You did ask, didn’t you? Well, here is the answer. (I had to look it up, despite my being pretty good at both math and Greek. More on the latter below.) Anyway, an oloid is the object shown in the image below, of course.

Looks like a Möbius Strip, doesn’t it? If it’s not, how are they different?

Well, we could look at Wikipedia’s “official” definition of an oloid:

It is the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies on the edge of the other circle.

If that isn’t clear — and it really isn’t — Wikipedia goes on to explain further:

The distance between the circle centers equals the radius of the circles. One third of each circle’s perimeter lies inside the convex hull, so the same shape may be also formed as the convex hull of the two remaining circular arcs each spanning an angle of 4π/3.

At this point, I’m about to give up. Maybe I should ask Claude to explain how an oloid differs from a Möbius Strip. Here’s what it (he?) said in response:

An oloid is a solid object; a Möbius strip is a surface. That’s the core of it — one has volume and could sit on your desk as a printed lump, the other is essentially a ribbon with no thickness at all.

How each one is built

The oloid comes from two identical circles standing at right angles to each other, positioned so each one passes through the other’s centre. Stretch a tight skin around that pair — like shrink wrap — and the shape you get is the oloid. Paul Schatz came up with it in 1929.

The Möbius strip is much simpler to make: cut a strip of paper, give one end a half twist, and glue the ends together.

The important differences

The Möbius strip has one side and one edge. Run your finger along the surface and you come back to where you started having covered what looks like “both” faces without ever crossing an edge. The oloid is perfectly ordinary in that respect — inside and outside, two distinct sides, no topological trickery.

The oloid is a precise, rigid shape. Change the spacing of those two circles and it stops being an oloid. A Möbius strip is a topological idea — long, short, fat, thin, it’s still a Möbius strip as long as there’s an odd number of half twists.

Where they actually overlap

Both surfaces are “developable,” which means they can be unrolled flat without stretching or tearing. That’s why the oloid rolls so strangely — it tumbles along in a wobbling motion while its centre of gravity stays at a constant height, and as it rolls, every part of its surface touches the ground. People sometimes hear that and assume it must be one-sided like a Möbius strip. It isn’t; it just develops its whole outer surface as it goes.

One nice bit of trivia for a printer: an oloid’s surface area works out to exactly 4πr² — the same as a sphere with that radius. It also prints beautifully on an A1 Mini as a solid, and it’s genuinely fun to roll across a table.

OK, that’s a lot better. For additional context, ponder that last sentence. The whole reason I found this object is that it was one of those listed as things to print on my A1 Mini! And that’s what the photo up at the top of this post shows.

Finally, what does Greek have to do with it? Only because the etymology includes (or may include) an interesting mistake: it should be a holoid, not an oloid. But the creator of the word, who may or may not be Paul Schatz (the discoverer of the object at any rate), apparently made a subtle but important mistake in reading the Greek word. According to Gemini (Claude’s technological cousin):

The term oloid was coined by Paul Schatz in 1929 as a playful, shortened version of “polysomatoloid,”derived from a new morphological science he named polysomatology. An alternative etymological proposal connects it to the Greek word olos, meaning “whole” or “all,” reflecting how the entire surface touches the ground during a roll.

Of course that is not the Greek word meaning “whole”! As you know from English words like “hologram” and “holistic,” the Greek word meaning “whole” begins with an h. So how did this mistake happen? Ah, that’s what’s interesting about it! Here — enlarged for your convenience — are holos vs. olos in the actual Greek. Even if you know absolutely no Greek, you can see why they might be easily confused:

ὅλος          ὄλος

Categories: Linguistics, Math, Technology