Introducing the Scutoid, Geometry’s Newest Shape

The scutoid allows skin cells to remain packed tightly together even over curved surfaces

This shape, dubbed the scutoid, had no name until researchers found it while modeling how skin cells pack together. University of Seville and Lehigh University

Most of us only need to master the classic shapes like circles, squares, triangles, and a handful of polygons to get along in this world. But that’s not all that’s out there—there are dozens of funky shapes that scientists, engineers and biologists have classified, including things like the hemihelix, discovered in 2014, which resembles a kinked Slinky. Now, biologists have found another new shape, dubbed the scutoid. It's likely found in your armpits, up on your nose and all over your face, as it's a shape your skin cells take as they bend.

Bruce Y. Lee at Forbes reports that the new shape, described in a paper in the journal Nature Communications, helps solve a long-standing conundrum about human skin. Millions upon millions of epithelial cells are packed together to create human skin, which is pretty good at being air- and watertight. On a totally flat surface, columns, prism, or cube-shaped cells could be squeezed close enough together to create such a strong barrier. But the human body has few, if any totally flat surfaces (apologies to Channing Tatum’s abs), meaning cubes and columns don’t work. And epithelial cells need to do some pretty extreme bending and curving during embryonic development too.

To solve the mystery, researchers in the U.S. and Europe collaborated on a computer model using a process called Voronoi diagramming to figure out just how epithelial cells are packed together. According to a press release, the best solution was a totally new shape the team dubbed a scutoid, since it resembles a top-down view of a beetle’s scutellum, part of its shell. The shape looks like a long five-sided prism with a diagonal face sliced off one end, giving that end six sides. That makes it possible to pack scutoids together with alternating five-sided and six-sided ends making up the surface, allowing the shapes to make curved surfaces without pulling apart. Don’t worry if it’s hard to envision—the team had trouble making sense of it too, until one of the scientists and his daughter modeled it using clay.

“During the [computer] modeling process, the results we saw were weird,” co-author Javier Buceta of Lehigh University says in the release. “Our model predicted that as the curvature of the tissue increases, columns and bottle-shapes were not the only shapes that cells [...] developed. To our surprise, the additional shape didn’t even have a name in math! One does not normally have the opportunity to name a new shape.”

Jessica Boddy at Gizmodo reports that the team then found scutoid-like shapes in the epithelium of zebra fish and the salivary glands of fruit flies. While Sesame Street will probably not be singing a ditty about the scutoid anytime soon, the shape could have important uses in medicine. “For example, if you are looking to grow artificial organs, this discovery could help you build a scaffold to encourage this kind of cell packing, accurately mimicking nature’s way to efficiently develop tissues,” Buceta says in the release.

“We believe that this is a major breakthrough in many ways,” co-author Luis Escudero of the University of Seville tells Boddy. “We are convinced that there are more implications that we are trying to understand as we speak.”

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