# Cyclic symmetry in three dimensions

In three dimensional geometry, there are four infinite series of point groups in three dimensions (*n*≥1) with *n*-fold rotational or reflectional symmetry about one axis (by an angle of 360°/*n*) that does not change the object.

They are the finite symmetry groups on a cone. For *n* = ∞ they correspond to four frieze groups. Schönflies notation is used. The terms horizontal (h) and vertical (v) imply the existence and direction of reflections with respect to a vertical axis of symmetry. Also shown are Coxeter notation in brackets, and, in parentheses, orbifold notation.

** C_{2h}, [2,2^{+}] (2*)** and

**of order 4 are two of the three 3D symmetry group types with the Klein four-group as abstract group.**

*C*, [2], (*22)_{2v}*C*applies e.g. for a rectangular tile with its top side different from its bottom side.

_{2v}In the limit these four groups represent Euclidean plane frieze groups as C_{∞}, C_{∞h}, C_{∞v}, and S_{∞}. Rotations become translations in the limit. Portions of the infinite plane can also be cut and connected into an infinite cylinder.