With a lathe, we are told, all other machine tools can be built, including a milling machine. Granted that might be a slight exaggeration, but [Maximum DIY] was still able to use his budget ...

Contrary to CNC Milling Lathe machining is for circular geometries (stock is commonly a solid/hollow cylinder) but a hexagon or square can be turned down to a cylinder. Instead of spinning the tools, ...

Most professionals would put a polygon on the end of a turned part using a milling machine ... demonstrates you can turn a polygon on a lathe. Polygons on shaft ends are surprisingly common ...