Siobhan Roberts in the New York Times:
“The symmetry of an object is described in terms of an action or transformation performed on the object,” said Doris Schattschneider, professor emerita of mathematics at Moravian University. “An object has symmetry or is symmetric if it appears unchanged after the transformation.”
Given its patchwork construction and graphic patterns, a soccer ball can have two types of symmetry: reflection symmetry and rotation symmetry. Reflection symmetry means what it sounds like: that the object “has two identical halves that are mirror images of each other,” in Dr. Schattschneider’s words. Rotation symmetry means an object looks exactly the same as its starting position after a rotation of less than 360 degrees. For instance, a square looks identical four times when rotated every 90 degrees about its center. A perfect cube has a total of 24 such rotational symmetries — rotating around various axes piercing face-to-face, corner-to-corner, and edge-to-edge.
More here.
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