Abstract
A statement in an earlier paper that there is a topological limit to the sharing of corners in a network of three-dimensional cells analogous to metal grains is shown to be wrong. New space-filling irregular polyhedra sharing faces with as many as 20 neighbors are sketched. No plane-faced space-filling polyhedron can exist that meets the requirements of surface-tension equilibrium at interfaces and junctions. A relation is derived for the sum of angles at each vertex in a three-dimensional space-filling array of plane-faced polyhedra.
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