In contrast to earlier structure determinations of SnGa6Te10 and PbGa6Te10 (space group R32), which showed disordered distributions of Sn and Pb, it could be shown for SnGa6Te10, PbGa6Te10 and the new SnAl6Te10, that weak superstructure reflections can be observed in well crystallized samples, which indicate an ordering of Sn(Pb) in all three phases. The black, air stable solids (exept the Al-compound, which is air-sensitive) crystallize trigonally in one of the two enantiomorphic space groups P3121 and P3221. Symmetry considerations based on group-subgroup relations show the relationship between β-manganese and the trigonal structures of the title compounds, which are actually nonmetallic, filled β-manganese phases. Their structures consist of a sublattice of Te atoms, closely related to the topology of the β-manganese structure, in which two of four distorted octahedral (“metaprismatic”) holes per pseudocubic unit cell are occupied by Sn(Pb). Furthermore 12 of 100 distorted tetrahedral holes are occupied by Al(Ga) atoms. It can be shown, that only the ordered Sn (Pb) distribution breaks the rhombohedral symmetry of R32 and requires P3121/P3221. The complex three-dimensional connection pattern of tetrahedra and metaprisms is discussed with respect to the crystal chemical functionality of distinct atoms and the aid of electrostatic lattice energy calculations based on the MAPLE formalism. Finally some comments concerning the probably isotypical structures of CaAl6Te10, CaGa6Te10 and PbIn6Te10 are given.