d20 ~ Wednesday, May 17, 2023

How to make an icosohedron, a.k.a. a 20-sided die, a.k.a. a d20 if you play D&D.

I bought a pack of split 3" wood balls. They are available here; the same product is also on Amazon. Wooden balls in this size are easier to find in split form, and that probably makes the project easier anyway.

Determining the sizes of the faces and edges requires some complicated math. Fortunately, there is an online calculator. The radius of the ball (split or full) that you want to cut the icosohedron out of is the "circumsphere radius", so plug that in, and have it solve for "edge length". Two things to keep in mind are (1) measure the actual radius of the ball, don't just use the nominal radius, and (2) the edge length will be a straight line, not an arc over part of the sphere. So use a tool like a caliper for measurements rather than a measuring tape or tape measure.

On each half ball, find the center ("pole"). Use your caliper to find points one edge-length away from the pole, and draw a circle. Then use the caliper to divide that into 5 equal triangles.

I found it easier to draw straight lines if I held the two halves together as a sphere and look straight at where each line had to go.

Clamp a half-ball into a vice. Put some soft scrap wood around it so the vice doesn't smush it. Then use an electric sander to flatten all the triangles. It's a good idea to get more half ball pieces than you need and do some practice sanding first.

When you've done this for both halves, it's time to glue them together, with the edges of each sides "pentagon" skewed from each other so that we can create a middle row of triangles. Then sand those flat.

Eventually you end up with an icosohedron. You'll probably end up working your way around evening things up for a bit...

Next I stained the wood. A dark stain hid what was left of the lines I'd drawn with a Sharpie--in retrospect I'd recommend just using a pencil!

After staining the wood, there's various ways to add the numbers. I used a gold paint pen. You could try carving them, or using decals, or indenting them with dies, if you want to get fancy.

Next you'll probably want to apply some kind of clear finish, for protection, and just to make it nice and shiny :)

I tried a spraycan of gloss sealant, but it seemed to just soak in and not have much effect, so then I brusehd on some good old-fashioned shellac, and that did the trick.