The structure of the quasicrystalline approximant Al13Co4(100) has been determined by surface x-ray diffraction (SXRD) and complementary density-functional-theory (DFT) calculations. Thanks to the use of a two-dimensional pixel detector, which speeds up the data acquisition enormously, an exceptionally large set of experimental data, consisting of 124 crystal truncation rods, has been collected and used to refine this complex structure of large unit cell and low symmetry. Various models were considered for the SXRD analysis. The best fit is consistent with a surface termination at the puckered type of planes but with a depletion of the protruding Co atoms. The surface energy of the determined surface model was calculated using DFT, and it takes a rather low value of 1.09J/m2. The results for the atomic relaxation of surface planes found by SXRD or DFT were in excellent agreement. This work opens up additional perspectives for the comprehension of related quasicrystalline surfaces.