A tube and ball truss system for making a structural lattice which includes a plurality of hollow metal balls spaced in a three-dimensional array, each ball having a set of radial through-openings as well as an access opening on one side, adjacent ones of the balls being interconnected by metal tubes having an outer cylindrical wall and a central axially extending core joined by integral webs, the ends of the core having axially tapped holes engageable by clamping bolts extending through the through-openings in the balls. The ball surface is locally flattened to form land surfaces surrounding the through-openings for flat seating of the end surfaces of the tubes; indeed, the land surfaces are recessed to provide shallow socketed engagement and precise alignment with the ends of the tubes.