Place the 3/4-by-16-by-28-inch plywood panels one at a time onto the table of a miter saw. Adjust the miter saw to cut a 45-degree angle. Cut the 28-inch ends at a 45-degree angle. The 45-degree angles should extend in on the inside edges of the panels, so the four panels fit together like a picture frame along the angled edges to form a box.
Sand the cut edges with a fine-grit sanding block until smooth. Assemble the panels together to form a box. Apply wood glue to the adjoining edges and clamp the assembly at both ends with frame clamps. Allow the glue to dry 24 hours and remove the clamps.
Place the 3/4-by-28-by-28-inch panel over one of the open ends of the box assembly. Hammer finish nails through the panel into the edges of the box assembly every 4 to 6 inches.
Lay the 3/4-by-15-1/4-by-37-inch panels on a work surface measure. Mark a 3/4-inch-wide by 7-5/8-inch deep notch in the center of one 37-inch side of each panel with a tape measure and pencil.
Cut the notches out with a jigsaw by following along the pencil lines carefully. Sand the cut edges with a fine-grit sanding block until smooth. The notches allow the boards to interlock and form an X-shaped divider.
Cut the edges that are 15-1/4-inch wide of the 3/4-by-15-1/4-by-37-inch panels at opposing 45-degree angles to form a pointed edge on each end. The pointed edge allows the panels to slide into the box assembly.
Interlock the two 3/4-by-15-1/4-by-37-inch panels by sliding the two notches together to form an X divider.
Apply two coats of wood finish to the X divider and box assembly. Allow the first coat to dry four hours and apply a second coat. Wait 24 hours and slide the X divider into the box assembly.