Geometry: Plane Tiling Mathematica Package
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.


The function 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


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.






Assorted graphics manipulation functions lets you transform or cut graphics.

StarMotif
with parallel lines in four directidions using CutPolygon
, then scaling the polygons apart.
Assorted functions generates lattices or networks colored regularly. Here are some examples of triangular network with regularly directed edges.





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.

