What shape do grains of aluminum-copper-iron quasicrystals have?

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quasicrystal Figure 1: Hexagonal lattice of atomic sites.

Grains of aluminum-copper-iron quasicrystals take the shape of a pentagonal dodecahedron.1

This structure features 12 faces, each of which is a regular pentagon. The grains exhibit icosahedral symmetry, characterized by axes of fivefold rotational symmetry passing through the centers of these pentagonal faces, as well as twofold and threefold rotational symmetry axes passing through the edges and vertices, respectively. This geometric arrangement is consistent with the internal atomic structure of the material, which displays symmetries that are crystallographically forbidden in conventional crystals.1