Click flag to see three different rotational symmetries in a pattern from the Alhambra palace. The rotating outlines highlight a 6-fold, 3-fold, and a 2-fold rotational symmetry (together known as 6-3-2 symmetry). Stop, then press "t" to see translational symmetry. The whole pattern can shift left or right, up or down, and the pattern outlines stays the same. Spacebar restores outlines' original positions.
There are dozens of tiling patterns in the Spanish Alhambra palace tilings, showing different kinds of symmetry. There are 17 planar symmetry groups evident there (no more are possible), and they are the same 17 symmetries used in crystallography. These show the basic rules of reflection, rotation, translation and “glide reflection.” I used one particular Alhambra pattern to show three kinds of symmetry. You can also shift ("translate") the pattern up, down, sideways, and the pattern is the same. I drew the original picture in photoshop, roughly copying one I saw in a photo from the Alhambra, in Granada. You can spot it in an episode of the very old series "the Ascent of Man" by Bronowski.
