Rotation

We say a crystal has a symmetry axis of rotation when we can turn it by some degree about a point and the pattern looks exactly the same.

Think of the center of a pizza. If it is made so that all the pieces are the same size and have the same ingredients in the same places, then the pizza could be turned and you couldn't tell the difference. This means the pizza has rotational symmetry. The pizza on the left has rotational symmetry of 60 degrees.

What other foods have rotational symmetry?

If we look at crystals, a rotation of 180° followed by another rotation of 180° is equivalent to a rotation of 360° (we're back where we started). We call this a "two-fold axis," because repeating the operation twice returns the object to its original position. Crystals can have only 1-fold, 2-fold, 3-fold, 4-fold, and 6-fold rotation axes. Higher order rotation axes such as 5-fold, 7-fold, and higher cannot occur in crystals.