D20 Project (Part I)

I got an intro-level bandsaw for Christmas last year and it has been very useful for making short work out of tiny things I would normally have to manually (and messily) cut free-hand or attempt to cut on the table saw.  Come to think of it, the table saw option would probably be even more messy, what with all the blood and detached fingers laying around afterwards.  

Also, it would probably be scream-ier.

After the last project I was looking for something to do that was pretty much the opposite of building yet another table or picture frame, but still within my very limited skill set.  Also, I wanted to keep the number of steps small and the cost as low as possible.  I happened to glance at a set of gaming dice I had on the near-random-item shelf in my garage, and I had my project.

Using the equipment I had access to and limited by the amount of time I was willing to spend on this project, I knew there was no way I could get perfectly uniform triangles that, when assembled, would result in a perfect 20-sided Platonic solid with no gaps.  Sure, I suppose I could have farmed out the cutting to eMachineShop or had someone 3D print me the parts, but owning a giant, flawless d20 that I just glued together like a kit would be pointless... Well, even more pointless than building one myself from scratch is what I mean.  

Shut up.

Anyway, I know that the angle adjustments on my table saw are maybe good for plus or minus one degree, depending on what angle you are actually at.  The angle adjustments on the bandsaw are even less precise.  Moving the guides around adds even more uncertainty unless you want to measure and re-measure after each and every adjustment.  I had no desire to spend days and days making sure I was cutting cheap cedar boards to worryingly high tolerances.  I wanted to make this project as assembly-line-like as possible while doing all the steps myself, so a minimum-hassle approach was needed.

Me so lazy...

A 20-sided die has 20 equilateral triangles for faces. I didn’t really care what the final size of the die was going to be, just as long as it was “pretty big”.  After doing what turned out to be a large amount of completely unnecessary geometry, I stumbled into this now-obvious method for cutting my triangles without needing to measure anything:

1) Place board to be cut between the blade and the fence and note the width.  My cedar boards were labeled 6” x 6’ meaning they were actually 5 1/2 inches wide.  This stupid world...

2) With the blade perpendicular to the work surface, change the angle of the slide to -30 degrees and lock it down.  You won’t need to move it again.

3) Line up the corner of the board with the blade and make your first cut.  Discard the piece you just sawed off.

4) Flip the board and slide it until it is just touching the fence.

5) Move the fence out of the way.  Why?  Well, I needed to because the kickback cowl on my saw is not designed to prevent kickback of pieces that are smaller than the blade diameter.  With the fence touching the workpiece and, having nowhere else to go, my first new triangle shot back at me like a ninja star once the last little bit of wood had been cut through,  nearly shattering my thumb.  Of course, if that’s your idea of a good time, by all means don’t move the fence.

6) Cut the board.  Congratulations! You now have an equilateral triangle with sides that are about 1.15 times the board width (the math is left as an exercise for the student).

7) Move the fence back into its original place.

8) Repeat 4 through 8 until you run out of wood or you have enough triangles to do whatever you need triangles for.

Ok.  I have 20 cedar triangles and it took me about 30 minutes.  Awesome.  Now what?

For the next step I needed to find out what angle the triangles needed to be mounted to each other at.  According to the Internet, the dihedral angle between two adjacent sides of a regular icosahedron is 138.2 degrees, so, (obviously) I needed to set my bandsaw to cut 20.9 degree chunk out of each side of the triangles. Ah, Wikipedia... you know so much... Now if only you knew the best way to recover from an atomic wedgie and get my lunch money back... Sigh...

I made a jig to hold the triangles with the hope that it would help me quickly up my bandsaw cuts.  It didn’t work out.  The pic to the left shows one of the triangles after cutting the three sides to what should have been the correct angle (or at least close enough).  It looks fine in the pic but the cuts were actually way too non-uniform for even my pretty liberal definition of “good enough”. 

So, then, time to go to Plan B.  Well, really, time to scream goodbye to Plan A in a drunken rage, angrily invent Plan B, realize that “Plan B” is actually a trade name for something totally unrelated, then calm down and settle for Plan C. No, wait... that’s taken, too.  Oh, you gotta be kidding me!  All the way to Plan H?  Fine.  “Plan I” it is.

Back at the table saw I set the guide angle to zero and the blade angle to 21 degrees. I cut and flipped the board until I had enough wood for 30 wedges, which I then cut in half on the bandsaw.  I glued the wedge halves to the “bad” side of the wood like you see in the pic. 

After the glue dried I drilled pilot holes in the wedges and began to attach the triangles to each other.  The nails helped keep some of the pieces in place while the glue dried, but I found using a self-tapping wood screw instead of nails worked much better. 

After attaching five more triangles to each of the “end caps”, I had two ten-triangle halves that fit together a lot more nicely than I thought would have been possible. Here it is after the halves were glued together.  

Although I think that the “gaps” you see between the pieces (a result of the “Plan I” approach and the fact that the wood I used was thicker than zero inches) look cool, they needed to be filled with something to make the entire structure a lot more sound.  

(To be continued...)