Math
Wallpaper groups
Draw a seed motif and generate all 17 wallpaper groups using lattice translations, rotations, reflections and glide reflections.
Try this
Select any of the 17 wallpaper groups. Click to append a vertex to the seed stroke; it repeats by exact lattice isometries. Gold marks its start, purple indicates reflected copies, white outlines a conventional translation cell.
Equations used in the module
Equations x′ = Ax + t in fractional lattice coordinates Allowed rotation orders: 1, 2, 3, 4, 6 Reflection det A = −1; glide = reflection + parallel translation Fundamental-domain area = conventional cell area / general-position multiplicity
