The structure comprises, in combination, lattice elements (1) with successive sides (1A) inclined in opposite directions; longitudinal connecting pieces (1B) and partial longitudinal connecting pieces (1C) for the joining of successive lattice clients (1) in alignment with each other; links (3) for connection between longitudinal connecting pieces (1B, 1C) of adjacent lattice elements (1) which have been brought together; components for mechanical connection (5, 7) between successive lattice elements (1) and/or components for mechanical and electrical connection (24, 26) between successive lattice elements; adaptors (61, 71) which may be fitted to said longitudinal connecting pieces (1B, 1C) for lighting or consumer units to be combined with the reticular structure.