Linear Networks and Convex Polytopes

It is shown that the set G,] of immersed linear networks in that are parallel to a given immersed linear network and have the same boundary as is a convex polyhedral subset of the configuration space of movable vertices of the graph G. The dimension of G,] is calculated, and the number of its maximal faces is estimated. As an application, the spaces of all locally minimal and weighted minimal networks with fixed boundary and topology in are described. Bibliography: 21 titles.