Ebert et al. [Phys. Rev. Lett. 77, 3827 (1996)] have fractured icosahedral Al-Mn-Pd single crystals in ultrahigh vacuum and have investigated the cleavage planes in-situ by scanning tunneling microscopy (STM). Globular patterns in the STM-images were interpreted as clusters of atoms. These are significant structural units of quasicrystals. The experiments of Ebert et al. imply that they are also stable physical entities, a property controversially discussed currently. For a clarification we performed the first large scale fracture simulations on three-dimensional complex binary systems. We studied the propagation of mode I cracks in an icosahedral model quasicrystal by molecular dynamics techniques at low temperature. In particular we examined how the shape of the cleavage plane is influenced by the clusters inherent in the model and how it depends on the plane structure. Brittle fracture with no indication of dislocation activity is observed. The crack surfaces are rough on the scale of the clusters, but exhibit constant average heights for orientations perpendicular to high symmetry axes. From detailed analyses of the fractured samples we conclude that both, the plane structure and the clusters, strongly influence dynamic fracture in quasicrystals and that the clusters therefore have to be regarded as physical entities.