  Each simplicial complex and integer vector yields a vector configuration
whose combinatorial properties are important for the analysis of contingency
tables. We study the normality of these vector configurations including a
description of operations on simplicial complexes that preserve normality,
constructions of families of minimally nonnormal complexes, and computations
classifying all of the normal complexes on up to six vertices. We repeat this
analysis for compressed vector configurations, classifying all of the
compressed complexes on up to six vertices.
