The local structure of simple liquids is significantly different from that of corresponding crystalline systems. Signatures of fivefold local ordering have been previously found, but current knowledge is limited to pair distribution, leaving considerable uncertainty in the determination of the geometrical structure. New x-ray absorption experimental results on liquid and undercooled liquid copper, interpreted using an advanced data-analysis method based on multiple-scattering simulations, are shown to contain direct information on triplet correlations making feasible a reliable determination of the bond-angle distribution and fraction of nearly icosahedral configurations in liquids.