Tessellation patterns that have fascinated mathematicians since Kepler worked out their systematics 400 years ago — and that more recently have caught the eye of artists and crystallographers — can now be seen in the laboratory. They first took shape on a surface more perfectly two-dimensional than any sheet of paper, a single layer of atoms and molecules atop an atomically smooth substrate. Physicists coaxed these so-called Kepler tilings “onto the page” through guided self-assembly of nanostructures.