Topological properties of cellular structures based on the staggered packing of prisms
M. Amaral Fortes · Journal de physique · 1989
The three-dimensional cellular structures, formed by parallel columns of base-to-base packed prisms, with staggered bases in adjacent columns, are analysed for various topological properties, including the average number of faces in the cells, F, and the quantity mF, defined as the average number of faces in cells adjacent to F-faced cells. This class of cellular structures has tetravalent vertices and three faces at each edge, and is therefore of the topological type usually found in natural cellular structures. It is shown that in the prismatic cellular structure F can vary between 8 and infinite. When all prisms have the same height, a simple equation can be obtained for mF, which shows that mF is linear in 1/F whenever the random trivalent planar network that defines the topology of the bases of the prisms follows Aboav's law, i.e., a linear relation between mi and 1/i, where mi is the average number of sides in cells adjacent to an i-sided cell in that planar network. This is the first known example of a linear relation between mF and 1/F in a three-dimensional cellular structure.