Wallpaper Groups: Part Two

Welcome back! In Part One of this blog series, I described how any 2D repeat pattern can be mapped to one of 17 wallpaper groups that describes the rotations, reflections, and other symmetries it contains.

You can read Part One here for some background and examples from the first 3 types of patterns.

In this post I’ll share 3 more types of patterns.

Group pg

Patterns in this group contain only glide reflections.

There is no point in the pattern where you can rotate it and get the same design back. In this leaf pattern, you can see that there are no rotations because all the leaves are pointing in the same direction. So if you rotate it around any point, the leaves will all point in a different direction.

There are also no reflections; to see this, try to draw a line where the pattern is a mirror image of itself. It doesn’t exist in this pattern.

There are glide reflections, and I’ve shown one such glide reflection axis with a dashed line. If you imagine the lower rectangle as the tile, then to match up with the top tile, you would need to reflect it over the dashed line and move it up (reflection and glide).

Group cm

Group cm patterns cannot be rotated, but they do contain reflections and glide reflections.

In this example, the pattern can be reflected along the solid lines. If we ignore the variety of colors, then the pattern can also be glide-reflected along the dashed line.

Group pmm

This group contains reflections in two directions and 180° rotations where the reflection lines intersect.

This pattern was inspired by a protea flower before it bloomed. The pattern can be reflected across each of the solid lines, and rotated 180° at each of the pink squares, where the reflection axes intersect.

This is another example of a pattern in group pmm.

That’s all for this post! In the next post we’ll keep moving on through the other pattern groups. Once you start to get the hang of this way of defining repeat patterns, it is fun to analyze the patterns you see around you. What kinds of rotations and reflections can you see in your clothing or textiles around your house?

I love talking about this topic, so if you have any questions or thoughts, please leave a comment!

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