List of Planar Symmetry Groups - Frieze Groups

Frieze Groups

The 7 frieze groups, the two-dimensional line groups, with a direction of periodicity are given with five notational names. The Schönflies notation is given as infinite limits of 7 dihedral groups. The yellow regions represent the infinite fundamental domain in each. Simple example images are given as periodic tilings on a cylinder with a periodicity of 6.

,
IUC
(Orbifold)		 Geo Schönflies Coxeter Fundamental
domain		 Example
p1
(∞∞)		 p1 C∞ +
p1m1
(*∞∞)		 p1 C∞v
,
IUC
(Orbifold)		 Geo Schönflies Coxeter Fundamental
domain		 Example
p11g
(∞×)		 p.g1 S2∞
p11m
(∞*)		 p.1 C∞h
,
IUC
(Orbifold)		 Geo Schönflies Coxeter Fundamental
domain		 Example
p2
(22∞)		 p2 D∞ +
p2mg
(2*∞)		 p2g D∞d
p2mm
(*22∞)		 p2 D∞h

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