I. HEGEDÛS: `GAUSS´ THEOREMA EGREGIUM FOR TRIANGULATED SURFACES, Per. Pol. Civil Eng., 36/3 (1992), 291-307.

KEYWORDS: triangulated surfaces, polyhedra of triangle facets, single-layer space grids, extrinsic and intrinsic measures of surfaces, Gaussian curvature, inextensional deformations, static-kinematic, analogies

ABSTRACT: The paper deals with fundamental geometric assumptions of the static-kinematic analysis of triangulated surfaces. First, intrinsic and extrinsic properties of triangulated surfaces as analogues of those of smooth surfaces are introduced, then static-kinematic analogies between triangulated surfaces and pin-jointed single-layer space grids are dealt with. It is shown that Gaussian curvature of smooth surfaces cannot be interpreted for triangulated surfaces, and space grids, however, statements of Gauss´ Theorema Egregium can be replaced for statements concerning simple and useful connections between their intrinsic and extrinsic measures.