Paper by Erik D. Demaine

Therese Biedl, Timothy M. Chan, Erik D. Demaine, Martin L. Demaine, Paul Nijjar, Ryuhei Uehara, and Ming-wei Wang, “Tighter Bounds on the Genus of Nonorthogonal Polyhedra Built from Rectangles”, in Proceedings of the 14th Canadian Conference on Computational Geometry (CCCG 2002), Lethbridge, Alberta, Canada, August 12–14, 2002, pages 105–108.

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 of 90°, 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.

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The paper is 4 pages.

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Last updated September 3, 2017 by Erik Demaine.