Acutely Triangulated, Stacked, and Very Ununfoldable Polyhedra
Abstract
We present new examples of topologically convex edgeununfoldable polyhedra, i.e., polyhedra that are combinatorially equivalent to convex polyhedra, yet cannot be cut along their edges and unfolded into one planar piece without overlap. One family of examples is acutely triangulated, i.e., every face is an acute triangle. Another family of examples is stacked, i.e., the result of facetoface gluings of tetrahedra. Both families achieve another natural property, which we call very ununfoldable: for every $k$, there is an example such that every nonoverlapping multipiece edge unfolding has at least $k$ pieces.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 DOI:
 10.48550/arXiv.2007.14525
 arXiv:
 arXiv:2007.14525
 Bibcode:
 2020arXiv200714525D
 Keywords:

 Computer Science  Computational Geometry
 EPrint:
 8 pages, 6 figures. To appear at the 32nd Canadian Conference on Computational Geometry (CCCG 2020)