The shapes of icosahedral quasicrystalline (IQC) particles were determined in melt-spun ribbons of alloys based on the Al-Mn-Be alloy system. The sizes of the quasicrystalline particles ranged from a few tenths of nanometres up to 1 μm. Therefore, different methods were employed for characterizing their shapes: projection of quasicrystalline particles using transmission electron microscopy (TEM), cross-sections of IQCs on metallographically polished surfaces, and observation of deep-etched samples and extracted particles using a scanning electron microscope (SEM). It was discovered that icosahedral quasicrystalline particles preferentially grow in three-fold directions and have a tendency for faceting and adopting the shape of a pentagonal dodecahedron. The evolution of quasicrystalline shapes is systematically presented.