Lay your 8-inch board flat and vertical. Draw a 3-inch line down from the 2 1/2-inch center of the top 5-inch edge. Use your square to make sure the line is perpendicular to the 5-inch edge. Draw two more lines, one on each side of the first, that are the same length and parallel, 1 inch away from the first. Repeat this step on the other 8-inch board.
Drill a 2-inch hole through the 8-inch board, using the end of the first line drawn for the center. The other two lines should rest on the tangent of the hole drilled.
Cut along the two lines with your bandsaw. These grooves in the boards will eventually hold your katana.
Position the two 8-inch boards parallel, on their 3-inch edge, with their grooves facing down. Space the boards 11 inches apart. Place the 13-inch board on top of the ends of the 8-inch boards. The corners should be flush. Drill four 3/32-inch pilot holes through the 13-inch board and into the ends of the 8-inch boards. Two holes should enter the 1/2-inch center of each 8-inch board and should be spaced 6 inches apart. Drill a 1/4-inch deep counter-sink hole into each pilot hole on the 13-inch board, and screw the boards together.
Sand the katana stand with your medium-grade, then fine-grade sandpaper. Wipe the stand down with your tack cloth, and apply your wood stain. Let the stand dry according to the instructions.
Place the katana inside its sheath, and set the sheath inside the grooves in the 8-inch boards.