Bearded Geology

In celebration of winter weather (or disdain of it, your choice), I thought I'd do a brief post on beds, but not the geological kind. This post is mainly in response to a bedsheet set made by Cannon that I own. The following image is a photograph of the snowflake pattern on my bed sheets. For those of you who have taken a mineralogy class (especially my mineralogy labs), what kind of rotational symmetry do you see in the three different snowflake patterns? I see five-fold, six-fold, and eight-fold rotational symmetry: In crystallography, there are only five rotational symmetry patterns: one-fold, two-fold, three-fold (triangular), four-fold (square), and six-fold (hexagonal). You can repeat patterns with these symmetries across a two-dimensional plane in some arrangement to fill the entire plane. Five-fold, seven-fold, and anything higher is forbidden in classical symmetry; you cannot repeat these patterns in any arrangement without leaving gaps between the pattern.  In the above i