Tighter Bounds on the Genus of Nonorthogonal Polyhedra Built from Rectangles
| Citations: | 2 - 2 self |
BibTeX
@MISC{Biedl_tighterbounds,
author = {Therese Biedl and Timothy M. Chan and Erik D. Demaine and Martin L. Demaine and Paul Nijjar and Ryuhei Uehara and Ming-wei Wang},
title = {Tighter Bounds on the Genus of Nonorthogonal Polyhedra Built from Rectangles},
year = {}
}
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Abstract
We prove that there is a polyhedron with genus 6 whose faces are orthogonal polygons (equivalently, rectangles) and yet the angles between some faces are not multiples , so the polyhedron itself is not orthogonal. On the other hand, we prove that any such polyhedron must have genus at least 3. These results improve the bounds of Donoso and O'Rourke [4] that there are nonorthogonal polyhedra with orthogonal faces and genus 7 or larger, and any such polyhedron must have genus at least 2. We also demonstrate nonoverlapping one-piece edge-unfoldings (nets) for the genus-7 and genus-6 polyhedra.
Citations
| 29 | Unfolding some classes of orthogonal polyhedra - Biedl, Demaine, et al. - 1998 |
| 22 | Ununfoldable polyhedra with convex faces - Bern, Demaine, et al. - 2003 |
| 7 | When can a net fold to a polyhedron - Biedl, Lubiw, et al. - 1999 |
| 3 | Nonorthogonal polyhedra built from rectangles - Donoso, O’Rourke - 2002 |
