Lower edge-density conjecture for normal convex mosaics in three-dimensional space

Let $\mathcal{M}$ be a normal, convex mosaic in $\mathbb R^3$ whose cells have unit volume, and let $\underline{\rho}_1(\mathcal{M})$ denote its lower edge density. Lower edge-density conjecture. One has

$$\underline{\rho}_1(\mathcal{M}) \geq \frac{3\sqrt{3}}{2}.$$

Equality is attained, for example, when the cells of $\mathcal{M}$ are the regular triangle-based right prisms described in the cited decomposition theorem. This conjecture gives the proposed lower bound for edge density among all normal, convex three-dimensional mosaics; the stated prism examples show that the bound is sharp.