The unfolding of a polyhedron along its edges is known as a vertex unfolding if adjacent faces are allowed to be connected not only at an edge but also at a vertex. Demaine et al.  showed that every triangulated polyhedron has a vertex unfolding. We extend this result to a tight polyhedron, where a polyhedron is tight if its non-triangular faces are mutually non-incident.
"Vertex Unfoldings of Tight Polyhedra." Tokyo J. Math. 37 (1) 127 - 134, June 2014. https://doi.org/10.3836/tjm/1406552434