List of planar symmetry groups

From Wikipedia, the free encyclopedia

You have new messages (last change).

This article summarizes the classes of discrete planar symmetry groups:

  1. 2 infinite set of point groups
  2. 7 Frieze groups
  3. 17 wallpaper groups

Contents

[edit] Point groups

There are two classes of point groups, rotational and reflectional.

Point groups:

Example Symbols

Example C5		 Cn (n)
Cyclic group

Example D6		 Dn (*n)
Dihedral group

[edit] Frieze Groups

There are also 7 Frieze groups in the plane which have a fundamental line of symmetry and infinite fundamental domains.

Example
pattern		 Conway
symbols
patterns for the 7 frieze groups
  1. (∞∞)
  2. (∞x)
  3. (∞*)
  4. (*∞∞)
  5. (22∞)
  6. (2*∞)
  7. (*22∞)

[edit] Wallpaper groups

There are 17 wallpaper groups in the plane with finite fundamental domains.

Rotation
p2 (2222)
parallelogrammetic
p4 (442)
p3 (333)
p6 (632)
Maximum symmetry per lattice type
pmm (*2222)
rectangular
cmm (2*22)
rhombic
p4m (*442)
square
p6m (*632)
hexagonal
Mixed
p3m1 (*333)
p31m (3*3)
p4g (4*2)
Other
pm (**)
p1 (o)
pg (xx)
pmg (22*)
cm (*x)
pgg (22x)

[edit] See also

[edit] External references

Retrieved from "http://en.wikipedia.org../../../l/i/s/List_of_planar_symmetry_groups.html"