Iterated midpoint hexagons have centroids that lie exactly on a fixed line from the second iterate due to algebraic features special to the hexagonal case.
The Finite Fourier Series and Elementary Geometry
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Exact colinearity of centroids of iterated midpoint hexagons
Iterated midpoint hexagons have centroids that lie exactly on a fixed line from the second iterate due to algebraic features special to the hexagonal case.