Let's start with point symmetry, i.e., operations that leave one point invariant. This is just like the group theory you learn in quantum mechanics, but the labels and symbols we'll use are the crystallographic symbols you'll find in the International Tables for Crystallography.
First, we'll look at rotation axes. These are called n-fold axes. The amounts of rotation are 360/n degrees. Here are some examples and symbols.
Other point operations:
If the mirror is in the plane of the board, the symbols look like this:
Two other kinds of point operations are the inversion center and the rotatory inversion operations.
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