Voltage graph embeddings and the associated block designs

The voltage graph construction of Gross (orientable case) and Stahl as well as Gross and Tucker (nonorientable case) is extended to the case where the base graph is embedded in a pseudosurface or a generalized pseudosurface. This theory is then applied to produce triangular embeddings of K_4(n); they in turn yield an infinite class of partially balanced incomplete block designs.