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To make the jig, cut one end of two 5" x 1" x 1" strips of hardwood at a 45-degree angle. Screw the strips of hardwood onto a 10" x 5" x 1" piece of plywood so they form a 90-degree angle (Image 1). Use a framing square to measure the angle, making sure it is exactly 90 degrees (Image 2).
Determine the desired length of the finished octagon (O). Cut the work piece in the shape of a perfect square, with the length of its sides (S) determined by the following formula: S = 2.414 x O. Cut the square S inches on each side.
Calculate the rip distance (R) from the formula R = 2.914 x O. Set the rip fence at distance R. Place the jig against the rip fence so that the point where the two strips meet is against the fence.
To use the jig, align one corner of the square work piece with the 90-degree angle on the jig (Image 1). Hold the work piece on top of the jig as you send it through the table-saw blade (Image 2). Repeat step 4 to cut off the remaining three corners of the work piece.