Re:Ugly Gerry – Gerrymandering font
by jxf on Wednesday January 25, 2023 @11:16PM
(#34527623)
Sure you can. For example, regular triangles, squares, and hexagons can all tile the plane, and they're all convex. There are an infinite number of sets of convex shapes which tile the plane.
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Re:Ugly Gerry – Gerrymandering font
by irishsultan on Thursday January 26, 2023 @04:42AM
(#34529651)
Unless state boundaries suddenly become convex it's definitely impossible. Ignoring state boundaries you have the issue that you need approximately equal numbers of population. It's possible that you can still tile the plane with convex shapes, but I'm not quite sure how to approach a proof (or disproof).