The Dodecahedron

I haven’t done a Maker’s Grimoire exercise in a while, and it’s sort of time.  I’m a big fan of paper-prototyping, first of all, and second of all I’m fascinated by the Platonic Solids.  Once upon a time, a student’s understanding of geometry would be rooted in the study of the polygons first of all, and then in the polyhedrons which could result from those shapes… including this one.  Plus, I’m fascinated by Rosicrucian-Vault’s wooden dodecahedron how-to.  But I don’t want to build one in wood before I’m really confident of my construction abilities in wood.  On the other hand, I understand paper quite well. So much so that I drew up a Dodecahedron template in Pages (which is a word processor. No way should it be used for graphic design. Really!)  And then I added some tabs to that pentagon, and made a template. Print out twelve templates on colored cardstock, and you too can build a dodecahedron… and you can do it right, with three yellow faces, three blue faces, three green faces and three red faces, and label them with the months of the year or the Zodiac signs and so on.

Dodecagon — construction Process

First, of course, you’re going to take three of the cut-out pentagons, and assemble them. As you do so, you’re going to wind up with a structure rather like this — a trio of weird flaps glued together in a weird star formation, like this.  Don’t worry.  It gets better, just not right away.  Once you add in a fourth pentagon, you have something that looks more like a university chorus stage performance, with those odd sound baffles behind the risers so that all the choristers can see the conductor.

Dodecagon — construction Process

You keep adding pentagonal panels to your model, and glue them in place (or use tape, but tape is wonky — use glue.) Gradually, your structure begins to be oddly sphere-shaped, but not sphere-shaped.   And at this point, things begin to get tricky.

See, the template I made has three flaps attached to the sides of the pentagon.  Which is awesome, really.  And most of the time, it’s fine.  But once things reach this point in the construction,  sometimes one of those flaps has to be cut off. But it has to be the right flap.  Which means doing a bit of fitting and second-guessing before it all gets assembled correctly.

Dodecagon — construction Process

So… this is how the pieces look as you’re fitting them together, and figuring out which foldable tabs need to stay attached, and which ones need to be cut off.  As a general rule, only cut one tab off at a time — because they’re hard to re-attached, and relatively easy to leave on until the last minute.  Gluing and fitting the last two or three panels into place is a tricky job… Do the pre-fitting first.

Dodecagon — construction Process

You will get a fairly large dodecagon out of this. It isn’t a small sphere — it’s large enough for some children to throw back and forth as if it were a dodge-ball… though of course it isn’t one of those. Here’s one of them with several common objects alongside to show scale.

Dodecagon — construction Process


And that’s how you build  a dodecahedron big enough to play dodge-ball with.  Of course, there are real mathematical advantages which come from a study of the Platonic solids. They raise questions about area and volume, about points and vertices, and edges and all kinds of mysterious questions which are not easily answerable.  It’s practical usefulness is less clear.  I suppose the inside of this thing could have been taped, and the thing filled with sand as a doorstop… but it would need some rigidity to accomplish that, I think.

But there’s also the benefit of teaching kids to work with sharp tools like scissors or knives, and cut out precise shapes and glue them together. They’re going to want to build clear, obvious and beautiful models… and they can’t do that with those dull, unsharpened scissors with blunted tips. These are not the sort of models that can be assembled slapdash.  There’s an art here…

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  1. […] Well, not so here.  For a kid to pick up a hand-powered crank drill, and point it at a kid from twelve feet away, and pretend it’s a weapon (do all ad hoc blaster pistols go “pew! pew! pew pew pew!”?)  should be a clear sign to anyone and everyone that this kid has no idea what the tool is.  He’s not being aggressive, necessarily — he just can’t imagine what such a tool is for, because he’s never seen one in use.  For the knowledgable, informed child, a quite different result emerges: things with holes in them.  She has newfound power, because now she knows how holes are made — she’s done it.  Obviously, you can think about changing the world with tools you’ve used; you can’t change the world if it requires tools you haven’t used, unless you can imagine and then build those tools. […]

  2. Please don’t go to any trouble on my account, Andrew! But, certainly I’m never one to turn down a favor, so if you feel up to it, then by all means! A key signature die would be a nice toy with which to quiz the kiddos. As for its size, I’m pretty sure it’s not a big deal to scale the pdf file up and down when I print it, but I imagine roughly 50% of its current size should do nicely. Do you have an easy way to design key signatures? If not, I can probably whip up some graphics for it pretty easily.

    • Dear Quin,

      You mean, like A-flat major and E sharp minor and C major and G minor and so on?

      What twelve would you like?

    • Well, basically, I wouldn’t require the actual words “Eb major” and so forth– as I said, I’ve already got blank dodecahedra that I just write the 12 chromatic notes on with magic marker. But a slightly larger dodecahedron that I could fit a whole graphical representation of key signature on– staff, clef, and all, a la the sort given in this picture ( but without the English words giving the answer away– well, that would be quite useful for quizzing in a much more dynamic way than flashcards.

      I can provide you with the graphics for the musical notation if it’s not something you have easy access to.

  3. As for practical application with dodecahedra, well, I’m not sure about with quite the same large size you’re making, but they’re awfully useful as dice for musical practice. A local craft store has been selling large blank dodecahedron dice for about three bucks each– I keep on buying them out to give as gifts to music students. Each side corresponds to a note in the chromatic scale, and it’s quite handy to randomize what key you’re going to practice an exercise in, or to quiz students on key signatures, or to let the universe provide a few starting pitches for a new composition.

    Thanks for the dodecahedron plans– I was actually looking for something similar last year! (For making large “language dice” with different English of questions on each face. Ended up making two six sided dice instead.)

    • What size would you like? I can adjust the size of the face to make differently sized dice— and if you want, I can put the key signature on the sides for you, so it’s just a matter of print-and-assemble.

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