Using an abstract shape as a significant quality of a puzzle piece.
Geometry is a interesting quality that seems like a visual quality but is actually more of a numeric quality. A player will see a shape, like a square, or triangle, in the game world, but the square and triangle can exist entirely in the abstract — you can understand what a triangle is without needing to see it.
Live Examples:- Poly Sticks: Arithmetic, Geometry
This is how geometry differs from a shape quality. In geometry, it's the abstract form that is significant, not the visual shape. For example, if a puzzle needed to represent the number 3, it might use a triangle, as it has three sides.
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Assume everything in this reference is a working draft, there's prone to be some mistakes and inconsistencies. I figure it's best to publish and get feedback rather than write for years in secret. The terms will change, the structure will shift, and the bugs will be chased out. It'll take a while.