A regular hexagon makes

A regular hexagon has six sides, and its symmetry allows it to rotate around its center. Each rotation that results in the hexagon looking the same corresponds to one of the vertices pointing in the same direction as before.

To determine the angles of rotation for a regular hexagon:

1. The full circle is \(360^\circ\).
2. The hexagon can be rotated around its center by an angle of \( \frac{360^\circ}{6} = 60^\circ\).

This means that the hexagon can be rotated by any multiple of \(60^\circ\) and still look the same. Therefore, the acceptable rotations are:

- \(0^\circ\) (no rotation)
- \(60^\circ\) (first vertex)
- \(120^\circ\) (second vertex)
- \(180^\circ\) (opposite vertex)
- \(240^\circ\) (fourth vertex)
- \(300^\circ\) (fifth vertex)

After \(360^\circ\), the hexagon returns to its original position.

Thus, the regular hexagon makes turns on itself at multiples of \(60^\circ\) until coming around full circle.