Odd Symmetry designs... Better, worse, or just different?

Note: I prefer to use the words symmetry and angle for clarity. Maybe it's just me but "slope" instead of angle and "rotational angles" instead of symmetry and the other phrases like those make me feel like I am in the class of a professor that really does not understand the subject he is talking about and uses fancy words to cover up that fact.

So if odd symmetries were just discovered... Does that mean that all the trillions (3-sym), pentagons (5-sym), and hundreds of other odd symmetry shapes and designs that I and other designers/cutters have created and cut for the last few hundred years did not exist until just recently?

Contrary to what some people seem to think odd symmetry designs have been around for a very long time and they were not "just discovered" by some one recently.

Trillions with an odd 3-symmetry have been around for... well hundreds of years, so have pentagons (5-symmetry) and many others. Odd indexes and odd symmetry designs are in fact nothing new at all and been done long before we were ever born.

Actually there has been quite a few different indexes over the years that were/are made to either accommodate odd numbered (3,5,7,9...) symmetry, or designed specifically for odd symmetry.

An index that is used and been around since the beginning of faceting is the 80 index. It was not "just discovered" the 80 index has been used for decades. The 80 index is particularly good for 5 sided stones and yes, 5 is an odd number, and yes, pentagons have been cut for centuries too.

OK, I think there needs to be some distinctions here about odd symmetry.

There are some odd numbered indexes that are just odd, no even symmetries are possible on them.

For example Ultra Tec makes a 77 index, that is solely for odd symmetry, 7-sym and 11-sym specifically. There is really no even symmetry usable on a 77 index.

Note: There were many people designing for the 77 index a long time ago (including me although I have not released many designs). Ultra Tec to this day gives away several designs created for a 77 index when you purchase the index from them.

There are also indexes like the 80, and 120 that can be used for either odd or even symmetry designs. Both of these indexes are very common and so are designs done on them.

Odd symmetries that faceters use daily - Typical odd symmetries would be 1-sym, 3-sym (trillions), 5-sym (pentagons).

Odd symmetries that are seldom used with the exception of novelty cuts - Not commonly used are 7-sym, 9-sym, 11-sym, 13-sym and so on...

Really the only practical odd symmetries are sym-1, sym-3, and sym-5. The common usage of these symmetries proves my point. Just look at all the trillions, pentagons, and unusual 1-symmetry designs around. Look in any design books you have handy, you will find a lot of these design symmetries.

Why are 7-sym, 9-sym, 11-sym, 13-sym, ect... not used very often? Well the reasons are very obvious if you think about it. Below are some examples...

Above Left: A seven sided round (7-sym) on a 77 index gear.
Above Right: A seven sided (7-sym) outline scaled to L/W=1.33 on a 77 index gear.

As you can see above the 77 index and seven sided shape/outline will work fine in a round shape. Although round design options are slim because 7 is not devisable, so splitting off facet placements is quite limited.

Limited splits/facet placements means a very limited amount of variations that can be created. In other words because 7 is a prime number and not divisible by anything but 1 and 7, there is no way to make a lot of design outlines and tiers for facets. Just try to get a rectangle or an oval out of a 7-sym or 9-sym. You will soon see what I mean.

The left out line is scaled to L/W=1.33 and as you can see because of the odd number of facets a 77 index will certainly not work for ovals, squares, trillions, rectangles and so on. The odd sides just will not work, at least not in any traditional sense.

Here is another example:

Above Left: A nine sided round (9-sym) on a 72 index gear.
Above Right: A nine sided (9-sym) outline scaled to L/W=1.33 on a 72 index gear.

Here again notice the odd number of facets and unevenly shaped outline. A 9-sym will work for a round design but is just uneven if it is scaled, like the 7-sym. A 9-sym will obviously not work for any other shape but round without a lot of fancy designing. Again because 9 is not easily divisible (with the exception of 3) there are no real options for facets and tiers.

The main reasons odd symmetries like 7, 9, and 11 are not commonly used?

Poor Optical Performance - It is important to also realize that even if you get a shape (besides a round) that is 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(s) will almost always have a large light leakage area because there is no facet opposite of it/them 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 am mainly speaking of shapes other than rounds. As you can see in the samples above there is just no (or very few) pleasing shapes that can be created with odd numbered symmetries.

Very Limited Facet Placements - Like I said earlier, odd numbers are not easily divisible and there fore facets (including girdle out lines) cannot usually be placed evenly. This dramatically effects optical performance and also the looks of the design..

Yields - Last but not least yields on quality natural rough come into play and in general symmetrical designs will produce a higher yield. There are of course some exceptions, but generally crystal shapes tend to be even/symmetrical.

I have heard people claim that professional cutters/designers do not use odd symmetry because there is a "profit motive" to promote 96 index designs.

This statement is utter and complete garbage. This kind of statement shows the lack of understanding and plain ignorance that the people who make the statement have of faceting and the faceting business.

What sells, and what people like, hobby and professionals both are the designs that have universal appeal and quality performance. If odd index/symmetry designs had any advantage at all, professionals and hobbyists alike would use them with out question. It is about what works best.

I keep saying it... A quality design, is a quality design. It does not matter what index or symmetry a design is created with.

That being said there are indexes (32, 64, 80, 96, 120) that lend themselves to designing more than others, a 96 index is one of these types of indexes. There are naturally some shapes that also work better for gemstones and are more pleasing the the eye.

For example, trillions are an odd symmetry (3-sym) and are cut/promoted very heavily in the commercial as well as the hobby market for the simple reason that they work. If 7 or 9 symmetry stone designs worked better than 8 symmetry stone designs we would be cutting them. They do not work better, that is a simple proven fact.

Does that mean a 7-sym and 9-sym and other odd symmetries will not work or are not good for anything? No, all these symmetries can be used for unusual shapes and odd or novelty designs. There are some odd symmetry designs that are quite nice and perform as well as, and in a few cases better than even symmetry designs.

What I am trying to say and show is that while both the 7-sym and 9-sym and other odd symmetries (excluding 1,3,5 of course) will work for rounds and possibly some novelty shapes and they often can make nice stones...

Odd symmetries are extremely limited and that is why they are NOT commonly used. There is after all a reason why in the last several hundred years of faceting there has not been many (if any) odd symmetry designs (excluding 1,3,5 of course) created and used.

Some notes and experiences of mine on using odd round symmetries;

It has been my observation that once over 7-sym in a normal round stone they all look the same. What I mean is that when looking at a round stones, people will spot a 7 sided stone. They might spot a 9 sided stone, if the stone is large enough to see the number of girdle facets, not usually though. Any round stone over 7 sides is seen as just a round, is a round is a round. People do not notice the difference.

I personally do see some flash difference in a 7 sided round depending on the design, maybe a 9 sided stone depending on size. But generally in my testing, cutting and questioning of customers when they saw my experimental stones there was not much perceived differences over a 7 sided stone. In other words they noticed the 7 sided stone but were not particularly impressed and did not see a difference over 7 sides in odd indexes.

People can talk about odd symmetry all they want.

The bottom like is that there is very little difference in performance and most people do not notice any difference over 7 sides.

Odd rounds will not make you friends among jewelers. By this I mean that a 9 sided stone is difficult to set in a standard 4-prong round setting. Just ask any jeweler.

In general odd symmetry stones will take a custom made head to be set. Most jewelers are not happy to set them unless it's a custom job, which is no problem with some jewelers. But keep in mind "custom" almost always means more cost for the setting.

Note: Hobby cutters set stones too. The ladies in the family generally end up with the stones, but setting stone is not just a professional issue.

Do not be surprised if you cannot do a lot with odd symmetries or that the main stream hobby and professionals alike will probably be cutting other more performance and/or practical designs.

Odd symmetries are nothing new. A lot of people have been there and done that... including me. If you like odd symmetries, by all means have fun. There certainly is some stone/designs that could be interesting.

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