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Generalized Generalizing the Cork Plug Problem

According to MathWorld's https://mathworld.wolfram.com/CorkPlug.html"Cork Plug" entry a cork plug is a shape that can stopper a circular, triangular, or square hole.

Link to image of Cork Plugenter image description here

Link to image of Cork Plug Projectionsenter image description here

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.

Generalized Cork Plug Problem

According to https://mathworld.wolfram.com/CorkPlug.html a cork plug is a shape that can stopper a circular, triangular, or square hole.

Link to image of Cork Plug

Link to image of Cork Plug Projections

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.

Generalizing the Cork Plug

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

enter image description here

enter image description here

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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Generalized Cork Plug Problem

According to https://mathworld.wolfram.com/CorkPlug.html a cork plug is a shape that can stopper a circular, triangular, or square hole.

Link to image of Cork Plug

Link to image of Cork Plug Projections

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.