Wallpaper Groups: Part Four

Wallpaper Groups: Part Four

This blog post will cover wallpaper groups that have 90° rotational symmetry. They differ in what kinds of reflections and glide reflections appear in their patterns.

Group p4

This group allows rotations of 90°, but has no reflections or glide reflections. I created this pattern specifically to try out this pattern group, since I had never made a p4 pattern “by accident”!

This piece was part of my “Pattern Studies” show in 2019.

Group p4m 

This pattern group contains one of my favorite patterns, the checkerboard. This group has 90° rotations and reflection lines at 45° to each other.

The left image below shows how the checkerboard fits into this pattern group. You can rotate the checkerboard pattern 90° from the center of any cream square or golden square. The blue lines show where you can reflect the pattern vertically, horizontally, and along the diagonal. The dashed black lines show where the pattern has glide reflections.

Next to the checkerboard is one of my pieces that belongs to the same symmetry group. I’ve rotated it so it has the same points of rotation and reflection lines as the checkerboard.


Here it is in its original orientation. I love those bright pink dots, painted in opera pink! 

Another one of my patterns that fits into this group (if you ignore the floral variation) is my aster tiles design:

Group p4g

This is one of my favorite pattern groups, because I think the patterns it contains are so visually interesting.

The first pattern I made in this group is my fan pattern. This group has vertical and horizontal reflections, but not diagonal reflections.

One way to look at this pattern is as a tiling of a pinwheel pattern, as shown on the left below. This tile can be rotated 90° from the center of the tile as well as at each corner.

The way I usually see the pattern is as the groups of 4 fans as shown in the middle. The “tall” groups are in dark pink, and the “wide” groups are in cream. These groups are rotated versions of each other.

The right image shows the rotation points, perpendicular reflection lines in pink, and glide reflection lines in cream.


Do you see these pattern groups anywhere in your home or wardrobe?

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