×

The icosahedron has a fascinating relationship to solid state structures! With an atom at its center, it represents a common configuration for small molecular clusters, as well as in the local atomic environments of liquid metals. However, frustration is encountered if you try to use these units as the basis for crystalline arrangements. As such, crystal structures featuring icosahedra tend to be quite complex, as they represent the tension between local packing and the constraints of repeating structure. With 20 equivalent faces, the icosahedron is also the base shape of the D20 dice. Icosahedra are seen in many viruses, where the protein capsules surrounding the nucleic acids of the virus often consist of protein subunits arrayed into an icosahedron. The icosahedron is also a Platonic solid, along with the tetrahedron, octahedron, cube, and, as we will see next, the dodecahedron.