In the course of a study on the role of magnesium in polar zincides of the heavier alkaline-earth elements, three intermetallic phases of the ternary system Ca-Mg-Zn were synthesized from melts of the elements and their structures were determined by means of single-crystal X-ray data. Starting from the binary zincide CaZn 11 , the phase width of the BaCd 11 -type structure reaches up to the fully ordered stoichiometric compound CaMgZn 10 [tI48, space group I4 1 /amd, a = 1082.66(6), c = 688.95(5) pm, Z = 4, R 1 = 0.0239]. The new compound CaMgZn 5 (oP28, space group Pnma, a = 867.48(3), b = 530.37(5), c = 1104.45(9) pm, Z = 4, R 1 = 0.0385) crystallizes in the CeCu 6 -type structure, exhibits no Mg/Zn phase width and has no binary border equivalent in the system Ca-Mg-Zn. Similar to the situation in CaMgZn 10 , one M position of the aristotype has a slightly larger coordination sphere (CN = 14) and is accordingly occupied by the larger Mg atoms. The third phase, Ca 2+x Mg 6-x-y Zn 15+y (hP92, space 219 group P6 3 /mmc, a = 1476.00(5), c = 881.01(4) pm, Z = 4, R 1 = 0.0399 for Ca 2.67 Mg 5.18 Zn 15.15 ) forms the hexagonal Sm 3 Mg 13 Zn 30 -type structure also known as μ-MgZnRE or S phase. A small phase width (x = 0-0.67; y = 0-0.58) is due to the slightly variable Ca or Zn content of the two Mg positions. The structure is described as an intergrowth of the hexagonal MgZn 2 Laves phase and the CaZn 2 structure (KHg 2type). All compounds exhibit strong Zn-Zn and polar Mg-Zn covalent bonds, which are visible in the calculated electron density maps. Their structures are thus herein described using the full space tilings of [Zn 4 ] and [MgZn 3 ] tetrahedra, which are fused to polyanions consisting of tetrahedra stars, icosahedra segments etc. and the large (CN = 18-22) Ca cation coordination polyhedra. Pseudo bandgaps apparent in the tDOS are compatible with the narrow v.e./M ranges observed for other isotypic members of the three structure types.