We report structural and optical characteristics of single three-dimensionally (3D) confined GaAs/ AlAs structures grown by molecular beam epitaxy on [100] oriented square mesas patterned onto GaAs (001) substrates. By fabricating single structures and using AlAs barrier layers, we were able to clearly attribute luminescent spectral peaks to spatial origins in the grown structures. Observation with a scanning electron microscope and an atomic force microscope indicated that the structures on the mesas were pinched-off or truncated pyramids limited by sidewall {011} facets and a mesa-top facet. The observation also led to estimation of lateral width in the 3D confined structures, which decreased in proportion to a decrease in pattern width ranging from 1.6 to 0.2 mu m. This proportionality can be explained by adatom migration on the sidewalls towards the bottom region of the patterned substrates. The optical properties of the grown structures were investigated by microphotoluminescence measurements at 8 K. Photoluminescence (PL) images were first measured to attribute luminescent spectral peaks to quantum-well (QW) heterostructures spatially originating in a truncated pyramidal structure. We next performed spectroscopy on single 3D confined structures of various lateral widths by positioning and holding the mesa top of one isolated pyramidal structure at a time under laser illumination, The PL and PL excitation spectra exhibited distinct exciton peaks about 10 meV wide. As the lateral width decreased, the vertical layer thickness estimated by their emission wavelength increased, but it saturated at smaller lateral widths. The saturation can also be explained by the adatom migration on the sidewalls. When excitation power was lowered, PL spectra became a cluster of sharp peaks. Each sharp peak may be due to the recombination of the exciton trapped in QW layer thickness fluctuation. The cluster thus suggests that the broad spectral width is caused mainly by wide variation in QW layer thickness of 3D confined structures.