Let $S$ be a finite set of tetrahedrons in $\mathbb{R}^3$. Let $S$ be tetrahedral complex in a sense that if two tetrahedrons intersect, the intersection is a face of both. In what follows we view tetrahedrons and their faces as *closed* sets in $\mathbb{R}^3$. Let the underlying topological space $|S|$ (domain occupied by all tetrahedrons with the topology inherited from $\mathbb{R}^3$) be manifold with boundary.

Let $T$ be arbitrary subset of tetrahedrons from $S$. Let $\partial T$ consist of those 2-simplices, which are faces of exactly one tetrahedron from $T$. Let $|\partial T|$ be the underlying topological space.

Suppose $|\partial T|$ is homeomorphic to a 2-sphere. Does it follow that $T$ is homeomorphic to a 3d ball? If not, what would be a counter-example?