The structures of two novel Zintl phases, Ba6Mg5.2Li2.8Si12 and BaMg0.1Li0.9Si2, are presented. Both compounds contain chains in cis-trans conformation. The silicon partial structure of Ba6Mg5.2Li2.8Si12 (C2/m; a = 1212.0(1), b = 459.78(4), c = 1129.10(9) pm; beta = 91.77(2)degrees; Z = 1) is built of unbranched, planar Si-6 chains while BaMg0.1Li0.9Si2 (Pnma; a = 725.92(5), b = 461.36(3), c = 1169.08(8) pm; Z = 4) consists of infinite Si-n chains. The compounds show all electronic and structural characteristics that are typical for the special subset of Zintl phases with highly charged planar anions. The structures of the new compounds, as well as that of Ba2Mg3Si4, can be derived from the common parent type BaMg2Si2. It is shown that a comprehensive picture of a chemical twinning based on BaMg2Si2 can be derived.