By the reflection-generation theorem, an element of is a product of at most two reflections. The determinant of a reflection is . If the determinant is , the element is one reflection. If the determinant is , it is either the identity or a product of two reflections in nonparallel planes.

A product of two reflections in nonparallel planes fixes only the origin: a nonzero fixed vector would make the two normal vectors parallel. Hence a nonidentity element of is a rotation about .