Powder X-ray diffraction, electron diffraction and electron microscopic experiments, including high-resolution electron microscopy, have revealed that the Al─Cu─Fe icosahedral phase has a higher degree of structural perfection than other known icosahedral phases. This icosahedral phase exhibits clear equal thickness fringes in bright and dark-field images and also sharp diffraction spots with small Bragg angles, both of which have not been observed in other icosahedral phases. A scaling rule by the golden mean τ along the fivefold, threefold and twofold axes was found in reciprocal space of this icosahedral phase. In the high-resolution electron micrographs observed along the twofold axis, this scaling rule was also recognized to be present in real space. This fact suggests that the Al─Cu─Fe icosahedral phase belongs to a different class of icosahedral phase from the one to which belong other icosahedral phases having a scaling rule of τ3.