Topology and transformations in cellular structures

Abstract Two- and three-dimensional structures respectively composed of polygons and trivalent polyhedra, connected to give the minimum edge valency of vertices, are analysed from the topological and thermodynamic point of view. Both structures are classified into three categories, namely: saturated, unsaturated and periodic structures, and their topological properties are reviewed. The unit topological operations through which structures of a given dimension transform into one another are the basic steps in cell growth, which results from the excess free energy of faces, edges and vertices. It is possible to define forces acting on these elements which are responsible for the transformation of the structures. Using this thermodynamic approach it is shown that the unit operations occur in such a way that growth takes place. A general formalism for predicting the kinetics of growth is developed.

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