The low-temperature icosahedral phase, which forms below approximately 700°C near the alloy composition Al71Pd21Mn8has been investigated by means of electron diffraction. Precise analysis of diffraction patterns indicates that the Bravais lattice of the low-temperature phase isPtype, different from the formerly proposedFtype. The six-dimensional lattice parameter of this newP-type lattice is determined to beaP= 20.881 Å by powder X-ray diffraction and is related to the high-temperatureF-type iscosahedral phase byaP= τaF, where τ andaFdenote the golden mean and the six-dimensional lattice parameter respectively of the high-temperature phase. The low-temperature transformation can be understood by a small breaking ofFsymmetry caused by superlattice ordering. A model of the required configuration of atomic surfaces (acceptance regions) is discussed by using the six-dimensional ‘diamond’ lattice. This diamond lattice has a lattice parameteraF2= 2aFand is related to the aboveP-lattice by a scaling transformation.