For constructing such a thing out of wood, you will need:
- A band saw
- A disc sander
- 5-minute, 2-part epoxy
- Wood putty
- Sand paper
- A utility knife
- Your favorite Bob Vila flannel shirt (optional).
You will need to begin by drawing 12 congruent pentagons onto a piece of wood, or multiple pieces of wood more likely. Ideally create yourself a perfect pentagon using a rule and compass or computer software can also do this for you. In either case, you will need a template to keep your pentagons consistent. To minimize the amount of wood needed, arrange these pentagons in a way that minimizes empty unused space on the wood. Make sure your lines are dark enough to see, and then take your piece of wood to your band saw. Be sure to wear safety goggles.
Take your wood to band saw and cut out your twelve pentagons. Error on the side of cutting outside the lines. You can sand these down later, but you can't add more wood back on. Again, these can be cut out by other means as well, such as with a laser.
Once you have your twelve pentagons, you will then need to take these pentagons to the disc sander. A disc sander is needed over any other type of sanding tool, because you can change the angle at which you are sanding, and the angle is the important part. We are now sanding the five edges, so that they will perfectly line up with the other faces of the dodecahedron when we get to the gluing process.
A dihedral angle is the angle between to joined faces of a polyhedron. The disc sander needs to be set to half of the dihedral angle, as the joining face will take up the other half of the angle. For a dodecahedron, the actual dihedral angle is about 116.6 degrees. Half of that would be 58.3 degrees, and this is what we need. However, the sander needs to be set to the complementary angle of 121.7 degrees (180 - 58.3). This can be set with a protractor. I personally cut out a piece of wood on the laser with the proper angle as a I didn't have a protractor handy at the time. Either way, it will not be exact, but you should get it as close as you can.
Set one of your pentagons on the disc sander, the side with the pencil marks facing you. Make sure you are wearing eye protection and begin sanding. Sand until you have sanded right on the pencil line. Keep the edge of the pentagon even with the face of the sander. Repeat the process five times per pentagon for all twelve of them.
|11 out of 12 Faces Pieced Together|
Those first three pieces are the hardest. After that, I recommend gluing one piece on at a time, adjusting each single piece with the sander as needed.
When you are done, it is very possible that there may be a gap between one or more of the edges. Use some wood putty to fill in any such gaps, and let it dry over night. Then sand down the wood filler with some sandpaper and use the utility knife to cut off any excess epoxy (cut away from your face, man).
Put on a coat of primer and then do with it what you will.
I recommend a series of meditations with the thing just as a plain white symbol. At some point you may wish to paint it in appropriate symbolism. This could be to paint it black or white, pertaining to the quintessence and the universe. You may also elect to paint the twelve faces in symbolism and/or colors of the zodiac.
The Easy Way OutOr you could just use some sturdy, easier to use, material such as corrugated cardboard. Cut out twelve congruent pentagons, tape together using your favorite tape. For the dodecahedron, just know that three pentagons meet at every vertex (not that you could make it any other way).
Be warned that masking tape doesn't hold up very well under paint. I made a set of all five Platonic Solids this way and had to use a layer of gesso on top of the paint to keep the tape from peeling.
|The Five Platonic Solids Painted in Elemental Colors|