Step 1
Dry-assemble the work pieces by placing the angled edges of the 22.5 degree miters together. The long points of the angles should fit flush with each other, as should the short points of the angles. Check all joints for gapping. If you have gaps, adjust a miter saw one degree to the left or right and trim one of the work pieces. Check the fit again and, if necessary, recut the mating piece; always alternate which piece you cut from when fine-tuning the angles.
Step 2
Reassemble the work pieces after trimming, again without glue. When all of the 22.5 degree angles are tight, apply glue to the angled ends on all the pieces and assemble the pieces.
Step 3
Place a nylon strap clamp around the completed assembly. Nylon strap clamps apply pressure evenly to any shape. Tighten the clamp until glue oozes out all the 22.5 degree joints. If the finished assembly will have fewer than eight sides or pieces, cut support blocks from scrap wood to support any open areas so that when the clamp is tightened, the joints close up. Allow the clamped assembly to dry overnight.
Step 4
Remove the nylon clamp. Shoot two, 1-inch pin nails through each miter joint, evenly spacing the nails and penetrating the centers of both pieces.