I read that circles and any other shapes with constant width will not fall down a slightly smaller hole. I've also seen it posted online that equilateral triangles also behave the same way.
At least for the triangular case, it makes sense that it must be equilateral because for a very thin pizza shape, the smallest edge is much smaller than either of the other 2 edges.
And any even sided, equilateral n-gon seems like it would have the problem of the square. The length between the diagonals is larger than the length of one of the edges.
So would the behavior of the equilateral triangle extend to any odd sided N -gon?