TITLE: Nonconvex manhole covers
QUESTION [32 upvotes]: One common reason given for the circularity of manhole covers is that they can't fall through the manhole. For convex manhole covers, this property is equivalent to having constant width — if you have different widths, just orient the cover so that the shorter width slides through the larger one. Since convex polygons can't have constant width, this rules them out for manhole covers. However, for nonconvex shapes, a longer width does not necessarily give you a longer hole.
Is it possible to have a nonconvex polygon that cannot be moved through a hole of the same shape?
Some Clarifications:

The hole has zero thickness.
I was thinking of the polygon being simply connected. But if this matters I would like to know the answer both ways.

REPLY [5 votes]: What about a square with four thin slices taken out of it?
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