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Good Math by Mark C. Chu-Carroll

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Different Kinds of Symmetry

There are more kinds of symmetry than just mirrors. For example, look at the folloiwng figure, which shows multiple symmetries on a hexagon. A hexagon has two different kinds of mirror symmetries. But going beyond the mirror symmetry, it also has rotational symmetry: if you rotate a hexagon by 60 degrees, it’s indistinguishable from the hexagon before rotation.

images/pdf/hex-sym.png
Figure 12. Multiple symmetries—hexagon: Hexagons have multiple symmetries—two kinds of mirror symmetry and a rotational symmetry.

All sorts of transformations can be described by groups as long as there’s some way in which the transformation can be performed ...

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