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We extend Which convex pentagon gives least packing density? by going from convex pentagons to general ones. Question: Which pentagon gives the least packing density on the Euclidean plane? Note: All ...

Reference: https://en.wikipedia.org/wiki/Smoothed_octagon Background: The smoothed octagon is conjectured to have the lowest maximum packing density of the plane of all centrally symmetric convex ...

Background: Consider trying to cover the largest possible scaled copy of a planar region $C$ with specified shape with n instances of a tile $T$ of specified shape and size. Several families of this ...