Finding New Shapes in Foam

In the summer of 2018, a group of researchers announced they’d discovered a new geometrical shape, the scutoid. They found the scutoid, a sort of twisted prism, in the shape of epithelial cells packed between curved surfaces. Having heard of this new geometry, a different group of physicists wondered if they could find scutoids elsewhere, specifically, in the cells of a foam. As shown in the picture above, they did.

To visualize a scutoid, first image a prism. Take two polygons with an equal number of sides and connect them. But if you imagine packing such prisms between two curved surfaces, you’ll quickly see that it won’t work. They just don’t fit together. Instead, one face may adopt, say, six sides, while the other takes on five. To join those two end faces, one of the sides will have to have a Y-shaped junction and a triangular face. This is a scutoid.

You can see two such shapes in the image above. In the left bubble, the far side forms a pentagon, while the near face is a hexagon. On the right, the bubble has six faces in the background and eight in the foreground. And between them, you can just see the triangular face that connects the two scutoids.

It’s not only exciting to find scutoids in a new, non-biological medium; it suggests a physical mechanism behind their formation. Foams are a well-known example of energy minimization. The fact that scutoids are found in a curved foam suggests that the shape itself is connected to energy minimization, something that could help us understand how biological scutoids grow and form. (Image and research credit: A. Mughal et al.; via Physics World; submitted by Kam-Yung Soh)

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