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The notions of a {\em local minimal} network, that is, a graph being shortest locally, and an {\em extremal} network, that is, a critical point of the functional of normed length, arise in the generalization of the Steiner problem: among all the networks spanning a given finite set of points of the Euclidean plane, find a network of minimal length. A solution of this problem is called a {\em shortest} network spanning the set. It is well-known that in the case of arbitrary normed planes the class of local minimal networks is wider than the class of extremal networks. The structure of local minimal networks is described very well in the literature. There are criteria (Ivanov, Tuzhilin) telling us whether a local minimal network is an extremal one, but these criteria do not give explicitly the geometrical structure of extremal networks. In our talk we pay more attention to $\lambda$-geometry (the unit ball in this norm is the Euclidean regular $2\lambda$-gon inscribed in the Euclidean unit circle) and geometric criteria describing extremal networks on these planes.