When challenged to make a twenty sided widget (icosahedron) from solid wood, I looked about on these here intertubes for some assistance to no avail. Lot’s of guides on making the polygon out of paper and even a few about shaving and gluing a bunch of equilateral triangles together for a hollow creation. I had to figure it out on my own, so I thought I’d share.
For anyone that would be interested in purchasing some handmade ones from my etsy store, please feel free to contact me there or in the comments below!
Start with a Cube:
While looking at a borrowed D20, I noticed that there appeared to be triangle pairs that were the same on six opposing sides of the die. So i figured out how to make one starting with a cube. The blue lines above show the orientation of the shared edges for these triangle pairs.
42 really is the answer:
Another thing the D20 I borrowed taught me was the angle difference between these paired sides was 42 degrees. If we set the blade on whatever saw we’re using (bandsaw, tablesaw, mitersaw, etc.) to 21 degrees and then cutting one of the faces of the cube right to the middle, it will get us all the right angles.
Cut Two Opposing Sides:
Using this 21 degree cut, we will cut off the top and the bottom of two opposing sides, which will result in the shape above. Now to reorient the cube, to cut the next pair of opposing sides.
It’s important to ensure the new 42 degree edge you’re creating does not connect across adjacent cube sides. Refer back to the “start with a cube” picture if needed, they all need to be oriented differently. Should you mistakenly cut two adjacent sides at the same orientation, congratulations, you get to start over.
Cut Four Sides:
Once we’ve flipped the cube over to address the next pair of opposing sides, use the same process to cut the top and bottom of each.
Cut Six Sides:
One more reorientation of the original cube and we can dispense of the last remaining original sides. Should look something like the shape above.
(EXTRA: If you had accidentally set your blade angle to 30 degrees, all these sides should be pretty close to perfect pentagons, and you got yourself a nice dodecahedron.)
Cutting Corners: (See what I did there?)
You may be tempted to set your saw back from that obnoxious 21 degree setting, but wait. You need to keep it there all the way through. The last step to finishing up this d20 is to deal with what used to be the corners of the original cube. I found it best to draw out the cuts on the surface so I wouldn’t get lost half-way through this step. Essentially, you’ll be cutting a equilateral triangle where three of the pentagons meet, NEVER on the long edge you created in the middle of the six sides on the cube. Confused? I don’t know how else to say it, but if you turn the thing around in your hands and scribble it out first, I think it will make sense.
Well, there you go. Wasn’t that easy?
This was also a good excuse to learn how to use blender.