arXiv cs/01100592001-10cs.CGcs.DM

由矩形构造的非正交多面体

Nonorthogonal Polyhedra Built from Rectangles

Melody Donoso, Joseph O'Rourke

备注：: 19 pages, 20 figures. Revised version makes two corrections: The statement of the old Lemma 14 was incorrect. It has been corrected and merged with Lemma 13 now. Second, Figure 19 (a skew quadrilateral) was incorrect, and is now removed. It played no substantive role in the proofs

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摘要：

我们证明了任何亏格为零或亏格为一的多面体都是由矩形面构成的正交多面体，但也存在亏格为七的非正交多面体，它们的面都是矩形。这导致了Biedl，Lubiw和Sun提出的问题的解决[BLS99]。

英文摘要：

We prove that any polyhedron of genus zero or genus one built out of rectangular faces must be an orthogonal polyhedron, but that there are nonorthogonal polyhedra of genus seven all of whose faces are rectangles. This leads to a resolution of a question posed by Biedl, Lubiw, and Sun [BLS99].

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。