A tiling of the plane (or tessellation) is a covering of the whole plane with tiles so that no tiles overlap and there are no gaps. Polyhedra are three-dimensional solids that are bounded by plane faces. How many are there, and can we construct and classify them? ‘Tilings and polyhedra’ describes the different types of tilings and polyhedra that are possible, beginning with regular tilings made up of regular polygons, semi-regular tilings, and irregular tilings. There are only five types of regular polyhedra—the tetrahedron, cube (or hexahedron), octahedron, dodecahedron, and icosahedron—but there are numerous semi-regular polyhedra, including prisms and antiprisms.