VW  CVM 1.1 
In order to construct a wallpaper function with pmg symmetry, our recipe instructs us to combine terms like cos(nX)cos(mY) and sin(nX)sin(mY) with certain parity restrictions . Early in our work with wallpaper we tried the function
which does indeed conform to the pmg recipe.
One easily checks that this does have the necessary translations, halfturns, reflections, and glide reflections to qualify as a wallpaper function with group pmg , but surely the most striking thing about the picture is the presence of antisymmetries.
The most noticeable antisymmetries may be the negating vertical mirrors. In addition to these, a thorough search reveals negating halfturns, glide reflections, and negating translations halfway along the diagonal of the cell.
The cell diagram for the pmg wallpaper shown above. Negating isometries are shown in green. 
In this example, by accidentally choosing the sum
A threedimensional view of the graph of this function illustrates that the blue mountaintops are
exact inversions of the fiery pits. The mirror lines are clearly visible as
straight lines running toward a vanishing point in the distance.

