Besides conventional rectangular lattices, EM.Cube's [[Planar Module]] can also handle complex non-rectangular periodic lattices. For example, many frequency selective surfaces have skewed grids. In order to simulate skewed-grid periodic structures, the definition of the grid has to be generalized. A periodic structure is a repetition of a basic structure (unit cell) at pre-determined locations. Let these locations be described by (x<sub>mn</sub>, y<sub>mn</sub>), where m and n are integers ranging from -8 to 8. For a general skewed grid, x<sub>mn</sub> and y<sub>mn</sub> can be described by:
x:<submath>x_{mn</sub> } = m&DELTA;\Delta x + n&DELTA;\Delta x'<br /math> y:<submath>y_{mn</sub> } = n&DELTA;m\Delta y + m&DELTA;n \Delta y'</math>
where &DELTA;<math>\Delta x </math> is the primary offset in the X direction (X Spacing) controlled by index m and &DELTA;<math>\Delta x' </math> is the secondary offset in the X direction (X Offset) controlled by index n. The meanings of &DELTA;<math>\Delta y </math> (Y Spacing) and &DELTA;<math>\Delta y' </math> (Y Offset) are similar with the roles of indices m and n interchanged. To illustrate how to use this definition, consider an example of an equilateral triangular grid with side length L as shown in the figure below.
[[File:image121.png]]
Figure 1: Diagram of an equilateral triangular periodic lattice.
From the figure, it is obvious that the y coordinate of each row is fixed and identical, thus &DELTA;<math>\Delta y = L </math> and &DELTA;<math>\Delta y' = 0</math>. While in each row the spacing between adjacent elements is L, there is an offset of L/2 between the consecutive rows. This results in &DELTA;<math>\Delta x = L </math> and &DELTA;<math>\Delta x' = L/2</math>. To sum up, an equilateral triangular grid can be described by &DELTA;<math>\Delta x = L</math>, &DELTA;<math>\Delta x' = L/2</math>, &DELTA;<math>\Delta y = L </math> and &DELTA;<math>\Delta y' = 0</math>. In an EM.Cube [[Planar Module]] project, the secondary offsets are equal to zero by default, implying a rectangular lattice. You can change the values of the secondary offsets using the boxes labeled '''X Offset''' and '''Y Offset''' in the '''Periodicity Settings Dialog''', respectively. Triangular and Hexagonal lattices are popular special cases of the generalized lattice type. In a triangular lattice with alternating Rows, &DELTA;<math>\Delta x' = &DELTA;\Delta x/2 </math> and &DELTA;<math>\Delta y'=0</math>. A Hexagonal lattice (with alternating rows) is a special case of triangular lattice in which &DELTA;<math>\Delta y = v3&DELTA;\sqrt{3\Delta x/2}</math>.
=== Interconnectivity Among Unit Cells ===