Example Diagrams of Symmetry Groups

  1. Introduction
  2. Rosette groups
  3. Frieze groups
  4. Wallpaper groups


The following Diagrams illustrate the structure of symmetry groups in the euclidean plane. For this the blend over from an example ornament to a corresponding structure diagram. The example ornaments all come from the 1910 book The Grammar of Ornament by Owen Jones. Originally I created these images for my Diploma Thesis.

The diagrams are available primarily in the vector image formats PDF and SVG. They both tile a small rasterized version of the ornament which is embedded into the image files, and overlay the diagram. For this reason, the images require little storage memory and are still available in a quality suitable for print. The different sizes small and large therefore have little impact on the file size. Instead they affect the dimensions of graphical elements. The smaller images are well suited for two columns per page, while the larger ones look better using the full page width.

Both file formats were generated from the same raw material using different programs. I suggest you don't try to convert between these formats yourself, as most programs will perform such a conversion by rasterizing the whole image. High resulution raster images can be created from the vector formats. This is probably easier from SVG, e.g. Inkscape can export bitmaps from SVG files.

cc-by-sa License

The diagrams of symmetry groups displayed on and linkt to from this page are licensed under a Creative Commons Attribution-Share Alike 3.0 Germany License. So you must mention me, Martin von Gagern, as the author when you reuse these images, and you must also include a license notice. For additional rights and requirements please see the license deed, the full offical license text.

Rosette Groups

C1 C1
C4 C4
C6 C6
D1 D1
D4 D4
D11 D11

Frieze Groups

11 11
1g 1g
1m 1m
12 12
m1 m1
mg mg
mm mm

Wallpaper Groups

p1 p1
p2 p2
pm pm
pg pg
cm cm
pmm pmm
pmg pmg
pgg pgg
cmm cmm
p4 p4
p4m p4m
p4g p4g
p3 p3
p3m1 p3m1
p31m p31m
p6 p6
p6m p6m
cc-by-sa License