The structure of the Al 2 O 3 - SiO 2 - MgO - P 2 O 5 sub> in the subsolidus area. The partition of the system into elementary tetrahedrons is shown, their volumes and degrees of asymmetry are calculated, a topological graph of the relationship of tetrahedra is constructed, and a geometric-topological characteristic of the phases of the system under study is given. For some pseudo-binary and three-component sections, the temperatures of the eutectics, as well as their compositions and the lengths of the connections are calculated. Areas of system compositions suitable for the technology of heat-resistant ceramic and heat-insulating materials are given. Tab. 4, ill. 3, bibliography: 23 titles.