Definition:Symmetric Design

Definition
A block design with parameters $v, b, r, k, \lambda$ is said to be symmetric if $b = v$, and (consequently) $r = k$.

That is, where:
 * the number of blocks is equal to the number of points

or equivalently:
 * the number of points belonging to each block is equal to the number of blocks in which each point is contained.

Note
The symmetry does not mean the incidence matrix is symmetric (it often is not).