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A face of a projective triangulation removed for its geometric realizability. (English) Zbl 1236.05136

Summary: Let \(M\) be a map on a surface \(F^{2}\). A geometric realization of \(M\) is an embedding of \(F^{2}\) into a Euclidian 3-space \({\mathbb{R}}^{3}\) with no self-intersection such that each face of \(M\) is a flat polygon. In [C.P. Bonnington and A. Nakamoto, “Geometric realization of a triangulation on the projective plane with one face removed”, Discrete Comput. Geom. 40, No.1, 141–157 (2008; Zbl 1148.52011)], it has been proved that every triangulation \(G\) on the projective plane has a face \(f\) such that the triangulation \(G-f\) on the Möbius band obtained from \(G\) by removing the interior of \(f\) has a geometric realization. In this paper, we shall characterize such a face \(f\) of \(G\).

MSC:

05C62 Graph representations (geometric and intersection representations, etc.)
52B99 Polytopes and polyhedra

Citations:

Zbl 1148.52011
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References:

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