Electron cryo-microscopy of 'single particles' is a powerful method to determine the three-dimensional (3D) architectures of complex cellular assemblies. The pyruvate dehydrogenase multi-enzyme complex couples the activity of three component enzymes (E1, E2 and E3) in the oxidative decarboxylation of pyruvate to generate acetyl-CoA, linking glycolysis and the tricarboxylic acid cycle. We report here a 3D model for an 11 MDa, icosahedral pyruvate dehydrogenase sub-complex, obtained by combining a 28 Å structure derived from electron cryo-microscopy with previously determined atomic coordinates of the individual E1 and E2 components. A key feature is that the E1 molecules are located on the periphery of the assembly in an orientation that allows each of the 60 mobile lipoyl domains tethered to the inner E2 core to access multiple E1 and E2 active sites from inside the icosahedral complex. This unexpected architecture provides a highly efficient mechanism for active site coupling and catalytic rate enhancement by the motion of the lipoyl domains in the restricted annular region between the inner core and outer shell of the complex.