Shape #12: Oloid

It's a wobbler

The oloid is a sculpture and a toy. It looks a little bit like a duck bill. Unlike an actual duck’s bill, it rolls smoothly along a flat surface. It’s a wobbler. It was invented (or discovered) by Paul Schatz in 1929, the by-product of his successful attempt to turn a cube entirely inside-out.

Schatz was born in Germany in 1898. He received a technical training and won awards for achievement in math and science. According to his foundation’s website, he was sent to the front in World War I as a radio operator. But when he came back from the war, he didn’t want to do science any more. He began training as an artist, a sculptor.

In 1922, Schatz went to a lecture by Rudolf Steiner. Steiner was an occultist, spiritualist, esotericist. He was the founder of anthroposophy, a movement that aimed to bring the precision of science to the study of the spiritual world. Schatz was smitten, and became a devoted anthrosophist in his life and work.

I don’t know anything about this stuff. But I think what this meant for Schatz was that his art should have the precision of science but some sort of, like, deeper meaning? A sort of marriage between technology and spirituality?

Practically, though, what it meant was this: Paul Schatz really wanted to turn shapes inside out. And before too long, he figured out how to do it.

“While working on an urn on November 29, 1929, Paul Schatz accidentally discovered the inversion of the Pentagon dodecahedron,” says his bio. Soon after, he came up with the inversion of the cube. He did it by cutting up the cube into three parts, the middle section being a ring of tetrahedrons. You might call this a kaleidocycle, or a flextangle, a great shape on its own merits. It turns in on itself entirely. But Schatz wasn’t done yet.

Schatz with his flextangle.

As he turned this ring of connected tetrahedrons in and out, over and over again, he noticed that a certain shape was being traced out. Not be the corners of the flextangle, it was something else—a diagonal in the ring—that traced out a big, sweeping, circularish path.

This was the oloid, and please just watch the video, which shows this so much better than I possibly could.

You can see in the video that the oloid is made from two interlocking circles. Technically this isn’t the oloid. It’s just the oloid skeleton. To make it the oloid, imagine placing snug-fitting elastic over the circular frame.¹ The elastic would snap to the surface.² You’ll get that duck bill that we had at the beginning. It will roll.

What started as the by-product of Schatz’s investigation of the mind/soul interface turned out to be something else entirely: a tremendous amount of fun. The shape wobbled! It’s a delight to see in action, just meandering in a more-or-less straight path.

There are all sorts of instructions for creating these oloids at home. If you have a craft knife and plenty of patience, you can make it out of paper. If you are Australian and a machinist and have insane amounts of patience, you can drill it out of literal metal.

You can 3D print it. One guy online made it out of LEGO and string. You can make it out of beautiful wood.

Here it is in barebones, made out of plastic cup lids by a total crafting idiot (me):

The wonderful thing about the oloid is that, even in paper-cup form, it wobbles and rolls. This model isn’t terrific, because of how it was made by an idiot (me) sitting around the office, brutalizing coffee lids. But it rolls!

I have a very easy time anthorpomorphizing this motion. Wobbling along a snaking path is a very human way to move. Spiritual unity? A new kind of art? I’ll have to keep thinking about that, but any time someone uses math and science to make something so much fun to watch, we’re going to count that as a win. Do yourself a favor today, find a couple of circles and make yourself an oloid. It’s the shape of the week.

BONUS OLOID CONTENT

1. The “convex hull.”

2. Remarkably, the surface area of the oloid is exactly the same as it would be for a sphere of equal radius.