In general usage, symmetry most often refers to ... and reflected across a horizontal plane). A footprint pattern like the above example, if extended to infinity in either direction, is invariant ...

This is one simple example of a tiling of the line that has translational symmetry. In two dimensions, there are many familiar examples of tilings of the plane that have this property as well. In each ...

For example, a mirror symmetry implies that our patterns will line up if we ... Since this restriction applies to all periodic decorations of the plane, these are widely referred to as the 17 ...