Vertex-unfoldings of simplicial manifolds

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

Research output: Contribution to conferencePaperpeer-review


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.

Original languageEnglish (US)
Number of pages7
StatePublished - 2002
Externally publishedYes
EventProceedings of the 18th Annual Symposium on Computational Geometry (SCG'02) - Barcelona, Spain
Duration: Jun 5 2002Jun 7 2002


OtherProceedings of the 18th Annual Symposium on Computational Geometry (SCG'02)


  • Edge-unfolding
  • Facet cycles
  • Facet paths
  • Facet-vertex incidence graph
  • Hinged dissections
  • Manifolds with boundary
  • Polyhedra
  • Ridge-unfolding
  • Simplicial manifolds
  • Triangulated 2-manifolds
  • Unfolding
  • Vertex-unfolding

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics


Dive into the research topics of 'Vertex-unfoldings of simplicial manifolds'. Together they form a unique fingerprint.

Cite this