  Tutte's embedding theorem states that every 3-connected graph without a $K_5$
or $K_{3,3}$ minor (i.e. a planar graph) is embedded in the plane if the outer
face is in convex position and the interior vertices are convex combinations of
their neighbors. We show that this result extends to simply connected
tetrahedral meshes in a natural way: for the tetrahedral mesh to be embedded if
the outer polyhedron is in convex position and the interior vertices are convex
combination of their neighbors it is sufficient (but not necessary) that the
graph of the tetrahedral mesh contains no $K_6$ and no $K_{3,3,1}$, and all
triangles incident on three boundary vertices are boundary triangles.
