The crystal structure of averievite, Cu5O₂(VO₄)₂·nMX has been determined. Trigonal system, space group P3, a = 6.375(1), c = 8.399(1) Å, V = 295.6(1) ų, Z = 1, D_x = 4.01(1) g/cm³. The atomic arrangement is characterized by infinite nets parallel to (001) composed of [OCu₄]⁶⁺ tetrahedra linked via corners in hexagonal rings. The bases of neigbouring tetrahedra are in one plane and their non-shared corners are turned to the opposite sides. The [VO₄]^3- tetrahedra are attached to the bases of [OCu₄] tetrahedra. There are large (R >3.2 Å) channels in the structure where large molecular particles can enter. The comparison of the averievite structure with related compounds (in particular, copper oxovanadates) is given from the point of view of [OT₄] polyion crystal chemistry.