A cube has 24 rotational symmetries. These are the orientation-preserving motions that return the cube to an indistinguishable position, including the identity rotation and 23 nontrivial rotations.
The rotations fall into three main families. Around the three axes through opposite face centers, a cube can turn by 90°, 180°, or 270°, giving 9 rotations. Around the six axes through opposite edge midpoints, it can turn 180°, giving 6 more. Around the four body diagonals joining opposite vertices, it can turn 120° or 240°, contributing 8. Together with the identity, the total is 1 + 9 + 6 + 8 = 24.
A common mix-up is the number 48. A cube has 48 total symmetries when reflections and inversion are included, but only 24 preserve orientation and count as rotations. Another possible confusion is 13: that is the number of rotational axes, not the number of rotational operations. The cube’s rotational symmetry group is the octahedral group, isomorphic to the permutation group S₄.