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According to MathWorld's "Cork Plug" entry a cork plug is a shape that can stopper a circular, triangular, or square hole.

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Could you create a plug that could stopper a circular, triangular, square, or pentagonal hole?

In general, are there any sets of non-disjoint shapes that couldn't all be stoppered by a single 3D plug?

What if we let the plug grow and shrink while preserving its shape in order not to be thwarted by sets of holes with enormously dissimilar sizes?

It intuitively seems like a 3D stopper should be able to stopper any 3 arbitrarily selected shapes and also that many stoppers should be able to rotate to fill infinitely many 2D holes, but I am unsure how to determine what sets of holes are possible.

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    $\begingroup$ Interesting question. It may benefit from clarity as to what one means by a "shape," and to "stopper." For a start, one might require that a "shape" be convex, and to say that a shape "stoppers" a plane figure if (at a minimum) the plane figure is the image of some orthogonal projection of the "shape" onto some plane. The question math.stackexchange.com/questions/4993457/… ("Are 4 shadow projections enough to fully identify a convex 3d shape") is vaguely related to this one. $\endgroup$ Commented Aug 20 at 22:34

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