Nonorthogonal Polyhedra Built from Rectangles
<|reference_start|>Nonorthogonal Polyhedra Built from Rectangles: 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].<|reference_end|>
@article{donoso2001nonorthogonal,
    title={Nonorthogonal Polyhedra Built from Rectangles},
    author={Melody Donoso and Joseph O'Rourke},
    journal={arXiv preprint arXiv:cs/0110059},
    year={2001},
    number={Smith Technical Report 073, Oct. 2001; revised May 2002},
    archivePrefix={arXiv},
    eprint={cs/0110059},
    primaryClass={cs.CG cs.DM}
}