Clathrin-coated vesicles are important vehicles of membrane traffic in cells. We report the structure of a clathrin lattice at subnanometre resolution, obtained from electron cryomicroscopy of coats assembled in vitro. We trace most of the 1,675-residue clathrin heavy chain by fitting known crystal structures of two segments, and homology models of the rest, into the electron microscopy density map. We also define the position of the central helical segment of the light chain. A helical tripod, the carboxy-terminal parts of three heavy chains, projects inward from the vertex of each three-legged clathrin triskelion, linking that vertex to 'ankles' of triskelions centred two vertices away. Analysis of coats with distinct diameters shows an invariant pattern of contacts in the neighbourhood of each vertex, with more variable interactions along the extended parts of the triskelion 'legs'. These invariant local interactions appear to stabilize the lattice, allowing assembly and uncoating to be controlled by events at a few specific sites.