Introduction: Wooden Dodecahedra
The simple dodecahedron: heralded as the Shape of the Universe, this "fifth element" was the very last of the Platonic solids to be discovered. The Pythagoreans of old realized that you could derive Irrationality from the mathematics hidden in its geometry, and drowned one of their members for divulging its secrets to the public.
At great personal risk of death by drowning, we are bringing this knowledge back to the public. In this Instructable we will teach you how to make a wooden dodecahedron with just a few bits of scrap wood, some hardware, and a mitre chop saw.
Step 1: Wooden Dodecahedra - the Jig Is Down
This might seem like the hardest part, but really it's the simplest. And safest. You'll see what we mean.
Cut a plywood circle, 10" in diameter, with a 1/4" hole in the dead center. About 1" from the edge of this circle, drill five 1/4" holes, spaced evenly about the circumference. For those of you fearing to delve too deeply into the secrets of mathematics, each hole is separated by an arc of 72 degrees. Following along in the image, this is the red line and the five non-marked holes along along its path. The marked holes are extra, for giggles. You don't have to make them.
Screw down four rectangular pieces to create an empty square whose inside dimension is just barely larger than 4". Into each of these rectangular pieces, insert two 1/4-20 threaded screw inserts. These will help hold your soon-to-be dodecahedron firmly in place.
Step 2: Wooden Dodecahedra - the Jig Is Up
Mount your shiny new jig on a handy port-a-board, putting a 1/4-20 bolt through the central hole so your disk can rotate. Make sure to position your disk to it's tangent to one edge of the board - this is the edge that will get clamped to the fence of your chop saw.
You'll also want to drill a 1/4" hole through the mounting board, aligned with one of your outer holes, so you can pin the disk in place later.
Step 3: Wooden Dodecahedra - the Block
Cut up a stack of 4" x 4" pieces of your favorite wood - plywood, mdf, purple heart, maple walnut crunch, etc - it's totally up to you. JUST NO CHIPBOARD.
Glue them together into a block, about 1" taller than a cube. Clamp them, let them dry overnight, and then affix the block in your jig by tightening all those 1/4-20 bolts you so thoughtfully made inserts for.
Of course, you could also use a solid piece of lumber, 4" x 4" x 5", but then you won't end up with beautiful striated layers. Now, onto the dangerous part...
Step 4: Wooden Dodecahedra - Measuring
...measuring!
Set your saw blade at an angle of 26.57 degrees. This process is greatly aided by our third-favorite tool of all time, the Magnetic Angle Cube!
The actual mathematical dihedral angle is based upon the golden ratio φ (phi), but therein lies the whole Irrationality / Drowning conundrum. Told you measuring was dangerous. So trust that approximation is ok sometimes, and even the wildly inaccurate 26.4 degrees worked for us here.
Step 5: Wooden Dodecahedra - Cutting #1
Position your jig rig so the block is within striking distance of the saw. You want it so that when you rotate the disk, the saw blade can contact your block at each stop.
Make sure your jig board is clamped tightly to the saw table, your block is clamped tightly within the jig, and your pin is in place to stop the jig from rotating.
Ok deep breath here we go. Very slowly, very purposefully, like a rhythm gymnast lifting her baton one last time as her routine ends, bring the saw blade down across your piece. Excellent. Now rotate your jig so the next hole is aligned, pin it in place, and cut again. Repeat until you've cut five facets into your now-slightly-recognizable dodecahedron.
Step 6: Wooden Dodecahedra - Cutting #2
Now you will have to slightly reposition the jig rig and trim the five sides again, generating a slightly smaller top face. Repeat this process until the length of your shortest diagonal edgeis the same length as the top horizontal edge. Symmetry.
Step 7: Wooden Dodecahedra - Cutting #3
Keeping the saw blade at the same angle, slide your jig rig further down the bench so you're now cutting into the block rather than away from it. Start cutting at that shortest edge that we talked about last step, and work your way around the five positions.
Be careful not to cut into the base of your jig, or the steel screws holding it together. Setting the vertical stop on your saw is a good idea, unless you're of the persuasion that sparks and sawdust DO mix.
Step 8: Wooden Dodecahedra - Liberation
Pop the block out of your jig and take it over to the bandsaw. Set up a distance guide and cut off the excess, right where the mitre saw cut-marks end. Just like at the barbershop, cutting off too little is better than cutting off too much.
Step 9: Wooden Dodecahedra - Finishing
Take your now-nearly-complete dodecahedron over to the belt sander and finish up those faces. You might have to do a little more sanding on the bottom face, depending on how close you made that bandsaw cut. Feel free to stain, varnish, polish, or spit-shine it however you see fit.
Et voila, a beautiful Key to the Universe for all to enjoy.
Undrownedly yours,
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A very special thanks to Artisan's Asylum, our studio HQ and a wonderful makerspace that enables projects like this.