#noperthedron

#noperthedron

Some say the reason most manhole covers are round is that a circle cannot fall through a smaller circular hole. Which of these other two-dimensional shapes cannot fall through a hole that is the same shape but slightly smaller? Shapes 1, 2 and 3 can all fall through their own holes. Shape 4 cannot. Challenge problem: Can you find another shape that cannot fall through a slightly smaller hole of the same shape?

One can imagine propping a cube up on its corner and boring a large-enough square hole vertically through it to fit a cube of the same size as the original. Later, mathematicians found more and more three-dimensional shapes that eventually came to be called Rupert: they are able to fall through a straight hole in an identical shape. In 2017 researchers formally conjectured that all 3D shapes with flat sides and no indents, known as convex polyhedrons, are Rupert.