The metal-rich compounds R4PdMg (R = Ca, Eu, Tb-Lu), R4AgMg (R = Ca, Yb), R4PtMg (R = Eu, Tb-Lu), and R4AuMg (R = Ca, Eu, Yb) were synthesized by induction melting of the elements in sealed tantalum tubes in a water-cooled sample chamber. All samples were characterized by powder X-ray diffraction. The structures of Ca4Ag0.948Mg and Yb4PdMg were refined on the basis of single-crystal X-ray diffractometer data: Gd4RhIn type, F 4̄3m, a = 1434.6(1) pm, wR2 = 0.0269, 523 F2 values, 18 variables for Yb4PdMg and a = 1485.78(7) pm, wR2 = 0.0188, 617 F2 values, 20 variables for Ca4Ag0.948Mg. For the first time small defects on the 16e transition metal site of a Gd4RhIn-type compound have been observed, and the first compounds of this structure type with the divalent rare earth elements europium and ytterbium as well as with calcium are reported. The striking structural motif of these compounds (exemplary for Ca4Ag0.948Mg) is the clear segregation of two alkaline earth elements into two different substructures, calcium forming trigonal prisms around the silver atoms and magnesium forming covalently bonded tetrahedra (Mg-Mg 328 pm). The latter are embedded in larger cavities of the adamantane-like three-dimensional network of edge- and corner-sharing AgCa6 trigonal prisms. This is evident from the chemical bonding analysis of the electronic structure by ab initio calculations. The density of states shows s-like metallic conductivity with an active role played by the Ag d states within the valence band and for the bonding with calcium. Temperature-dependent magnetic susceptibility data of Eu4PdMg and Eu4PtMg show Curie-Weiss behavior above 230 K with experimental magnetic moments of 7.94(1) and 8.00(1) μB per Eu atom for the palladium and platinum compound, respectively. Ferromagnetic ordering is detected at the comparatively high Curie temperatures of 150.1(5) (Eu4PdMg) and 139.1(5) (Eu4PtMg) K. Magnetization measurements at 3 K show full parallel spin alignment and the typical behavior of soft ferromagnets.