The atomic structure of icosahedral B4C boron carbide is determined by comparing existing infra-red absorption and Raman diffusion measurements with the predictions of accurate ab initio lattice-dynamical calculations performed for different structural models, a task presently beyond X-ray and neutron diffraction ability. By examining the inter-and intra-icosahedral contributions to the stiffness we show that, contrary to recent conjectures, intra-icosahedral bonds are harder.