I did also briefly consider some of the fancy router bits that allow you to bring four pieces of wood together in mostly flat grain. This seemed overly complex and I didn't want to spring for the router bit. I finally decided on a simple mitre with a piece of poplar in the middle. With modern glues, an accurate 45 degree angle and the poplar adding strength I figured it would do the trick. Everything seemed to come together nicely and I added some nice coasters to the bottom of the foot to ensure there would not be any undue stress when dragging the desk around.
Final result was a leg with edge grain running on all four sides and you can't see the seam at all.
The rails and styles were all done with mortise and tenon joints and the drawers were finger jointed. I have a Forrest 3/8 saw blade for my table saw and a box jig that allows me to create box joints very quickly and accurately. I used full extension drawer slides and applied an oak front. The overall dimensions are 40 inches wide, 20 inches deep and 30 inches tall. The rails are 5 inches high and the legs are 2 1/2 inches. The finish is a wipe on poly. The thing weighs a ton but should last a lifetime.

