  In a convex mosaic in $\mathbb{R} ^d$ we denote the average number of
vertices of a cell by $\bar v$ and the average number of cells meeting at a
node by $\bar n$. Except for the $d=2$ planar case, there is no known formula
prohibiting points in any range of the $[\bar n, \bar v]$ plane (except for the
unphysical $\bar n, \bar v < d+1$ 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 $[\bar n, \bar v]$ plane. To explore this
phenomenon we introduce the harmonic degree $\bar h= \bar n\bar v/(\bar n +
\bar v)$ of a $d$-dimensional mosaic. We show that the observed narrow strip on
the $[\bar n, \bar v]$ plane corresponds to a narrow range of $\bar h$. We
prove that for every $\bar h^{\star} \in (d, 2^{d-1}]$ there exists a convex
mosaic with harmonic degree $\bar h^{\star}$ and we conjecture that there exist
no $d$-dimensional mosaic outside this range. We also show that the harmonic
degree has deeper geometric interpretations. In particular, in case of
Euclidean mosaics it is related to the average of the sum of vertex angles and
their polars, and in case of 2D mosaics, it is related to the average excess
angle.
