I've been thinking about the fact that an n×n square grid has as many cells as a triangular lattice with n triangles on each side.
Is there a nice continuous bijection between them? When n is odd, you can at least keep one line of symmetry throughout.

@christianp There are more or less systematic ways to do it, but deciding what property to attempt to preserve along the way is a kicker.

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@christianp I think it may be impossible to do 5x5 while preserving at least 1 original adjacency on each element.

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