Waterman Polyhedra

The Waterman polyhedra display the convex hull of grid points within radius from the origin. This Demonstration approximates these polyhedra. Normally, much more code and processing would be needed to display the objects perfectly, but a human brain can dismiss the extraneous points and see the intended object.
At level 0, only the grid points exactly from the origin will be shown. When no points at that distance exist, such as , a point at the origin is shown instead. When a level greater than 1 is selected, points at distances , , and so on will also be shown.

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