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I show my construction below; you might want to try to find a solution yourself before proceeding $-$ it makes for a neat puzzle. There may well be other ways to do it. … QEF I guess that a physical model won't make for a hard puzzle to reconstitute into either one or three cubes (e.g. the AB, C, and D parts of the $6$-cube are independent) but would still make a nice …

That's a standard inequality, though perhaps not well enough known for the usual "take it to stackexchange" comment. Denote by $\partial \Sigma$ the boundary of any set $\Sigma$ in the plane. In the …

[Edited to include some 8-unit variations and a new 7-unit setting] [...and to report on another 7-unit setting by N.Predrag, and 6-unit variations by H.Reddmann] Ed Dean already gave a good example ( …

Here's an "irreversible chess" construction that's fundamentally different from the ones so far based on Ed Dean's scheme. The essential pieces and pawns are in boldface: Position A: White Kh1, Ra1, …

[Edited to correct the final position (which didn't work before: 2 Bh1+! Bg2 3 Rf1 Bb1 etc.), and — while I'm at it — to remove a few superfluous pawns] Here's yet another mechanism, which also allows …