  Based on the work of Durhuus-J{\'o}nsson and Benedetti-Ziegler, we revisit
the question of the number of triangulations of the 3-ball. We introduce a
notion of nucleus (a triangulation of the 3-ball without internal nodes, and
with each internal face having at most 1 external edge). We show that every
triangulation can be built from trees of nuclei. This leads to a new
reformulation of Gromov's question: We show that if the number of rooted nuclei
with $t$ tetrahedra has a bound of the form $C^t$, then the number of rooted
triangulations with $t$ tetrahedra is bounded by $C_*^t$.
