How To Draw A D20 Step By Step

When challenged to make a 20 sided widget (icosahedron) from solid wood, I looked near 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 agglomeration of equilateral triangles together for a hollow creation. I had to effigy information technology out on my own, so I thought I'd share.

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Offset with a Cube:

start with a cube

get-go with a cube

While looking at a borrowed D20, I noticed that there appeared to be triangle pairs that were the same on half-dozen opposing sides of the die. So i figured out how to brand 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:

cut at 21 degrees

cutting at 21 degrees

Another thing the D20 I borrowed taught me was the bending difference between these paired sides was 42 degrees. If we fix the blade on whatsoever saw nosotros're using (bandsaw, tablesaw, mitersaw, etc.) to 21 degrees and then cut one of the faces of the cube right to the middle, it will get the states all the right angles.

Cutting Ii Opposing Sides:

two sides cut

Using this 21 degree cut, we will cutting off the pinnacle and the lesser of ii opposing sides, which will result in the shape higher up. Now to reorient the cube, to cut the next pair of opposing sides.

Information technology'due south important to ensure the new 42 degree border yous're creating does non connect across adjacent cube sides. Refer back to the "start with a cube" movie if needed, they all demand to exist oriented differently. Should you mistakenly cutting two adjacent sides at the same orientation, congratulations, you lot get to start over.

Cut Four Sides:

four sides cut

Once we've flipped the cube over to address the next pair of opposing sides, use the aforementioned process to cut the elevation and bottom of each.

Cut Six Sides:

cutting six sides

One more reorientation of the original cube and we can manipulate of the last remaining original sides. Should await something like the shape higher up.

(Extra: If you had accidentally prepare your blade bending to 30 degrees, all these sides should exist pretty close to perfect pentagons, and you got yourself a prissy dodecahedron.)

Cutting Corners: (See what I did there?)

cutting corners

Y'all may exist tempted to ready your saw back from that obnoxious 21 degree setting, but look. You need to continue it there all the way through. The last footstep to finishing upward this d20 is to deal with what used to be the corners of the original cube. I institute information technology all-time to draw out the cuts on the surface and then I wouldn't get lost one-half-way through this step. Essentially, y'all'll be cut 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 retrieve it will brand sense.

Finished:

twenty sided die