To get the desired angle for the wheel, divide 360 by the number of sides. I would most likely get as close as possible and wind up putting in a heavy duty spline, or tongue and groove the connecting points because warping, twists, splits, and other imperfections will make it pretty much impossible to get a perfect joint in construction grade lumber. By using splines, you could round out the wheels so the planter could roll around. Would have to have spokes of some sort to put the wheel on a shaft of steel pipe. Doesn't have to be a fancy construction to make it a movable planter. My wife likes to move stuff around in the garden and clever as this is, it will be heavy and awkward when filled with dirt and plants.
The more I do, the less I accomplish.