DOIAbstract
In a convex mosaic in Rd we denote the average number of vertices of a cell by v and the average number of cells meeting at a node by n. Except for the d = 2 planar case, there is no known formula prohibiting points in any range of the [n,v] plane (except for the unphysical n,v<d+1 strips). Nevertheless, in d = 3 dimensions if we plot the 28 points corresponding to convex uniform honeycombs, the 28 points corresponding to their duals and the 3 points corresponding to Poisson-Voronoi, Poisson-Delaunay and random hyperplane mosaics, then these points appear to accumulate on a narrow strip of the [n,v] plane. To explore this phenomenon we introduce the harmonic degree h=nv/(n+v) of a d-dimensional mosaic. We show that the observed narrow strip...
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