Abstract: Vertex configuration for a vertex in an orthogonal
pseudo-polyhedron is an identity of a vertex that is determined by the
number of edges, dihedral angles, and non-manifold properties
meeting at the vertex. There are up to sixteen vertex configurations
for any orthogonal pseudo-polyhedron (OPP). Understanding the
relationship between these vertex configurations will give us insight
into the structure of an OPP and help us design better algorithms for
many 3-dimensional geometric problems. In this paper, 16 vertex
configurations for OPP are described first. This is followed by a
number of formulas giving insight into the relationship between
different vertex configurations in an OPP. These formulas
will be useful as an extension of orthogonal polyhedra usefulness on
pattern analysis in 3D-digital images.