Discussion
Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The magnitude of the minimum angle of rotation is
Answer: A
The minimum angle is 120°.
A body diagonal of a cube passes through two opposite vertices. At each of those vertices three edges and three faces meet, arranged symmetrically around the diagonal. A rotation of one third of a turn, 120°, carries each of these edges and faces onto the next, so the cube looks the same.
A 60° rotation would need six-fold symmetry about the diagonal, which the three edges at a vertex do not have. 90° is the symmetry about an axis through the centres of opposite faces, and 180° is not the smallest such rotation.
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