When I was tightening up some bolts that used an Allen key, I started to
wonder: how do they make the hexagonal hole in the top of the bolt that the
key fits into ?

I imagine they drill a pilot hole and then enlarge it with a milling
machine, but the corners of the hexagon are angular, not rounded as you'd
expect a milling machine to make. Or do they finish it off with a very small
diameter milling tool so the corners, although still rounded, have a very
small radius or curvature and so look to be a sharp-cornered hexagon?