For most of us, what we understand by symmetry is left-right reflection. That is what stands out when we look at the world around us, whether it is a face, a leaf, or a church.
So many things seem neatly divided down the middle, one side the mirror image of the other.
It makes perfect sense and is wonderfully satisfying to look at.
But there are other types of symmetry apart from reflection symmetry, and there are more dimensions than just the two we normally use as a reference for symmetry.
The other types of symmetry include ROTATION, TRANSLATION, and GLIDE (translation+reflection), and SCALE.
Anyone who has tiled their bathroom or kitchen, using different types of tile, will have probably used two or more of these symmetrical layouts to create their pattern.
Spotting different symmetries in the real world can become an obsession - (read Marcus du Sautoy's book "Finding Moonshine").