Here is a previous post that goes into detail of how this works. iIn particular on manual lathes. There is also a spread sheet to help with setup for cutting any order of polygon from 3 and up. It also does it for two sides but is that a polygon if joined by two arcs? CNC machines can be programmed to cut flat sides but when done on a manual lathe you have to accept near flat. How close depends on the setup parameters but it can be very close, just not quite exact.
Turning-polygons-on-lathe

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