# Odd Symmetry Designs for Gemstones

Gems with odd symmetry designs include popular trillions as well as unusual 7-sided stones. Learn the limitations and possibilities of these cuts.

Contrary to what some seem to think, odd symmetry designs for gemstones have existed for a very long time. Trillions (3-symmetry), pentagons (5-symmetry), and hundreds of other designs have been cut for centuries. Odd indices and symmetries aren't recent discoveries. Actually, quite a few different indexes have been made to accommodate odd-numbered symmetry or specifically for odd symmetry designs. For example, the 80 index has been used since the beginning of faceting and is particularly good for five-sided stones.

## Oddities and Indices

For the sake of clarity, I prefer to use the words symmetry instead of "rotational angles" and angle instead of "slope."

Some odd-numbered indices are just odd. That means no even symmetries are possible on them. For example, Ultra Tec makes a 77 index that's solely for odd symmetry. Only 7- and 11-symmetry are possible with this index. A long time ago, many people, including myself, made designs for this index, too.

Some indexes, like the 80 and the 120, can be used for either even or odd symmetry designs. Both of these indexes are very common, and so are gemstone designs created for them.

Gem cutters use some odd symmetries daily, such as 1-symmetry, trillions, and pentagons. Others are rarely used, such as 7, 9 11, 13, etc.

## Why are Some Odd Symmetry Designs Rarely Used?

The only practical odd symmetries are 1, 3, and 5. In any faceting book, you'll find many gemstone designs based on these. So, why are 7, 9, 11, and 13 symmetries used so infrequently?

Let's look at an example.

### Seven-Sided/77 Index Design

As you can see, the 77 index and seven-sided shape/outline on the left will work fine in a round shape. However, round design options are slim, since seven is a prime number (divisible only by one and itself). Thus, splitting off facet placements is quite limited. There's no way to get a lot of design outlines and tiers for facets. (If you ever try to get a rectangle or oval out of a 7- or 9-symmetry, you'll see what I mean).

The outline on the right is scaled to L/W=1.33. As you can see, a 77 index will certainly not work in any traditional sense for ovals, squares, trillions, rectangles, etc., because of the odd number of facets.

Here's another example.

### Nine-Sided/72 Index Design

Again, notice the odd number of facets and unevenly shaped outline. A 9-symmetry will work for a round design but is just uneven if scaled. Without some fancy designing, a 9-symmetry just won't work for any other shape but round. Nine isn't a prime number but it's still not easily divisible. There are no real options for facets and tiers.

### The Limitations

Odd symmetries like 7, 9, 11, and 13 don't see common use for the following reasons:

• Poor Optical Performance: Even if you get a shape (besides a round) that's acceptable from an odd symmetry, the fact that you have an odd number of facets will severely limit what can be done optically. The extra odd facet will almost always have a large light leakage area, since there's no opposite facet to reflect light to and from. The light usually goes out the bottom of the design at the odd facet juncture.
• Poor Shape Choices: I'm speaking mainly of shapes other than rounds. As you can see in the examples above, odd-numbered symmetries create no (or very few) pleasing shapes.
• Very Limited Facet Placements: Odd numbers aren't easily divisible. Therefore, facets (including girdle outlines) can't usually be placed evenly. This dramatically affects optical performance and the looks of the design.
• Yields: Last but not least, gemstone faceting yields on quality, natural rough come into play. Generally, symmetrical designs will produce a higher yield. There are some exceptions, but crystal shapes tend to be even/symmetrical.

## Are Odd Symmetry Designs Better, Worse, or Just Different?

Some people have claimed professional gemstone cutters and designers don't use odd symmetry because there's a "profit motive" to promote 96 index designs. This is nonsense. Simply put, what sells are designs that have universal appeal and quality performance. A quality design is a quality design. It doesn't matter with what index or symmetry it's created. If odd symmetry designs or indexes had broad appeal or performed well optically, professional cutters would undoubtedly use them. In fact, trillions are an odd symmetry and are promoted heavily and cut frequently by both professionals and hobbyists. Why? Because they sell and perform well.

That being said, there are indexes (32, 64, 80, 96, and 120) that lend themselves to gemstone designing more than others. Some shapes naturally work better for gemstones and are more pleasing to the eye. Mathematically, these indexes offer many possible variations.

Does that mean odd symmetry designs like 7 and 9 just don't perform or are good for nothing? Not at all. Odd symmetries (except 1, 3, and 5) are limited but they can be used for rounds, unusual shapes, or novelty designs. They can often make nice gemstones. Some odd symmetry designs perform as well as, and in a few cases better than, even symmetry designs. Notwithstanding these possibilities, the mathematical and physical limitations of odd symmetries mean designers and jewelers don't commonly use them.

## Notes on Using Odd Symmetry Designs for Rounds

• Any round stone with over seven sides will usually pass as just a round. In my observation, people will spot a seven-sided stone when looking at rounds. If a stone is large enough to see the number of girdle facets, some may spot a nine-sided stone when looking at rounds. However, that is very unusual. Typically, people don't notice the difference beyond seven sides.
• I personally do see some flash difference in a seven-sided round, depending on the design, and sometimes a nine-sided stone, depending on size. My customers, however, rarely perceived any performance differences in anything over seven-sided when I showed them my experimental stones.
• Odd rounds won't make you friends among jewelers. A nine-sided stone is difficult to set in a standard 4-prong round setting. In general, stones with odd symmetry designs will need a custom-made setting. Remember, "custom" almost always means a higher cost. That might make you some jeweler friends.
• Don't act surprised if you can't sell your odd rounds. Mainstream professionals and hobbyists will be cutting other practical, higher performance gemstone designs.

Odd symmetries are nothing new. A lot of people have been there and done that, including me. If you like odd symmetry designs, by all means, have fun.

### Jeff R. Graham

The late Jeff Graham was a prolific faceter, creator of many original faceting designs, and the author of several highly-regarded instructional faceting books such as Gram Faceting Designs.

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