AlanWS
When I've cut hexagonal stock (as a driveshaft for a grain auger to use in moving sawdust to allow a shorter cyclone with a large bin -- unfortunately it didn't work well: planer shavings are not like grain,) the easiest way I found was to cut a rectangular cross section with a 1:1.732 ratio (sqrt 3). The short side measures the face to face distance across the final hexagon, and the long side is the point to point distance.

I cut it by tilting the tablesaw sawblade 30 degrees from square away from the fence, allowing 4 rip cuts without changing settings to establish the hexagon. Tweaking was needed only to make sure the cut met the short face halfway up.

A planing jig to hold stock at the correct angle, and a line ruled down the centers of the short faces, might make planing fairly easy. It's harder to describe than the tablesaw approach, which is why I let that leak into the hand tools section.

It's interesting that you need to plane four surfaces, whether you convert to a hexagon or an octagon.