The title compounds were obtained by reaction of the elemental components with an excess of aluminum after dissolving the matrix in hydrochloric acid. The compounds LnRe(2)Al(10) (Ln = Ho-Lu) crystallize with a new structure type, which was determined from single-crystal X-ray data of LuRe2Al10: Cmcm, a = 929.1(1) pm, b = 1027.7(2) pm, c = 2684.1(5) pm, Z = 12. The two different lutetium atoms of the structure are coordinated by four rhenium and 16 aluminum atoms, while the two rhenium positions are in distorted icosahedral coordination of two lutetium and 10 aluminum atoms. The 12 different aluminum atoms have between 12 and 14 neighbors, of which two are rhenium and one or two an lutetium atoms. The structure may be considered as a stacking variant of the recently determined structure of YbFe2Al10. Both structures are related to that of ThMn12. They contain hexagonally close-packed, puckered sheets similar to those known from the close-packed TiAl3-type structure. In LuRe2Al10 and YbFe2Al10 these sheets of the compositions Re2Al6 and Fe2Al6, respectively, alternate with less densely packed layers of the composition LnAl(4), The crystal structures of YbRe2Al10 (LuRe2Al10 type, 930.7(2) pm, b = 1029.3(2) pm, c = 2687.9(5) pm) and NdRe2Al10 (CaCr2Al10 type, a = 1293.7(1) pm, c = 517.4(1) pm) were also refined from single-crystal X-ray data. The refinements of the occupancy factors of these as well as those of 20 other intermetallic compounds with high aluminum content indicate a seemingly slightly lower (on average 2-3%) scattering power for the aluminum positions in all cases. This is ascribed to the differing electron distributions in the free and in the bonded aluminum atoms. The cell volume of YbRe2Al10 indicates a mixed or intermediate +II/+III valence of the ytterbium atoms.