Question

this image has rotational symmetry. what is the smallest number of degrees you need to rotate the image for it to look the same?

Explanation:

Step1: Identify rotational symmetry order

A soccer ball (truncated icosahedron) has 5-fold rotational symmetry around axes through the center of a black pentagon and the opposite pentagon. The order of rotational symmetry here is 5.

Step2: Calculate smallest rotation angle

Divide full rotation (360°) by symmetry order.
$\frac{360^\circ}{5} = 72^\circ$

Answer:

$72^\circ$