Surfaces of as observed in scanning tunnelling microscopy (STM) and low-energy electron diffraction (LEED) experiments show atomic terraces in a Fibonacci spacing. We analyse them in a bulk tiling model due to Elser which incorporates many experimental data. The model has dodecahedral Bergman clusters within an icosahedral tiling and is projected from the six-dimensional face-centred hypercubic lattice. We derive the occurrence and Fibonacci spacing of atomic planes perpendicular to any fivefold axis, compute the variation of planar atomic densities, and determine the (auto-) correlation functions. Upon interpreting the planes as terraces at the surface, we find quantitative agreement with the STM experiments.