Shape Shift

This surprising new polyhedron disproves a long-standing conjecture

- -Emma R. Hasson

CAN YOU DRILL A HOLE in a cube that an identical cube could fall through? Prince Rupert of the Rhine first asked this question in the 17th century, and he soon found out the answer is yes. 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. Nobody could prove them wrong—until now.