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Vertex-Unfoldings of Simplicial Manifolds

Erik D. Demaine·David Eppstein·Jeff Erickson·George W. Hart·Joseph O'Rourke
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Abstract

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.

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Erik D. Demaine, David Eppstein, Jeff Erickson, George W. Hart, Joseph O'Rourke. 2001-10-27. Vertex-Unfoldings of Simplicial Manifolds. https://arxiv.org/abs/cs/0110054

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