Abstract: If an embedding of a graph in the sphere is a quadrangulation of the sphere, then is necessarily bipartite. Assuming that has minimum vertex degree 3 and that all vertices in one block of have degree 4, we refer to as a spherical grid. We discuss general structural properties in spherical grids, then use these to completely characterize rotationally symmetric spherical grids having two vertices of degree , vertices of degree 3, and all other vertices of degree 4. Furthermore, we show how to represent all possible examples as nets. The talk will feature pictures and props.
