Flip Graph Connectivity in 3D

Is the flip graph connected for general-position points in $\mathbb{R}^3$? Given a set of $n$ points in $\mathbb{R}^3$, the flip graph has a node for each tetrahedralization of the set. Two nodes are connected by an arc if there is a 2-to-3 or 3-to-2 \textquotedblleft{}bistellar flip\textquotedblright{} of tetrahedra between the two simplicial complexes. In the plane, the flips correspond to convex quadrilateral diagonal switches; in $\mathbb{R}^3$, a $5$-vertex convex polyhedron is \textquotedblleft{}flipped\textquotedblright{} between two of its tetrahedralizations.