PlaneTiling is a Mathematica package that draws any of the 17 wallpaper patterns. This page shows some of examples of what this package can do.
WallpaperPlot allows plotting of any periodic wallpaper design. User specifies the symmetry type and motif. This means that it'll plot any periodic tilings, Islamic patterns, or Celtic knots designs. In this example, it has symmetry 3*3 (p3lm) and using pentacle as motif.WallpaperPlot can also plot the symmetry diagram of wallpapers. Shown here are wallpaper groups with 3-fold symmetries. Any symmetry element graphics can be user specified. For example, the last image displays the rotation elements of group *632 (p6m), using numbers instead of traditional symbols.
StarMotif with parallel lines in four directidions using CutPolygon, then scaling the polygons apart.
PolygonMotif and two StarMotif with different parameters, then the motifs are mapped to a triangular lattice generated by LatticeCoordinates.
LineTransform is recursively applied to a triangular network, then CookieStamp2DGraphics cuts out a nice hexagon boundary.
