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Mathematics

The Group of Symmetries of a Square: An Introduction to Groups

Quick fact

The symmetries of a square form a group known as the dihedral group D4, which contains exactly 8 distinct operations: 4 rotations and 4 reflections. This group appears in chemistry to describe the symmetry of molecules like xenon tetrafluoride.

Why this is interesting

Take a square piece of paper. You can rotate it or flip it—sometimes it looks exactly the same. How many different ways can you move it and still have it look identical? And what happens when you combine those moves?

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The Group of Symmetries of a Square: An Introduction to Groups

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