Low-tech, high-style cabinet panels
Clamp the stiles and rails onto the cabinet again, one side at a time. Measure the length and width of the panel openings, down to the bottom of the stile and rail grooves. Determine the right panel size by subtracting 1/16" from the smallest top-to-bottom measurements and 1/8" from the side-to-side width of the openings.
I make raised panels with an ordinary benchtop tablesaw and a hand plane, even though I have a big router that could easily spin a panel-raising bit. The reason I do this is appearance—long, slim and flat-faced bevels on panel edges look great and can't be reproduced with a router.
To duplicate this panel-raising method, tilt the tablesaw blade 15° from vertical. Set the saw fence to leave 1/4" of wood at the narrowest part of the taper and rip around all four panel edges. Then, fine-tune the rough bevel with a hand plane. My saw isn't big, but it can still handle these cuts in a single pass using a sharp blade. If your saw struggles with the cut, lower the blade and make each cut in two passes.
Next, draw reference lines on the face of each panel, a little further in than the farthest reach of the bevels. These are planing guides, and help create a consistent bevel.
Clamp a single panel to the edge of your bench with an end-grain side sticking out over the edge. Smooth the bevel face with a razor-sharp jack plane, working from one side of the panel to the other. You have three goals as you do this: smooth the bevel; increase the bevel width so it extends to the pencil lines; and make the outer edge of the bevel thin enough to fit into the stile and rail grooves. It's a trial-and-error technique, so stop every few strokes and test-fit a stile or rail over the panel edge.
When all the panels are completed, hand sand the bevels and faces with 240-grit sandpaper. Dry-fit the parts once more, then assemble permanently onto the plywood box with glue and pipe clamps. Stain the edge-grain panel edges before assembling to conceal any new wood that might become exposed as it shrinks over time.

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