# 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).