Geometry News!

I appreciate a nice polyhedron but as an area of interest it isn’t one prone to many events. The regular polyhedra were fully classified a very long time ago and while that’s just one set of an infinite space of 3D objects with polygonal faces. If you allow for curves or slightly curved, almost polygons then there is a lot to play with but not many objects stand out from the crowd.

Anyway, biology to the rescue! An article in Nature ( ) looks at the issue of cell-packing. Our cells are squishy 3D objects that pack together to form tissue. Now getting objects to pack together to fill a space efficiently is a well-known and difficult to solve problem if you dealing with anything other than cubes. Hexagonal prisms are a solution that crops up in nature in places such as basalt rock formations and bee hives (and presumably bee hives made out of basalt on some planet with magma bees and honey volcanoes).

In 2D one way of filling a plane with irregular but simple polygons is a Voronoi pattern. Arrnagments of cells in a layer looked at ‘top-down’ can (apparently) resemble that kind of pattern but that doesn’t help describe the 3D aspect of the cells. Prisms don’t work because the ‘top’ face may be smaller than the ‘bottom’ face. Frustrums (chopped off pyramids) don’t work because the ‘top’ and ‘bottom’ faces maybe polygons of different sizes and frustrums don’t neccesarily pack nicely. Enter the scutoid.

Scutoids are (apparently, I’m just reading the paper) messed up prisms. The example picture shows a shape with a pentagon-bottom and a hexagon-top and the vertices of each polygon joined by  curved edges with the exception of an additional triangular face. Flip the same shape upside down and they can nestle into each other. Which is sweet.


Fig1 from ‘Scutoids are a geometrical solution to three-dimensional packing of epithelia’ Nature Communications volume 9, Article number: 2960 (2018)


So not quite polyhedra, crazy mixed up nearly prisms that know how to pack. The picture of the beatle is there because of the distinct pattern of five shapes – specifically that little triangle at the top where the line between the carapace covering the wing splits. The combination of faces on the scutoid reminded the researchers of the beatle and the ‘scutoid’ name is derived from that.

Also I don’t know if you say “scoo-toid” or “scuh-toid”.

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3 responses to “Geometry News!”

  1. I’d go with the long “u” sound. It’s from the Latin, innit? “Scutum” meaning “shield”… and the first syllable in that word is a long, stressed one. Unless I’m misremembering my prosody, which can happen when you’re my age.

    I never knew “frustrum” was that generic a term – I thought it was a truncated cone, specifically. (As in the classic poem by Trurl’s Electronic bard: “Come, every frustrum longs to be a cone,” etc. etc.)

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  2. But I thought Voronoi was a family/district on Barrayar…

    I’m going with scoo-toid as well, like Steve No Relation.


    • No, you’re thinking of the Onoi family, who had their Vor prefix stripped due to their obnoxious and oni^Wannoying habits, incompatible wit hbeingf one of the Vor.

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