“Researchers discovered that epithelial cells — those covering the surface of many human organs — use a new geometric shape, the scutoid, so the tissues can curve. University of Seville

Unless you’ve been living under an oblong spheroid, you probably heard about the latest discovery in shapes: the scutoid. A team of Spanish biologists from the University of Seville modeled the scutoid to determine how epithelial cells pack together to form the barriers of skin, organs and blood vessels.

The researchers simply used mathematics to hypothesize a shape in nature — a shape necessary for the construction of multicellular organisms. When it became clear that the shape was new to geometry, they named it after the scutellum, the part of a beetle’s thorax that vaguely resembles the newly christened scutoid.

In the example of the scutoid, we can intuit much about the discovery of new shapes: where they come from and why we seek them to begin with.

The most basic form of shape discovery is simply viewing them in the natural world. The hexagon (a six-sided polygon), for instance, occurs in everything from soap bubbles and honeycombs to the clouds of Saturn. As writer Phillip Ball explored in the Nautilus article "Why Nature Prefers Hexagons," he explains how it’s a geometrically ideal shape for a number of functions. As such, the hexagon emerged from physical interactions and biological evolution. Humans just came along and named it.

Other shapes are less common in nature but emerge readily from geometry — or even uninformed imagination. Right angles, for instance, are rare in the natural world. A stroll through the wilderness will not present you with squares and rectangles. Indeed, research indicates that we might instead be hard-wired to prefer natural curves over straight lines. Yet we still construct cubes and use them to remake the world.

There’s a disconnect, however, between the sorts of shapes that can be conceptualized and those that that can be found or reproduced in the nature. Perfect circles, for instance, do not exist in our material realm. From a purely mathematical standpoint, we can easily construct a set of points in a plane that are equidistant from a given point. But, in reality, even the most finely crafted circles and spheres fall short of mathematical perfection. Even the quartz gyroscopic rotors built for NASA’s Gravity Probe B are still less than three ten-millionths of an inch from perfection.

The scutoid, however, seems to actually exist. We might not be able to *see* it, but scientists have mathematically modeled it as a solution for a biological problem. As such, should science one day abandon the scutoid in favor of another solution, the shape itself continues to exist geometrically.

So, to refresh, one can discover shapes by spotting them in nature, inferring their existence in nature or through an exercise in pure mathematics. It’s rare these days, but shape hunters occasionally turn up a new type of pentagon or even a new class of solid shapes.

So by all means, go out there and see what you can find — though please be aware that we already have quite a few mathematical shapes on file. The trapezo-rhombic dodecahedron is already taken — and Clickhole has dibs on the Triquandle.

Now That’s Impossible

Optical illusions such as the Penrose triangle exploit the same visual tendencies that make backward letters such an easy mistake in early grade school. A *p* and a *q* are distinctly different on paper, but if we interpret them as 3D images, then they are simply two views of the same object. The Penrose triangle cannot *truly* exist in 3D space, but we perceive it as a 3D object and this confounding figure is still composed in the *shape* of a triangle. Still, as Lionel and Roger Penrose proved, you *can* discover and name such objects — even if Oscar Reutersvärd created it years earlier.