  A closed connected hyperbolic $n$-manifold bounds geometrically if it is
isometric to the geodesic boundary of a compact hyperbolic $(n+1)$-manifold. A.
Reid and D. Long have shown by arithmetic methods the existence of infinitely
many manifolds that bound geometrically in every dimension.
  We construct here infinitely many explicit examples in dimension $n=3$ using
right-angled dodecahedra and $120$-cells and a simple colouring technique
introduced by M. Davis and T. Januszkiewicz. Namely, for every $k\geqslant 1$,
we build an orientable compact closed $3$-manifold tessellated by $16k$
right-angled dodecahedra that bounds a $4$-manifold tessellated by $32k$
right-angled $120$-cells.
  A notable feature of this family is that the ratio between the volumes of the
$4$-manifolds and their boundary components is constant and, in particular,
bounded.
