  Galaxy clusters exhibit a rich morphology during the early and intermediate
stages of mass assembly, especially beyond their boundary. A classification
scheme based on shapefinders deduced from the Minkowski functionals is examined
to fully account for the morphological diversity of galaxy clusters, including
relaxed and merging clusters, clusters fed by filamentary structures, and
cluster-pair bridges. These configurations are conveniently treated with
idealised geometric models and analytical formulae, some of which are novel.
Examples from CLASH and LC$^2$ clusters and observed cluster-pair bridges are
discussed.
