Explore Symmetries

35 different tessellation symmetries underlie the artworks on this site. For details about a symmetry, including a live diagram and example artworks, click its icon in the chart at right. below.

Related symmetries are grouped together in the chart, based on how many different ways tiles are oriented. For example, tiles in a “3-way” symmetry appear in 3 rotated orientations, while tiles in a “2-way with flip” symmetry appear in 2 flipped orientations.

In the chart, “flag” or “tree” graphics help show how tiles are rotated and/or flipped. The graphic is a tree when tiles are symmetrical across a central “mirror”, and a flag otherwise.

(To find symmetries by wallpaper group, Heesch type, IH type, or Mohr type, please see the Summary Table.)

Choose symmetry: