A unifying approach to descriptive geometry and mechanisms

Abstract Common polymatroidal structures are found in line drawings of polyhedra and two-dimensional frameworks composed of rods and joints. Moreover, those polymatroids are characterized by certain submodular functions, which are useful for practical calculation of the ranks of those polymatroids. A new start point is thus obtained for the unifying study on those subjects. Three different types of treatments of those subjects based on this unifying point of view are also presented.