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We report on a numerical model of quasi-1-D and quasi-0-dimensional semiconductor heterostructures. This model is strictly based on experimental structures of cylindrical nanocolumns of AlGaAs grown by molecular-beam epitaxy in the (1 1 1) direction. The nanocolumns are of 20-50 nm in diameter and 0.5-1 μm in length and contain a single GaAs quantum dot of 2 nm in thickness and 15-45 nm in diameter. Since the crystal phase of these nanowires spontaneously switches during the growth from zincblende (Zb) to wurzite (Wz) structures, we implement a continuum elastic model and an eight-band k→ · p→ model for polymorph crystal structures. The model is used to compute electromechanical fields, wave-function energies of the confined states and optical transitions. The model compares a pure Zb structure with a polymorph in which the Zb disk of GaAs is surrounded by Wz barriers and results are compared to experimental photoluminescence excitation spectra. The good agreement found between theory and features in the spectra supports the polyphorm model.