I came across this video of someone using a rotating tool to drill a square hole:
How the heck did they do it?Using a geometric phenomenon known as Reuleaux Triangles. I tried reading several explanations of these before stumbling across video of them in action:
Turns out you can also drill hexagonal holes:
I think my brain just broke.
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http://www.youtube.com/watch?v=zZpWcl1BKVk
http://www.youtube.com/watch?v=KUeQugasOkk