Wallpaper Groups: Part Five

Wallpaper Groups: Part Five

The final wallpaper groups allow for rotations of 120° (a third of a circle) or 60° (a sixth of a circle). I’m presenting these groups together since I find it helpful in each case to think of the diamond-shaped tile that you can identify in the pattern. That will make more sense after the first example!

Group p3

Patterns in this group have centers of rotation of 120° but no reflections. This isn’t a pattern group I have stumbled upon, so I reused my moon and sun motifs to try it out. The center of each sun is a center of rotation. The center point between the trio of half moon shapes and the center point between the trio of dots are also both rotation points.

The image on the right shows three of the tiles outlined. Each vertex is one of the centers of rotation.


Group p3m1

This next group has reflections. The diamond-shaped tile is symmetrical along its shorter diagonal (along the dashed blue line). If you extend those dashed blue lines, they are reflection lines for the entire pattern. All of the centers of rotation are at the intersections of the reflection lines.


Group p31m

In this group, we’ll also start with a diamond-shaped tile, but this time it will be symmetrical along the longer center line. Here I’m using motifs from my aster checkerboard pattern (see a scarf I made from this pattern on the right). I love how different the effect is from just changing the arrangement of elements!


I’ll show another couple of example from this group of collages I made. The key to distinguishing p31m from p3m1 is that p31m has centers of rotation that aren’t along the reflection lines.

It took me a bit to figure out what group these patterns belonged to. First I drew the reflection lines, and then identified the centers of rotation. One of the centers of rotation (the center point of the three tiles outlined) is not on a reflection line (the dashed blue lines), so that told me this pattern belonged to group p31m. Only after drawing the reflection lines and rotation points could I figure out what the diamond-shaped tile was.

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