Question

Find all the rotational symmetries of a cube.

Answer 1

Rotational symmetries of Cube-

Counting the possible orientations of the cube we know that there are 24 rotational symmetries, by considering faces, edges or corners and their respective number of orientations, giving 6 * 4 = 12 * 2 = 8 * 3 = 24.

If you also want to know the rotations, instead of just counting the rotational symmetries. The rotations are-

• 6 rotations around axes through the middle of one of 6 pairs of opposing edges, with a rotation of 180°.

• 8 rotations around axes through one of 4 pairs of opposing corners, with rotations of 120° and 240°.

• 1 identity rotation that does nothing.

• 9 rotations around axes through the middle of one of 3 pairs of opposing faces, with rotations of 90°, 180° and 270°.