Unlike the hexagonal cross-sections, core-shell NWs with triangular cross-sections possess both spontaneous and piezoelectric polarizations corresponding to the two orientations depicted in Fig. . The first case we discuss is the (0001) Ga-face triangular core-shell NW. Running the main_scf_dirichlet command at the MATLAB prompt in the triangular_Ga_face_coreshell folder will output the wavefunctions and total electron densities shown in Fig. For the N-face configuration, the polarization results in a large negative surface charge to accumulate at the (000 1) interface and smaller positive surface charges along both semipolar interfaces. Consequently, donor electrons in the NW are repelled from the N-face but attracted to the adjacent positively-charged surfaces. The system reaches an electrostatic equilibrium by creating a localized electron gas near the vertex opposite to the negatively-charged (000 1) interface. It is also worth noting that a few of the lowest-energy wavefunctions shown in Fig. are doubly (or almost doubly) degenerate. Specifically, the wavefunctions corresponding to E 2 and E 3 are nearly degenerate and resemble a geometric reflection of each other about the x = 0 plane. The wavefunctions corresponding to E 4 and E 5 are also nearly degenerate, with the former having two horizontal nodal planes and the latter having one horizontal nodal plane and one vertical nodal plane at x = 0. Similarly, the wavefunctions corresponding to E 6 and E 7 are almost nearly degenerate, with the former having three horizontal nodal planes and the latter having two horizontal nodal planes and one vertical nodal plane at x = 0. As the energy of the individual wavefunctions increases, the charge distribution expands further down each semipolar face, leading to a total electron density that is primarily localized at the vertex of the triangular NW. Additional calculations with the HADOKEN code (not shown in Fig. ) have shown that small core sizes tend to favor quantum 1DEGs, since the magnitude of the electron density at the vertex decreases (and starts to extend symmetrically along the two semipolar faces) as the core size increases.