Any finite projective plane of order is an (( configuration. Let be a projective plane of order . Remove from a point and all the lines of which pass through (but not the points which lie on those lines except for ) and remove a line not passing through and all the points that are on line . The result is a configuration of type ((. If, in this construction, the line is chosen to be a line which does pass through , then the construction results in a configuration of type ((. Since projective planes are known to exist for all orders which are powers of primes, these constructions provide infinite families of symmetric configurations.