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The crystal structure of the decagonal phase in the system Al–Ni–Rh (d-Al-Ni-Rh) was analyzed in the five-dimensional embedding approach based on single-crystal synchrotron X-ray diffraction data. The structure can be described as a quasiperiodic packing of partially overlapping decagonal and pentagonal columnar clusters with ∼ 21 Å diameter and ∼ 4 Å period along the tenfold axis.