Quasicrystals are non-periodic but well-ordered solids. Their unusual atomic structures foster peculiar surface properties such as low friction and enhanced oxidation resistance. This is well established at least for aluminum-rich icosahedral (i) quasicrystals. It is also very well known that sputter-annealed surfaces of i-Al-Pd-Mn possess step-terrace morphology even though a network of Bergman and Mackay clusters defines its bulk structure.;Using scanning tunneling microscope (STM) we have investigated clean fivefold surfaces of i-Al-Pd-Mn quasicrystals. In addition, we have examined the bulk structural models of icosahedral Al-Pd-Mn quasicrystals in terms of the densities, compositions and interplanar spacings for the fivefold planes. We focus on four models that contain no partial or mixed occupancies, but we have made some comparisons to a fifth model containing such sites. Each of the four models contains paired planes (layers) that can be separated into two main families on the basis of three features: the relative densities of the two planes, the gap separating the layer from the nearest atomic plane, and the Pd content in the topmost plane. We have compared these families with the available experimental data obtained for the fivefold surfaces. The experimental data and other arguments lead to the conclusion that the family with no Pd in the top plane is favored.;We have studied the nucleation and growth of Ag islands on the fivefold surface of the i-Al-Pd-Mn quasicrystal using STM. From 127 K to 300 K, the density of Ag islands remains constant but it drops as temperature increases beyond 300 K. To understand this behavior, we have developed a mean field rate equation model that takes into account the enhanced nucleation at traps relative to nucleation at regular terrace sites. The best fit to the model suggests that the critical sizes for the nucleation at both sites are large, especially at the traps, where six Ag atoms form stable clusters, and that binding between Ag atoms at the traps is stronger than at the regular terrace sites. In addition, we have identified these trap sites as the cut clusters in the aforementioned structure analysis.