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Step-by-step build — 6 steps. Also available as a print sheet.
Cut the four legs to 29-3/4" and taper them on a table saw with a tapering jig or with a jigsaw. Set them aside — they get their apron supports attached in the next step.
Mark the center width line on each blank, draw a half circle at 21-1/8" radius, offset that line 3/4", and cut with a jigsaw. Remove a 1-1/2" section from the center of two of the four pieces — that notch is for the center front leg.
Drill pocket holes in each support and attach it to a leg, tapers facing inward, with glue and pocket screws.
Cut the front apron pieces long, then cut a series of 1/8" kerfs along their length so they can bend to follow the curved apron supports. Cut the back aprons straight — they don't need to curve.
Attach both to the leg/support assemblies with pocket screws.
Cut the two half-round top panels from the plywood blanks and join them with a continuous hinge (or three hinges spaced evenly) along the straight edge — this is the fold line that lets the top swing open into a full circle.
Cut the fourth-leg aprons, slides, and stops per the cut list and assemble them so the extra leg can travel out from inside the back apron and lock at a position directly under the opened top.
Dry-fit this before final glue-up. If the leg binds or doesn't land squarely under the load when extended, the table will wobble the first time someone leans on the open half.
Attach the leg shelf and its supports between the legs for extra rigidity, then bring the top assembly onto the base. Edge-band every exposed plywood edge, sand the whole piece, and finish.