Self-assembled polyhedral structures are common in biology. The coats of many viruses, for example, have a structure based on icosahedral symmetry . The preparation of synthetic polyhedral molecular assemblies represents a challenging problem, but supramolecular chemistry [2-4] has now advanced to the point where the task may be addressed. Macromolecular and supramolecular entities of predefined geometric shape and with well-defined internal environments are potentially important for inclusion phenomena [5-8], molecular recognition [5,6] and catalysis . Here we report the use of self-assembly of molecular units driven by coordination to transition-metal ions  to prepare a cuboctahedron from 20 tridentate and bidentate subunits in a single step. The cuboctahedron is an archimedean semiregular polyhedron that combines square and triangular faces. Our self-assembled polyhedral capsules, characterized by NMR and electrospray mass spectrometry, are around 5 nanometres in diameter.