VW  CVM 1.1 
We refer to the reflection about the main diagonal of the square as M_{m}, the main diagonal mirror, and to reflection about the line joining midpoints of adjacent sides as M_{e}, the eccentric mirror. As usual, L is used for the related glide reflections, whose meanings we hope are clear from context. R_{4} will indicate rotation of a quarter turn about the origin. Some of these are indicated in the diagram.
The square lattice cell 
There is a bewildering variety of relationships among these isometries, but we list only a few useful ones: d M_{e} = M_{m}, M_{m} M = h^{2} R_{4}.
Every type for which the square lattice is needed has R_{4} as either a positive or negating symmetry. Therefore every pattern has a positive halfturn and we may start with terms of the kind listed for the rectangular cell types with halfturns . Because we require combinations of these terms, let us adopt shorthand notation as follows:
C^{+}(n,m) = cos(nX) cos(mY) + cos(mX) cos(nY)
C^{}(n,m) = cos(nX) cos(mY)  cos(mX) cos(nY)
S^{+}(n,m) = sin(nX) sin(mY)  sin(mX) sin(nY)
S^{}(n,m) = sin(nX) sin(mY) + sin(mX) sin(nY)
The terms with superscript + are invariant under R_{4}, while the others negate when R_{4} is applied.

