The crystal structure of the complex La43Ni17Mg5 ternary phase was solved and refined from X-ray single crystal diffraction data. It is characterized by a very large unit cell and represents a new structure type: La43Ni17Mg5 - orthorhombic, Cmcm, oS260, a = 10.1895(3), b = 17.6044(14), c = 42.170(3) angstrom, Z = 4, wR1 = 0.0598, wR2 = 0.0897, 4157 F-2 values, 176 variables. The crystal structures of the La-rich La-Ni-Mg intermetallic phases La4NiMg, La23Ni7Mg4, and La43Ni17Mg5 have been comparatively analyzed. The constitutive fragments of these structures are binary polyicosahedral core-shell clusters of Mg4La22 and Mg5La24 compositions together with binary polytetrahedral clusters of nickel and lanthanum atoms. The structures of the Mg-La clusters are described in detail as a unique feature of the analyzed intermetallic phases; the dodecahedral Voronoi polyhedra are proposed as a useful tool to characterize polyicosahedral clusters. The arrangements of the building units in the studied phases show some regularities; particularly the i(4)3, i(5)3 and L-i(4) units, made up of polyicosahedral clusters and analogous to the Kreiner i(3) and L units, are proposed as structural blocks.