The nature of the five-fold surface of Al70Pd21Mn9 has been investigated using scanning tunnelling microscopy. From high resolution images of the terraces, a tiling of the surface has been constructed using pentagonal prototiles. This tiling matches the bulk model of Boudard et al. (J. Phys: Cond. Matter 4, 10149 (1992)), which allows us to elucidate the atomic nature of the surface. Furthermore, it is consistent with a Penrose tiling T * ((P 1)r) obtained from the geometric model based on the three-dimensional tiling T * (2F ) . The results provide direct confirmation that the five-fold surface of i-Al-Pd-Mn is a termination of the bulk structure.61. 44 Br, 68.35 Bs, Since their discovery [1], quasicrystals have extended the boundaries of our knowledge, most strikingly in the redefinition of the crystal undertaken by the International Union of Crystallography in 1991 [2]. The reason for this lies in their unusual aperiodic structure, which in the case of i-Al-Pd-Mn and i-Al-Cu-Fe has been described mathematically with reference to a sixdimensional lattice D 6 [3,4]. The fact that a threedimensional atomic model [3,4] can be based on a threedimensional tiling projected from the D 6 lattice [5] leads us to expect the five-fold planes of the model to be related to a two-dimensional Penrose-like tiling [6,7].The unusual tribological behavior observed for quasicrystals raises questions concerning the nature of their surfaces [8]. Systematic studies by Gellman and coworkers indicate that the static friction coefficient for i-Al-Pd-Mn (on itself) is lower than that of most pure metals, and the slip-stick behavior commonly observed on crystalline surfaces is not present [9]. A complete understanding of these observations requires a knowledge of the quasicrystal surface structure [10]. It can not be assumed a priori that a quasicrystal surface is aperiodic itself or that it reflects a perfect truncation of the bulk structure. If this is the case, however, we would expect the structure of that surface to reflect the symmetry of a two-dimensional Penrose tiling [5][6][7]. Until now, however, this direct link between theory and experiment has not been made. This is partly because the aperiodic nature of quasicrystals makes it difficult to determine their surface structure. Surface diffraction techniques can not be exploited to achieve a full structural determination as they rely on a formalism developed largely for periodic structures [11,12]. Scanning probe microscopies offer an alternative, but even with these methods atomic resolution has so far proved elusive. It has been variously suggested that this is an inherent limitation of the electronic structure of these surfaces [13] or a consequence of defect-like protrusions observed in all studies to date [13][14][15][16]. In previous work, we introduced an approach based on tiling of scanning tunnelling microscopy (STM) images using regions of high contrast as vertices [15]. Though this approach produced partial tilings, the presence of large protrusion defects on the su...