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The structure of ζ´-Al80Mn16Co4 was analyzed using single-crystal X-ray diffraction. The diffraction pattern indicated that the ζ´-AlMnCo phase has a hexagonal unit cell with a space group P63/m, a = 30.5173(5) Å, c = 12.4742(2) Å, and the a-axis is 3 -times as large as that of the ζ-phases in the Al-Cr-Cu and Al-Cr-Ni systems. Mn atoms prefer icosahedral coordination similar to that of Cr in the ζ-phase, and the Co atoms are located in the interstitial area formed by the connection of the icosahedra. The icosahedral connection of the ζ´-phase is well characterized by the I3 cluster, a fragment of vertices sharing 3 icosahedra. The structural features of the superstructure are associated with the distribution of Co in the interstitial area.