Point group

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Symbol-free definition

A point group in dimension n is a subgroup of the orthogonal group O_n(\R), or equivalently, a group of geometric symmetries which leave a particular point fixed.

When we use the term point group, we usually mean not just the abstract group, but rather its embedding as a subgroup of the orthogonal group.

A point group can thus also be regarded as a faithful linear representation of a group in terms of only isometries.

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