Drilling a Hexagonal Hole
Drilling a Hexagonal Hole
By using a suitable roller restricted to rotate inside a hexagon, one can force a point on the roller to trace out an exact hexagonal path. This construction is due to the authors, inspired by a 1939 construction for a perfect square-hole drill. In this case, though, the roller does not touch all six sides of the hexagon, but it always touches sufficiently many sides to ensure rigidity within the ambient hexagon. As the roller rotates within the ambient hexagon, the center of the blue circle has a locus that is an exact hexagon. The red points are the points on the roller that touch the hexagon and enforce rigidity within it.