David Eppstein – Publications

Publications with Tomohiro Tachi

Rigid origami vertices: Conditions and forcing sets.
Z. Abel, J. Cantarella, E. Demaine, D. Eppstein, T. Hull, J. Ku, R. Lang, and T. Tachi.
arXiv:1507.01644.
J. Computational Geometry 7 (1): 171–184, 2016, doi:10.20382/jocg.v7i1a9.

We give an exact characterization of the one-vertex origami folding patterns that can be folded rigidly, without bending the parts of the paper between the folds.

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, doi:10.1016/j.comgeo.2021.101857.

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".

This is the second in a sequence of papers on ununfoldable polyhedra; see also "Ununfoldable polyhedra" and "Acutely triangulated, stacked, and very ununfoldable polyhedra".