We have investigated the oxidation behavior of the threefold-symmetry surface of icosahedral AlPdMn quasicrystal by low-energy electron diffraction and Auger electron spectroscopy. Upon oxygen exposure at 740K, the predominantly planar surface develops facets of an Al-oxide layer, each facet oriented along a high-symmetry direction of the icosahedral bulk structure. While the facets along the fivefold-symmetry directions are structurally well-ordered, the facets along the twofold- and threefold-symmetry directions are structureless. The results are compared with the oxide formation on the fivefold-symmetry surface of icosahedral AlPdMn quasicrystal.