David Eppstein - Publications

Publications with Hugo A. Akitaya

• Ununfoldable Polyhedra with 6 Vertices or 6 Faces.
  H. A. Akitaya, E. Demaine, D. Eppstein, T. Tachi, and R. Uehara.
  22nd Japan Conference on Discrete and Computational Geometry, Graphs, and Games (JCDCG³), Tokyo, Japan, 2019, pp. 27–28.
  Comp. Geom. Theory & Applications 103: 101857, 2022.
  

  We find a (nonconvex, but topologically equivalent to convex) polyhedron with seven vertices and six faces that cannot be unfolded to a flat polygon by cutting along its edges. Both the number of vertices and the number of faces are the minimum possible. The JCDCG³ version used the title "Minimal ununfoldable polyhedron".

• Face flips in origami tessellations.
  H. A. Akitaya, V. Dujmović, D. Eppstein, T. Hull, K. Jain, and A. Lubiw.
  arXiv:1910.05667.
  J. Computational Geometry 11 (1): 397–417, 2020.

  We study problems in which we are given an origami crease pattern and seek to reconfigure one locally flat foldable mountain-valley assignment into another by a sequence of operations that change the assignment around a single face of the crease pattern.