How to process regular hexagon with ordinary lathe, process route

If you must do it with an ordinary lathe. This requires some clamping skills, even fixtures, and it is dangerous. Try to lathe a middle cylinder with tapered ends, and the taper at both ends is 120. The diameter of the excircle is equal to the distance between the two inclined planes, and it is hexagonal when viewed from the front. Then remove two faces to form the regular hexagon you want. If the workpiece you want is thick, you need to add allowance and process six more faces.