  This paper introduces two-dimensional diagrams that are slight
generalizations of moment map images for toric four-manifolds and catalogs
techniques for reading topological and symplectic properties of a symplectic
four-manifold from these diagrams. The paper offers a purely topological
approach to toric manifolds as well as methods for visualizing other manifolds,
including the K3 surface, and for visualizing certain surgeries. Most of the
techniques extend to higher dimensions.
