An apparatus and method for synthesizing a combinatorial library comprising a plurality of chemical compounds such that the chemical composition of each compound is easily tracked. The library compounds are synthesized on solid-phase supports, which are spatially arranged in frames during synthesis according to a predetermined protocol, such that each solid-phase support passes through a series of unique spatial 2D or 3D addresses by which the chemical composition of each compound may be determined at any point during synthesis. Solid-phase supports include hollow tubular-shaped lanterns and gears.