Why do sound waves travel at the same speed in every direction in icosahedral quasicrystals?

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quasicrystal Figure 1: Hexagonal lattice of atomic sites.

In icosahedral quasicrystals, sound waves travel at the same speed in every direction because of the material's exceptionally high rotational symmetry.

While sound speeds in most materials vary depending on the direction of propagation relative to the crystal's axes, the icosahedron is geometrically closer to a sphere than standard crystal structures like cubes. This high degree of symmetry renders the speed of sound independent of the direction in which the wave propagates. Consequently, only two elastic constants are required to define the acoustic properties of these materials, whereas crystals with lower symmetry require significantly more—up to 21 constants in some cases.1