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A transformation of space (invertible map of the plane to itself) that
preserves distances is called an **isometry** of space. Every
isometry of space is of one of the following types:

- the
**identity**(which leaves every point fixed); - a
**translation**by a vector**v**; - a
**rotation**through an angle around a line*L*; - a
**screw motion**through an angle around a line*L*, with displacement*d*; - a
**reflection**in a line*P*; - a
**glide-reflection**in a line*P*with displacement vector**v**.

- 10.1 Formulas for Symmetries in Cartesian Coordinates
- 10.2 Formulas for Symmetries in Homogeneous Coordinates

*Silvio Levy
Wed Oct 4 16:41:25 PDT 1995*

This document is excerpted from the 30th Edition of the *CRC Standard Mathematical Tables and Formulas* (CRC Press). Unauthorized duplication is forbidden.