4, or 6 (the crystallographic restriction theorem). See also Point group Point groups in three dimensions Point groups in four dimensions One-dimensional symmetry group External links , Geometric Transformations and Wallpaper Groups: Symmetries of Geometric Patterns (Discrete Groups of Isometries), by Lance Drager. Point Groups and Crystal Systems, by Yi-Shu Wei, pp. 4–5 The Geometry Center: 2.1 Formulas for Symmetries in Cartesian Coordinates (two dimensions) Euclidean symmetries Group theory