Lay the two 12-by-28 plywood panels flat on a work surface. Mark the center of one 12-inch side on each panel, using a tape measure and pencil. Measure and mark a 3/4-inch-wide by 14-inch-deep slot from the center point on the two panels, with a tape measure, straightedge and pencil. A centered slot would be 3/8 inch wide on either side of the center point.
Cut out the slot on each panel with a jig saw. Sand the cut edges of the slot with a fine-grit sanding block.
Apply wood glue to the edges of the notches. Slide the two notched ends into each other to interlock the panels, forming an X shape. Wipe off any excess glue that seeps out with a damp cloth.
Center the 16-by-16-inch plywood panel over the top of the X-shaped base assembly; the corners of the square should reach out to the ends of the X pieces. Hammer finish nails every 2 inches through the top panel into the top edges of the X-shaped assembly.
Place the nail set onto the center of the finish nail heads and tap it with a hammer to set each nail slightly below the surface of the plywood. Fill each nail hole with wood putty using a putty knife. Allow the putty to dry 24 hours.
Sand the putty flush with the surface of the plywood using a fine-grit sanding block in the same direction as the wood grain. Apply a wood finish to the assembled square pedestal stand with a paintbrush. Allow the first coat to dry four hours and apply a second coat. Allow the final coat to dry 24 hours.