Theorem. Every isometry of R^{3} belongs to exactly one of the types in the following chart. With each type is listed its orientation behavior (+ if orientation-preserving), the dimension of its fixed point set (with -1 for ``empty''), and the minimum number of mirror reflections in a factorization of an isometry of that type as the composition of mirror reflections. The fact that the listed pair of numbers is unique to each row guarantees that no two of the types are conjugate and that there is no overlapping of types.
| Type | Orientation | Fixed Locus | Mirrors |
| Identity | + | 3 | 0 |
| Rotation ( <> 1) | + | 1 | 2 |
| Translation ( <> 1) | + | -1 | 2 |
| Screw | + | -1 | 4 |
| Mirror reflection | - | 2 | 1 |
| Reflective rotation | - | 0 | 3 |
| Mirror glide | - | -1 | 3 |