We report on InGaAs quantum disks (QDks) controllably formed on the top (001) facet of nano-patterned GaAs pyramidal platforms. The QDks exhibit pyramidal shape with special facets and varied dimensions, depending on the GaAs pyramidal buffer and the amount of InGaAs deposited. The formation of QDks is explained by the overgrowth of an InGaAs layer and thereafter coalescence of small InGaAs islands. Photoluminescence (PL) characteristics of ensemble QDks and exciton features of individual QDks together demonstrate that we may achieve a transition from zero-dimensional (0D) to two-dimensional (2D) quantum structure with increasing QDk size. This transition provides the flexibility to continuously tailor the dimensionality and subsequently the quantum confinement of semiconductor nanostructures via site-controlled self-assembled epitaxy for device applications based on single quantum structures.