On geometrically realizable Möbius triangulations

Let M be a map on a surface F2. A geometric realization of M is an embedding of F2 into a Euclidian 3-space R3 with no self-intersection such that each face of M is a flat polygon. In this paper, we characterize geometrically realizable triangulations on the Möbius band. ► In 1983, Brehm showed a Mö...

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Bibliographic Details
Published in:Discrete mathematics 2012-07, Vol.312 (14), p.2135-2139
Main Authors: Nakamoto, Atsuhiro, Tsuchiya, Shoichi
Format: Article
Language:English
Subjects:
Geometric realization
Möbius band
Triangulation
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Summary:Let M be a map on a surface F2. A geometric realization of M is an embedding of F2 into a Euclidian 3-space R3 with no self-intersection such that each face of M is a flat polygon. In this paper, we characterize geometrically realizable triangulations on the Möbius band. ► In 1983, Brehm showed a Möbius triangulation with no geometric realization. ► However, he did not characterize Möbius triangulations with geometric realizations. ► In this paper, we characterize Möbius triangulations with geometric realizations.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2011.06.007