  Donaldson showed that every closed symplectic 4-manifold can be given the
structure of a topological Lefschetz pencil. Gay and Kirby showed that every
closed 4-manifold has a trisection. In this paper we relate these two structure
theorems, showing how to construct a trisection directly from a topological
Lefschetz pencil. This trisection is such that each of the three sectors is a
regular neighborhood of a regular fiber of the pencil. This is a 4-dimensional
analog of the following trivial 3-dimensional result: For every open book
decomposition of a 3-manifold M, there is a decomposition of M into three
handlebodies, each of which is a regular neighborhood of a page.
