Proceedings of the Eighteenth Annual Symposium on Computational Geometry
We present an algorithm to unfold any triangulated 2-manifold (in particular, any simplicial polyhedron) into a non-overlapping, connected planar layout in linear time. The manifold is cut only along its edges. The resulting layout is connected, but it may have a disconnected interior; the triangles are connected at vertices, but not necessarily joined along edges. We extend our algorithm to establish a similar result for simplicial manifolds of arbitrary dimension.
Demaine, Erik D.; Eppstein, David; Erickson, Jeff; Hart, George W.; and O'Rourke, Joseph, "Vertex-Unfoldings of Simplicial Manifolds" (2002). Computer Science: Faculty Publications, Smith College, Northampton, MA.