This post has been in my drafts folder for a while. With the World Cup here, it’s time to post it! It’s a rule that a 3D assembly of hexagons must have at least twelve pentagons in order to be a closed polyhedral shape. This post takes a look at why this is true. First, some examples from nature. The stinkhorn fungus Clathrus ruber , has a largely hexagonal layout, with pentagons inserted.