  We prove that every complete finite-volume hyperbolic 3-manifold $M$ that is
tessellated into (embedded) right-angled regular polyhedra (dodecahedra or
ideal octahedra) embeds geodesically in a complete finite-volume connected
orientable hyperbolic 4-manifold $W$, which is also tessellated into
right-angled regular polytopes (120-cells and ideal 24-cells). If $M$ is
connected, then Vol($W$) < $2^{49}$Vol($M$). This applies for instance to the
Borromean link complement. As a consequence, the Borromean link complement
bounds geometrically a hyperbolic 4-manifold.
