Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about th...

Question

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

A. 120 degrees
B. 60 degrees
C. 90 degrees
D. 180 degrees

Accepted Answer

The minimum angle of rotation is 120 degrees. A cube has four body diagonals, each connecting two opposite vertices (corners) through the interior center. When one such diagonal is aligned with the vertical axis and the cube is rotated about it, the three faces meeting at the top vertex cycle among each other. The symmetry group of the cube includes 3-fold rotational symmetry about each body diagonal, meaning rotating by 360/3 = 120 degrees maps the cube onto itself.

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 A. 120 degrees B. 60 degrees C. 90 degrees D. 180 degrees