We tabulate the possible valley degeneracies that can emerge due to band inversion for all 11 centrosymmetric point groups in Table . Exemplary arrangement of the carrier pockets around k0 are illustrated for each point group in Figure . The valley degeneracies depend on the point group symmetry of k0. For example, the maximum valley degeneracy that can be induced by band inversion corresponds to the total number of symmetry elements (rotation and mirror) of the point group, because each symmetry element can map a pocket to distinct points around k0. All point groups (except S2) have multiple valley degeneracies that are possible from band inversion however. This is due to carrier pockets being positioned on symmetry planes or axes. For example, valley degeneracies of either 2, 6, or 12 can emerge from k0 belonging to the D 3d point group (Figure ), such as the L-point in rock-salt compounds and the Γ-point in tetradymite compounds. A valley degeneracy of NV = 2 emerges when the carrier pockets are located on the 3-fold rotational axis along the out-of-plane direction, NV = 6 when the pockets are on trisecting mirror planes, and NV = 12 when the pockets are offset from both symmetry objects. The valley degeneracy is determined by the degree to which the bands are warped in different directions. Warping effects are direction-dependent as permitted by symmetry, leading to e.g. either a two-fold or six-fold degenerate conduction band in Bi2Te3. It is important to note that the maximum valley degeneracy when k0 belongs to a low-symmetry point group, such as S2 where N max V = 2, is lower than the achievable valley degeneracy from a high-symmetry point group, such as O h where NV ranges between 6 and 48 (Table ). The surge in the valley degeneracy from the O h point group can be attributed to the comparatively higher symmetry, which maps a carrier pocket to more positions than a low-symmetry group. Moreover, if k0 is repeated multiple times in the Brillouin zone, an even greater increase in the valley degeneracy is possible. For example, sufficient band inversion in rock-salt SnSe leads to the formation of 6 carrier pockets around each L-point; since there are 4 distinct L-points in the rock-salt Brillouin zone, the valley degeneracy is collectively NV = 24. As a result, band inversion can induce high valley degeneracy when it occurs at a high-symmetry k0 that is repeated multiple times in the Brillouin zone.