In order to test for the true intrinsic properties of icosahedral i-Al-Cu-Fe quasicrystals, we performed investigations of magnetism, electrical resistivity, thermoelectric power, and thermal conductivity on a single-crystalline Al64 Cu23 Fe13 quasicrystal grown by the Czochralski technique. This sample shows superior quasicrystallinity, an almost phason-free structure, and excellent thermal stability. Magnetic measurements revealed that the sample is best classified as a weak paramagnet. Electrical resistivity exhibits a negative temperature coefficient with ρ4 K =3950 μΩ cm and R= ρ4 K ρ300 K =1.8, whereas the thermopower exhibits a sign reversal at T=278 K. Simultaneous analysis of the resistivity and thermopower using spectral-conductivity model showed that the Fermi energy is located at the minimum of the pseudogap in the spectral conductivity σ (ε). Thermal conductivity is anomalously low for an alloy of metallic elements. Comparing the physical properties of the investigated single-crystalline Al64 Cu23 Fe13 quasicrystal to literature reports on polycrystalline i-Al-Cu-Fe material, we conclude that there are no systematic differences between the high-quality single-crystalline and polycrystalline i-Al-Cu-Fe quasicrystals, except for the hindering of long-range transport by grain boundaries in the polycrystalline material. The so far reported physical properties of i-Al-Cu-Fe appear to be intrinsic to this family of icosahedral quasicrystals, regardless of the form of the material. © 2007 The American Physical Society.