When creating patterns that are basically flat from 3-dimensional materials, it is tempting to say that they have wallpaper symmetry. A better analysis uses the language of layer groups, which are groups of isometries of 3-space that leave a plane invariant. This article describes the relationship between wallpaper groups and layer groups, providing artistic illustrations of the principles involved. We explain how to create strands with desired symmetry and place them in space to make patterns that display a variety of weaving and looping.