In a sequence of temperature-dependent solid-state reactions in the system CaO-Al2O3-MgO the formation of the ternary phase Ca3Al4MgO10 or C(3)A(2)M has been studied. Whereas the compound could not be prepared at 1200 degrees C, a yield of 85 wt.-% of Ca3Al4MgO10 was obtained at 1320 degrees C (incongruent melting point: 1330 degrees C). Powder diffraction data compare well with results of previous investigations from the 1960s. Single crystals of Ca3Al4MgO10 could be retrieved from the sinter-pellets. Basic crystallographic data are as follows: orthorhombic symmetry, space group Pbcm, a = 5.14073(8), b = 16.7576(2), c = 10.70977(16) angstrom, V = 922.61(2) angstrom(3), Z = 4. Using synchrotron diffraction data it was possible to solve the crystal structure. Least-squares refinements resulted in a residual of R(|F|) = 0.021 for 1000 independent observed reflections with I > 2 sigma(I) and 97 parameters. The structure contains [TO4]-tetrahedra (T=Al,Mg) forming a three-dimensional (3-D) framework whose topological characteristics have been determined. Al-Mg distributions on the different T-sites have been studied. The calcium cations are located in voids of the network. More than 50 years after its first observation our investigation clarifies the crystal structure of a compound belonging to a system that is of relevance for several fields of materials science.