I was screwing around on this site this afternoon and my random scrolling happened to stop on the number 17. Apparently, that’s the number of wallpaper groups.

What’s a wallpaper group?

That’s what I wanted to know.

So I checked it out. Apparently, the wallpaper groups are the 17 possible symmetry groups in the plane. The groups classify patterns based on certain characteristics of symmetry. The Wikipedia page has a bunch of pretty pictures that help show the different symmetries as well as several patterns that fall into each group.

The groups themselves are named with Crystallographic notation. They start with either a p or a c (for primitive cell or face-centered cell, respectively) and then contain several letters or other letters to describe specific components of symmetry (read here!).

The shorthand name of one of the groups happens to be cmm (my initials!). Patterns with this type of symmetry can be turned upside down (e.g., be rotated 180 degrees) and still look the same. Its lattice is rhombus-shaped. It’s a pretty frequently-encountered pattern, as bricks (like in brick buildings) are often arranged utilizing this group of symmetry.

Here’s a pattern of cmm-type symmetry that I particularly like: