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Step-by-step build — 8 steps. Also available as a print sheet.
Set your table saw's bevel to 45° and rip the plywood sheet to a 12-1/2" width, with 12-1/2" being the longest measurement on the beveled edge (the short edge comes out to 11-3/4"). Test-cut on scrap first. Then rip the remaining strip 18-3/4" wide for the top, bottom, and shelf — the center offcut is scrap but can be used for extra shelves.
From the 18-3/4"-wide strips, cut two pieces 32-1/8" long. Mark and cut out the top and bottom shape from these, then use one as a pattern to cut the shelf slightly smaller (especially at the pointed corners). Drill 3/4" pocket holes in the top and bottom pieces as planned.
Attach the sides to the top and bottom. Drill the 3/4" pocket holes facing forward for attaching face frames later — an adjacent cabinet will hide them, or 1/4" plywood finishes an exposed end. Place bottom-shelf pocket holes facing down, and top-shelf pocket holes facing up, so both are hidden.
Rip the back brace down so both edges are beveled, matching the side ripping. Attach at the top and bottom of the carcass.
Finish off the back with the thin plywood panel, nailed and glued in place.
Rip the face-frame stock down to a 1-1/2" reveal on the short side, beveling the edge at 45° — test first to confirm accuracy. Build the face frame with glue and pocket holes (3/4" and 1-1/4" screws). Attach to the front of the cabinet, overhanging about 1/2" on each side.
Leave room for the door to swing open without hitting an adjacent cabinet. Build or buy a door sized to the opening, and attach with the 1/2" overlay, face-frame concealed Euro-style hinges — at least two per door for a 30"-tall cabinet.
Install the corner cabinet first, then work outward to adjacent cabinets. Screw into wall studs and make sure there's adequate support — these cabinets get heavy. Leave a 1/2" gap between cabinets for adjustment if your walls aren't perfectly square, aligning the face frames precisely and shimming the gap. Screw cabinets together from the insides, hiding a few screws face-frame to face-frame for a seamless look.
Sand every exposed surface and finish.