Tetrahedra passing through a hole:

This is from eight years ago, but was active again recently. The question is: what's the smallest-area hole in a plane through which you can push a unit tetrahedron? DPKR has a very pretty animated answer, but sadly it's not optimal: there's a triangular hole with smaller area \(1/\sqrt{8}\), known minimal for translational motion ( The problem for more general motion seems to be still open.

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