This baffling but beautiful union shows no end grain, and goes together easier than you might think.

Three-way-miter-joint parts flow into a delicate point at the corners. Yet hidden splines make these joints strong as well as decorative, letting you add drama to a variety of projects, such as the table shown at the end of the story.

Although simple to cut and assemble, the joint's miter cuts demand accurate saw and miter gauge setups. First align your tablesaw's miter slot dead-on parallel with the blade, and the blade 90° to the table. Next, install a miter gauge extension roughly 4" longer than your longest project part, and set the angle to 45°. For absolute accuracy, perform the frame miter test shown in the Shop Tip below.


Fine-tune your miters
This frame test will uncover even minor miter gauge misadjustments. Begin with strips of scrap cut at least 212 " wide and 10" long. Set the miter gauge to 45° and cut opposite sides in pairs. Fit three sides of the frame tightly together and check for gaps after inserting the fourth piece.

A gap on the inside of the frame means the miter gauge is cutting less than 45°, while a gap on the outside indicates an angle greater than 45°. When all eight cuts form four miters with no gaps, your miter gauge is dead-on accurate.

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As you plane stock to size, check each piece for squareness at all four corners and, using a caliper, Photobelow , check for equal width and thickness. Machine extra stock for practice cuts and stop blocks. For this demonstration, we ripped pieces 112 " square and 6" over length.


Cut the first pairs of miters

After fine-tuning your miter gauge and cutting a zero-clearance kerf in a miter gauge extension, hold or clamp the workpieces firmly against the extension and cut a 45° miter on one end, Photo below left . Turn the mitered edge up, and align the miter tip with the zero-clearance kerf, Photo below right . Cut the second miter, and check that the two cuts match and that the end comes to a sharp tip, bottom Photo . Repeat these pairs of miters on one end of each part.


To cut parts to length, clamp a 45° mitered stop block to the miter gauge, Photo below . This protects the pointed ends and keeps you from accidentally cutting miters on the wrong edge or face. Repeat the miter cuts on all parts.


Rout the spline slots

To reinforce these end-to-end joints, you'll add 14 "-thick plywood splines to slots in each miter. To prevent misalignments, precisely center each slot on the miter. Start by installing a 14 " straight bit in a table-mounted router, with the height 18 " less than half the thickness of your workpieces. Then set the router table fence to center the cut on the end of a scrap the same width as the parts.

Make a test cut on the scrap and measure from the cut and both edges of the scrap using a dial caliper, Photobelow  . Adjust the fence until the dimensions are equal on both sides of the slot.


Attach a stopblock to the router table fence to keep the cut from intruding onto the face or edge of the workpiece. Then rout slots into each miter, Photobelow  .


Cut splines to fit the slots

Measure the slot depth, and cut strips of 14 "-thick plywood 132 " narrower than the slot depth. Then bandsaw the strips into square splines and chamfer all edges of each spine by rubbing them against 100-grit abrasive on a flat surface. Each spline should drop just more than halfway into the slots, Photobelow .


Build the joints

Start by assembling four pieces to create a frame. Working on a dead-flat surface, such as a bench or saw table, insert the splines between each piece and check the fits for snugness. Then apply a white glue to the splines and the miters to be joined. We choose white glue because it dries clear and performs as well as yellow glue. Press the pieces of each joint tightly together and tape them in place on the top and bottom, Photobelow. Avoid dripping glue into the slots for the other two splines. If your project uses an opposing frame, assemble that as well. If your project uses a bound panel, insert it before taping the joints.


To connect two frames, glue and insert the two remaining splines in each joint, Photobelow left . Then glue the four connecting pieces in place and tape each joint securely, Photobelow right .


After the glue dries, remove the tape, and sand the joints smooth, as shown in Photobelow . Avoid accidentally sanding over the edges or points. Should you discover tiny gaps, fill them with a paste made from sanding dust of the same wood species mixed with white glue that's thinned 25 percent with water.


Try different variations

In addition to creating a simple cube or rectangle, you can modify three-way miter joints by adding loose or bound panels or panes of glass. To hold the loose top panel for this table, Photobelow , rabbet the inside top edge of each piece in the top frame before assembly.


For a more dramatic effect, rabbet the inside top edges of the top frame, and then cut grooves on centerlines beneath the rabbet to hold a bound panel so you can display items beneath an acrylic or glass top, as shown in the opening photo.