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We present a method for fabricating quantum dots using seeded self-organized growth of GaAs/AlGaAs heterostructures on substrates patterned with inverted pyramids. This method produces, at the tip of each inverted pyramid, highly uniform quantum dots whose size and position can be accurately controlled. In addition, a system of connected GaAs and AlGaAs two-and one-dimensional nanostructures is identified in the inverted pyramids using cross-sectional atomic force microscopy. A substrate removal technique is used to optimally prepare our samples for optical studies, allowing the increase of the luminescence efficiency of the quantum dots by up to three orders of magnitude. Micro-photoluminescence and cathodo-luminescence spectroscopy are used to study in detail the bandgap structure of the connected nanostructures identified in the pyramids, which constitute a complex, but controlled, barrier …