We interrupt our
regularly-scheduled website to bring you this bit of origami fun.
As a kid I was always fascinated by
origami, and I left our house littered with pointy little birds, animals and boxes. But as I grew up, and school became harder and computers became more interesting, I found that I would go for months or years without touching a piece of origami paper. It is a relaxing hobby, but it was hard to find time to relax.
Having kids changes the game, though. It gives you an excuse to reconnect with Lego sets and Hot Wheels, and in my case, origami. One of my kids brought home a
modular origami wreath from school, and I was impressed by its geometry and sturdiness. It set off an itch in me to find other modular origami patterns.
Modular origami is a branch of paper folding in which multiple folded pieces are joined together to make larger, more-complicated shapes. Of the common modular base units, I found the
Sonobe module to be the most interesting. I liked the way you could assemble a simple solid out of as few as three modules, and more interesting solids out of six, twelve, thirty or ninety modules. And many of these solids were intrinsically tied to the beautiful symmetry of the
Platonic solids.
Around the time I was playing around with Sonobe modules I ran across
a printable pattern for origami paper that, when folded into a classic water balloon, would make a tiny, cubic model of the earth. I liked the idea but not the execution. The paper was dense and several layers thick at some points and only a thin single layer in other places. It was hard to keep the shape smoothly cubic. I decided that a Sonobe-based pattern would work better.
I started by defining the locations in 3-D space of the triangles that make up the faces of each Sonobe solid. Each triangle was a half square that, when combined with three other half squares, would make up the two printed squares on each sheet of origami paper. Then it was a matter of figuring out the position in space of each printed pixel that would be part of each half square. For each of those pixel positions in space you can imagine a vector going from the center of the solid to that pixel position. And each vector could be converted into a longitude and latitude on an imaginary sphere sharing a center with the Sonobe solid. Look up those coordinates on a
free NASA map of the globe, and you know what to color the pixel. Repeat the process 719,999 times, and you have the patterns for a piece of origami paper.
The end result comes in four flavors: the 3-unit
triangular bipyramid know as “Toshie’s Jewel,” the 6-unit cube, the 12-unit stellated octahedron, and the 30-unit stellated icosahedron. My personal favorite is the cube. It doesn’t require a huge investment in time and fits together fairly tightly. (Plus, it reminds me of
Htrae,
AND just by chance, one of the two corners that falls on land is located on Japan...right on top of
Sonobe, Japan.)
I’m releasing all the patterns under a
Creative Commons license that will allow you to make copies, remix the work, or do just about anything you want with it. See the individual pattern files for specific details.
Happy folding.
