The tesseract is the four-dimensional counterpart to the three-dimensional cube, much as the cube is the three-dimensional counterpart to the two-dimensional square. The pale gray structure on the cover is a common way to represent a tesseract in three dimensions. On page 38 , Hannah Price describes both the rich theory of 4D lattices and the experimental tricks to simulate them in the 3D world. Inspired by the search for topological physics, the techniques work for ultracold atoms, photonics, acoustics, and electric circuits, among other systems. (Image by Robert Brook/Science Photo Library/Alamy Stock Photo.)