  The entropy region is constructed from vectors of random variables by
collecting Shannon entropies of all subvectors. Its shape is studied here by
means of polymatroidal constructions, notably by convolution. The closure of
the region is decomposed into the direct sum of tight and modular parts,
reducing the study to the tight part. The relative interior of the reduction
belongs to the entropy region. Behavior of the decomposition under
selfadhesivity is clarified. Results are specialized to and completed for the
region of four random variables. This and computer experiments help to
visualize approximations of a symmetrized part of the entropy region. Four-atom
conjecture on the minimization of Ingleton score is refuted.
