The results of theoretical calculations of the subsolidus structure of the four-component system MgO – CaO – Al2O3 – Cr2O3 are presented, taking into account the three-component compound Сa6Al4Cr2O15. Thermodynamic and geometric topological analysis methods were used to establish stable conodes in the specified system. When dividing the concentration tetrahedron MgO – CaO – Al2O3 – Cr2O3 into elementary ones with the involvement of a geometro-topological analysis, it is possible to make an unambiguous closure to the elementary tetrahedron of faces with incident edges (connodes) through a common vertex. The use of this method allows to minimize the number of necessary thermodynamic calculations. The tetrahedra of the MgO – CaO – Al2O3 – Cr2O3 system, taking into account the stable phases, is caused by the presence of three "internal" conodes passing through the three-dimensional space of the concentration tetrahedron: Сa6Al4Cr2O15 – MgO; MgCa3Al4O10 – CaCr2O4, CaCr2O4 – MgAl2O4, which determine the presence of 14 elementary tetrahedra in the subsolidus region. The lengths of conodes and volumes of elementary tetrahedra were calculated taking into account barycentric coordinates and elements of Euclidean geometry. The phases included in the composition of the tetrahedron with the largest relative volume and the smallest asymmetry CaCr2O4 – СaAl2O4 –MgAl2O4 – MgO (185.6 ‰ and 2.55, respectively) have the highest probability of existence in the system, which will allow the development of a sustainable technology for creating composite materials based on calcium aluminochromite cement, with periclase as an aggregate, without special techniques dosage of initial components. At the same time, in the event of a violation of the technological process, magnesium aluminate spinel will be synthesized in the composition of the unformed material, which will not lead to deterioration of the performance characteristics of the composite used. It should be noted that elementary tetrahedra with a high degree of asymmetry, which require appropriate dosage accuracy when predicting the phase composition of synthesized composite materials, are located in areas of the system that are not technologically advantageous from the point of view of obtaining unformed refractories based on special binder materials, and are interest for materials scientists in the ceramic and refractory industries.