A hexagonal grid is a grid formed by a tessellation of regular hexagons. Boards made of hexagonal grids are often found in strategy and role-playing games. This is useful because, in contrast to square grid and triangular grid boards, no two hexagonal cells meet only at a single point; touching cells share a common side.
In tiling and board contexts, the hexagonal grid may also be called a hexagonal lattice. However, in point lattice and packing contexts, that term usually denotes the triangular lattice.
The graph formed by the corners and sides of the hexagonal cells admits a brick-wall representation.
Consider a hexagon of cells consisting of one central cell and 
surrounding rings, where 
is a nonnegative integer.
It contains 
cells. These cells can be labeled bijectively by the
integers 0, 1, ..., 
so that the labels along each straight line of adjacent
cells form an arithmetic progression modulo
(Chang et al. 1995). This condition
differs from the equal line sums required for a magic
hexagon. For 
,
assign each cell a pair 
satisfying 
.
The illustrated label is the residue of 
modulo 19, so a step in each of the three grid directions
changes the label by a fixed residue.
