You see, dear reader, bees live in hexagonal cells; many turtles have shells made up of juxtaposed hexagons; so do armadillos and so did their giant ancestors the glyptodonts. The skin of the Caribbean copperfish also exhibits a hexagonal design, as does the bark of the tropical pineapple, the eyes of insects and, going into colder or smaller worlds, it turns out that snowflakes or the rings of benzene are also hexagonal. Why? The concise and elegant answer that Jorge Wagensber gives to this question in his book ‘La Rebelión de las Formas’ (The Rebellion of Shapes) is “because the hexagon paves the way”. 

By this he means that with equal hexagons the two-dimensional space can be filled completely, whether it is flat or curved, i.e. without leaving gaps between hexagon and hexagon. Of course, the hexagon is not the only shape that paves the plane; squares and rectangles also do this. However, circles, which are one of the most abundant shapes in nature, are not able to fill the plane. Therefore, we find that circles are plentiful but do not pave, squares and rectangles pave but are not plentiful, and hexagons pave and are plentiful. Very well, but why? Do the following experiment: spread out circles of fluffy material on a flat surface, the more circles the better as long as they don’t overlap; then start squeezing them together so that the circles cover as much of the flat space as possible. What happens? What happens is that the circles approach each other, come into contact with each other, push each other and gradually deform until they end up becoming hexagons that fill the plane.

When I discovered this, I thought that living in a hexagon was perhaps more natural (more like a product of nature) than living in a rectangle or a square, which are the shapes that generally surround home life in our cities. There are many sayings about ‘my four walls’ and it is true that, at first, one gets dizzy with six or more walls around. However, one soon discovers that with six walls one has more perspectives…

Extract from the article by CARLOS ALONSO ZALDÍVAR

Spanish Ambassador to Brazil (2008-2012).