Platelets of the Al—Pd—Mn decagonal phase have been observed to grow in epitaxy on the icosahedral modification of the same system. A resulting strain field in the icosahedral phase has been characterized using high-resolution electron microscopy. It appears that one fivefold axis is preserved, in coincidence with the tenfold axis of the decagonal phase. In the particular case of a thin icosahedral-phase domain squeezed in between two decagonal-phase platelets, the strain field can be qualitatively analysed in terms of combined phason–phonon strain fields.