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Sublime
EDIT: I just re-read the poly hole page and he is actually making the holes larger and then using the low polys so the edge lines up with the original circles diameter. So it still is printing undersized but he is using that to his advantage and it is not solving the issue, rather just hiding it.
Yes, if you multiply the radius of the polygon (which is measured center-to-vertex) by cos(180 / n) where n is the number of vertices, you get the apothem. By dividing the radius by this value (which of course is less than one, so dividing makes the number larger), your ideal circle becomes inscribed in the polygon rather than vice versa, so a shaft of that size will fit ideally (ignoring the tolerance issues that occur in reality). Since the properties of the plastic cause it to shortcut corners, setting just the right number of facets can actually result in a perfect circle when printed.
I use my own functions with most of the same math as Nophead's version.
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