Manhole covers are (usually) round so they don’t fall in the hole. Think about it. If manhole covers were square (and we’re assuming they have a small lip to them), you could turn it on its side then rotate it to drop it in diagonally. This is true for any polygon no matter how many sides it has (though, in reality, the number of sides would start to depend on the size of the lip as the number of sides grows). The limit of an *n*-dimensional polygon as *n* approaches infinity is a circle and this allows you to minimize the size of the lip.

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Wouldn’t an equilateral triangle work as well as a circle?

I believe that in three dimensions you can still get an equilateral triangle to work its way through, though I’m not absolutely positive of that. If I’m wrong then the conjecture would be true for any

n-dimensional polygon whenn> 3.