Thirty Days of Making: 3 of 5 Platonic Solids

I’m in Day 3 of a short series: Thirty Days of Making. Every day for the next thirty days, I intend to make something, anything, that is in some way connected to school. There won’t always be pictures, and I reserve the right to credit myself for things that I help my kids make. But I’ve decided that I need thirty days of maker success and maker failure under my belt to be a better designer.

I’ve decided that artwork counts, but not writing (unless it’s part of the art, like calligraphy). Digital work counts, but it has to be useful or publishable.

Some days there will be pictures, some days there won’t be. Each blog entry will contain a list of some of the materials and tools, a quick review of the success or failure of the Making, and a reflection on what i think i learned from the endeavor.

Reason for the Project:

Bored students in study hall. These particular kids were going directly from a study hall that I was proctoring to the field for a game.  I wanted them to succeed, of course, but I also wanted them to be distracted from messing with their friends in study hall who were genuinely studying.  And I was also itching with the recognition that the “Thirty Days Of Making” Challenge was in effect.  So I put them to work — tape and paper plates from the design lab, and then a series of instructions on folding.  Would you believe that one kid figured out the tetrahedron on his own, several minutes before I got there in the folding?  Mission achieved — level unlocked!

Results: Three of the Five Platonic Solids

The Icosahedron

These shapes are based on circular paper-folding, based on the works from  Hence the paper plates.  You can buy really fancy pieces of paper and make them that way; I prefer paper plates.  I bought these books on a lark after attending a workshop on teaching talented and gifted kids.  Some of the best money I ever spent on educational resources.  Lo and behold, this really resonated with them today.

So, I taught the methodology of folding a circle into a tetrahedron, and then taking two tetrahedrons and folding and taping them into an octohedron, and four tetrahedron models into an icosahedron.

The cube and the dodecahedron, the other two of the five Platonic Solids — named for Plato, although there’s evidence for a semi-continuous tradition of teaching them from around 40,000 years ago up until the fall of Rome — are not to my knowledge reproducible from folded circles.  But maybe they’re in the Whole Movement books I don’t have yet.  I’ve produced the dodecahedron in other circumstances, but not today. The sixth graders will have to get those on another occasion.

Reflection on My Learning:

I realized that I consider these five shapes, almost more than any other symbol, to be the core symbols of my spiritual tradition.  I regard the cross with reverence from my upbringing; I’m learning to regard the pentagram as a symbol of the Golden Ratio and the balance of nature; and there are other symbols that I hold in high esteem.  The Platonic solids, though — these I see as a kind of scripture, the unseen hand of mathematics and nature allowing for the creation of only five regular three dimensional shapes in all the known world.   These five can be combined, can be re-formed and stretched and molded and changed and transformed, but man… they’re always the same, no matter how poorly I build them.

Polyhedrons: octohedron

But I digress.

The real discovery in building them is that I don’t need the book any more.  They’ve imprinted themselves deeply enough on my consciousness that I just know how to fold and manipulate the paper to produce these shapes semi-automatically.  A kid started assembling his icosahedron incorrectly a couple of yards from me, and I motioned to him, that’s wrong.  He corrected his work, and he was was able to follow my meaning quite easily with just a few hand gestures and muttered words.  It’s a kind of magic.

So, I didn’t really learn anything from this, except that having a few tricks up my sleeve of this kind is a great thing.  Time to learn some new origami folds, and maybe some snowflakes.  It’s a useful magic to have.

Reflection on Learning in General:

I think building stuff is useful.  Carrying my three models across the parking lot at the end of the day, I ran into a parent of one of my students.  He was immediately fascinated by the models. “Folding paper again, Mr. Watt? You’re always so creative.”  He sounded dismissive, initially, but I intrigued him when I said these were three of the only five natural, regular shapes possible in nature.  “Really?” The notion that his son should learn that, or his daughter, startled him.  The notion that there was an underlying order to nature was astonishing.  So they have a learning purpose.  I just wish I could produce the other three shapes simply and easily from basic paper pieces.  I have templates in my files, but it’s not the same as picking up a piece of paper and building the model from scratch. Something to work on, I suppose.

I’d love to see every kid at my school be able to reproduce all three of these shapes, at least, and every adult.  If we could do that, certain bits of mathematical knowledge would become rather deeply implanted in us.  We could have Sierpinski’s Pyramid-building projects, and competitions for the best-constructed stellations.  I could build them all, I suppose, but then they’d sit there gathering dust.  And these are not things to gather dust — they’re things to be played with and considered while their mysteries implant themselves deeply in the minds of the players.


Four of five stars.  They didn’t keep my inattentive students completely out of mischief, but they helped. I think I need to build them a few more times, and build a few other things from the Whole Movement “Folding the Circle” series, like some of the stellated polyhedra, but these are pretty cool on their own.  And I feel like I’m connected with the universe after building them.

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  1. […] That said, it’s been clear to me that the experience of taking a 2D material like paper or plywood, and making it 3D, is a type of magical experience. I didn’t get the idea from Suzanne Collins, because I’ve written about this before in the context of fabric, and 3D geometric forms in paper. […]

  2. […] I love the platonic solids.  I’ve written about them before.  I think every kid should get a set for his fifth birthday, and learn what you can do with them. Actually, every kid should be given a set of five or six of them, so they can play with them in stacks and rows and walls and other formations. Heck, just give the kids dice, and let them learn to role-play the old-fashioned way. […]

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