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SKILL BUILDER: Tiling Trigonometry
APERIODIC TILINGS
Not every tiling is a pattern that repeats. If a
tiling is a result of a set of shapes that repeat
over and over but do not form a repeating
pattern, this is called an aperiodic tiling. There
are a number of these, and it has been a bit of a
mathematical competition for centuries to come
up with interesting tilings that use very few pieces
over and over. Many of these tiles have concave
vertices (cupped inward from the polygon’s
surface) in addition to the convex vertices (bulging
outward) we are used to seeing in our regular
polygons.
For example, one type of Penrose ...