A system for constructing spatial structures includes a nucleus into which a series of tubes lead, the tubes connecting adjacent nuclei. The nucleus is substantially spherical and hollow and is formed to two helmet-shaped pieces of different heights, having in their corresponding mouthpieces, flat annular fins which, when confronting each other, form flanges for coupling, by means of screws, the two pieces. The surface of the hollow sphere forming the nucleus has flat, round, annular, surfaced openings suitable for receiving the ends of the tubes to form the structure.