What they saw in them when they were raw suggested a form whether it was the crystalline shape or occlusion patterns. Though the occlusion patterns also become formal to an idea of pattern (for example, six lines or even a honeycomb pattern), gem cuts are obviously geometric and involve the concept of elegance applied to the stone.
Rarely are stones cut in a pattern that is beyond the priniciple of a uniform aesthetic that is human perceived when being cut in a artful way. Nature patterns could be cut into gemstone. Obviously geometric patterns have been cut into dice that roll.
Draw a new gem using things are points and faces of you, fitting what you are. Using groups of ideals that work together you may be able to form a gem of meaning which could be cut with symbols in faces. The points touching faces might be persons or deeds or events. Perhaps something else.