Cut 3D files
The Radiant Square Cut as exact geometry: 49 planar facets, real-world scale, ready for CAD,
rendering, printing and casting.
