From Triangle to Heart and Beyond

Hearts, pears, shields and the like can be some of the most challenging designs to cut—lots of steps. Nearly 21 years ago, I did a design called the Tri-Heart, design 10.037 found on www.facetdiagrams.org. To design this, I started with 3-fold, mirror-image symmetry on the pavilion. Recently a designer named Roland Arajs started with my Tri-Heart and played some more with the symmetry, creating his Vortex Tri-Heart. This inspired me to take another look at morphing other triangular designs into a hearts.

When designing and cutting a heart, there are two important advantages to starting with a triangular design. First, you can end up with a design that is easier to cut. With the usual 1-fold, mirror-image symmetry of a heart, you only get to cut one or two facets at the same angle and mast (or platform) height. This means lots of steps with a lot of time spent changing the settings on your machine and more chances for mistakes. With 3-fold, mirror-image symmetry, you can cut up to six facets at the same angle and mast height. With a suitable design (and careful dopping), the cutting sequence can be much simpler.

The second advantage is with optical performance. When light rays hit a pavilion that is a three-sided pyramid in shape with steeper angles than usual, interesting things happen. Many light rays bounce three times off pavilion facets instead of the usual two and then return to exit the crown. The result is better scintillation and better performance when the stone is tilted. This can be particularly beneficial for materials of lower refractive index—quartz, R.I=1.54, or even lower, glass, opal, fluorite, etc.

I started out with Trilliant C 13.067 by Basil Watermeyer, calculated by Norm Steele. The symmetry wasn't quite complete in the design in the database, so I tweaked it. I made the corners less sharp, moved some meets around. I optimized the angles for quartz, (but they also work well unchanged for CZ). Note the steep angles on the pavilion. This is to take advantage of the three-bounce principle. I duplicated angles wherever possible. I also made sure the steps 1 and 2 facets on the pavilion meet at a temporary center point, so it's easy to make the outline. I posted the design on www.facetdiagrams.org as design 13.067D. Here is a screenshot:

The next step on our path to a heart shape is to round off all three corners. Now we really only need to round off two corners for our heart, but if we round off all three, we can take advantage of GemCad's 3-fold symmetry to get six facets for the price of one. (We only need 4 four the price of one, but we'll return the extra two later). Below is the result. I call this version the Bulgy Trilliant. I posted this on www.facetdiagrams.org as design 13.175.

We are nearly there. To get a heart shape, we need only delete the "rounding" facets on the bottom corner and cut a flat on the top. Here is my Trilliant Heart. I posted it as design 10.060.

Note that the girdle line is not level on the flat side. You can carve a notch in the flat side if you have the equipment and know-how. There are just 15 steps, including the girdle and table!

Finally, what if we just round off one corner of our Trilliant? The result is my Trilliant Shield, which I posted as 23.063.

This is a re-cut option for a triangle with a chipped corner. You might notice that I kept the step names for all four designs. The heart is the only one with step 5.