| The symmetry requirement for cubic materials: Body diagonals (orange solid lines) of a cubic unit cell serve as the four axes of threefold rotational symmetry. They are the sufficient and necessary conditions for the cubic crystallographic point groups. On the contrary to some common misconceptions, cubic materials do not need to have any four-fold rotational symmetry.

Contexts in source publication

Context 1

... we focus our discussions on cubic materials characterized by the cubic crystallographic point groups. As illustrated in Figure 1, the symmetry conditions include four axes of threefold rotational symmetry that can be identified with the body diagonals of a cubic unit cell ( Bückmann et al., 2014;Dirrenberger et al., 2013;Authier, 2003). Rather counterintuitively, this symmetry requirement does not include any axis of four-fold (90 degree) rotational symmetry (Ashcroft and Mermin, 1976, p. 121). ...

Context 2

... materials are anisotropic elastic materials that satisfy the symmetry requirements illustrated in Figure 1, and their stiffness matrix is given by eq. 13. If the equal-speed criteria for longitudinal and transverse waves, as given in eq. 18, also holds in a cubic material, then we can have stable propagation of any spin angular momentum carried by bulk elastic waves. ...