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Step-by-step build — 6 steps. Also available as a print sheet.
Drill two 1-1/2" pocket holes on each end of the 17-3/4" rails. Attach a rail flush at the top of each leg pair and one 3" up from the bottom, pocket holes facing what will be the outside (the X detailing hides some; the shelf and top hide the rest). 2-1/2" pocket screws throughout.
Build all three as clones and stack them to check — the desk sits flat only if the leg sets agree with each other.
Lay a 2x2 diagonally across a leg-set opening, mark where the frame crosses it at both ends, and cut to the marks on the miter saw. Fit the full diagonal first, then scribe the two half pieces that meet it.
Don't chase the angles with math — scribing self-corrects for each opening's real dimensions. Glue and 2" brads. Do all three leg sets and accept that the Xs are trim: a whisper of gap at a tip disappears under stain.
Brad-nail and glue a 2x2 cleat across the inside of TWO leg sets only — these two become the bookshelf end of the desk. The third leg set stays cleatless for the knee space.
Pocket-screw two 1x10 boards edge-to-edge (3/4" holes, 1-1/4" screws) into a shelf panel, then drill 3/4" pocket holes around all four sides — two per side.
Rest the panel on the cleats between the two shelf-end leg sets and screw it to the sides through those holes. The shelf is doing double duty: book storage and the rigid box that squares that whole end of the desk.
Measure the actual space between the shelf assembly and where the third leg set lands, cut the six 2x2 stretchers to that measurement, and drill a single 1-1/2" pocket hole in each end. Connect with 2-1/2" pocket screws and glue, and tie the shelf to its adjacent stretchers with the 1-1/4" screws through the holes you already drilled.
Then add the three long 2x2s across the chair area — they keep the knee span from racking without putting a rail where your legs go.
Edge-join the four 2x6 planks with 1-1/2" pocket holes and 2-1/2" screws, clamping each seam flat as you drive. Flip the finished top face-down on a blanket, center the base upside down on it, and screw the base to the underside.
Sand hard — knock down every plank seam, break every edge — then stain and topcoat. The top takes elbows, keyboards, and hot mugs; give it two coats more than you think it needs.