Drilling Hexagon Holes

According to Barry Cox and Stan Wagon.
Reuleaux pentagon rotates inside hexagon.
Loci of various points on the pentagon are shown.
The red locus is the section of the drilled hexagon hole.
Its corners are sharp.
An inscribed round hole of the hexagon hole must be predrilled.STEP files of following videos:
- Drilling hexagon holes 2a
- Drilling hexagon holes 2b