9.22.2014: Strictly Platonic

3-D rendering of plant pots shaped like the five Platonic solids.

The tetrahedron is, without a doubt, the worst polyhedron in the world. Never mind the Escherian stellation of the small stellated truncated dodecahedron, or the downright Lovecraftian small retrosnub icosicosidodecahedron, which should have stopped two prefixes ago — no, no, it’s the tetrahedron that’s the very worst of the lot.

First, for some context: Fall is finally making its way towards Boston, bringing with it the first hints of the usual red-gold leaves and hazy skies and pumpkin spice overdoses that come with the season. But as much as I love fall in New England, my room overlooks a bare concrete courtyard that’s grim even in the height of summer, and unending grey skies do absolutely nothing for its charm. I wanted something green in my window to balance out the soon-to-be-overpowering greyness…and then I remembered that back in freshman year, I’d had succulent planters shaped like the Platonic solids on my to-do list of things to make.

Even with actual math involved, the Pinterest coefficient of geometric planters full of succulents was way too high for me, so I decided to plant herbs instead of succulents. They’d need slightly bigger pots, but at least that brought the coefficient down to something I could stomach. (And hey, at least I’m not dip-dyeing them neon.)

I figured making the pots would be pretty straightforward: model each of the polyhedra as a hollow shape, take off the top face, smooth out the edges, add some drainage holes, and they’d be ready to 3-D print.* And it did go perfectly smoothly, right up until I started working on the tetrahedron and realized that it has no top face. That complicated matters.

On top of that, I’d scaled all of the polyhedra to have equal volume…which turned out great for four out of five, but left the tetrahedron sticking out like a sore thumb.

3-D model of the Platonic solids, each with equal volume.

I gave up on my hopes of geometric perfection and scaled the tetrahedron down by eye to something that at least looked proportionate (as shown in the first picture.) I also decided to cut out the top portion of one of the sides of the tetrahedron — it still doesn’t match the others as much as I’d like, but I think it’s a reasonable compromise between preserving the shape of the tetrahedron and making it actually useful as a planter.

Once these are all printed, they’ll get a quick bath in acetone vapor to give the ABS plastic a glossy finish, and then it’s off to the windowsill with the lot of them. Maybe after that I’ll turn a retrosnub icosicosidodecahedron into a planter; it can’t possibly be more stubborn than that blasted tetrahedron.

*My initial plan was to make these out of red clay so they’d coordinate with terra-cotta pots, but a quick review of my sculpting ability nixed that idea pretty quick.


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