Study of quasicrystals may shed light on the most basic notions related to the quantum critical point observed in heavy fermion metals. Experimental measurements on an Au –Al– Yb quasicrystal have revealed a quantum critical point defining the divergence of the magnetic susceptibility as temperature tends to zero. It is suggested that the electronic system of some quasicrystals is located at a quantum critical point without tuning, while quasicrystals exhibit the typical scaling behaviour of their thermodynamic properties and belong to the well-known family of heavy fermion metals.