A Geometric Construction of Partial Geometries with a Hermitian Point Graph

In 1998 Mathon constructed algebraically a class of partial geometriespg (q − 1, (q2 − 1) / 2, (q − 1) / 2), where q is an even power of 3. The point graph of these partial geometries is the Hermitian graph constructed by Taylor. In this paper a geometric construction of Mathon’s partial geometries is given. The construction also works if q is an odd power of 3, yielding new partial geometries with a Hermitian point graph.