First we need to understand the challenge of gem cutting. To do this, start with the concept of the optician making a lens for your eyeglasses. What is the goal of the optician? To simply bend the light in such a manner as to make it enter the lens of your eye in the way that makes it most effective for you. It is a one way process.
A light source enters the lens, is bent then enters the eye.
The art and science of cutting gems has a double challenge, because it is both the light entering the gemstone, being internally reflected (making a u-turn inside the gemstone), then coming back out with the addition of color and sparkle. It is a two way trip for the light with the additional challenge of picking up color.

Light and the eye view the gem from top, the light enters the gem, then makes a u-turn and returns to the eye. Both the source of the light and the angle of the eye viewing the gem change, thus, making this task even more difficult.
To understand the difficulty of the changing position of the light in cutting a gem, imagine you wanted to skip a stone in a lake. You would bend to get lower, then throw the stone in a straight line. It would be in almost a ninety degree angle to the axis of your standing position. Imagine how the stone would skip.
Next, imagine you maintained exactly the same posture, including bent at the waist, threw the stone at the same angle, but you were suspended directly over the water and you were throwing it straight down. The stone would sink, not skip
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That is exactly the problem the gem designer has this problem. The designer knows that the light will not come from the best of all possible places alone, but from all over the place.
We need to begin a small discussion of gemstone cutting in three of it’s forms, specifically cabbing traditional flat faceting, and concave faceting.