A regular 24-sided polygon is rotated with its center of rotation at its center.

What is the smallest degree of rotation needed to map the polygon back on to itself?

The smallest degree of rotation is called the angle of rotation. This can be calculated by dividing the angle of full rotation by the number of sides of a regular polygon. Since a full rotation is 360 degrees, we divide 360 by 24.

Thus, the smallest rotation needed to map the polygon back to itself is 15 degrees.