A Face of a Projective Triangulation Removed for Its Geometric Realizability |
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| Authors: | Atsuhiro Nakamoto Shoichi Tsuchiya |
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| Institution: | 1. Department of Mathematics, Faculty of Education and Human Sciences, Yokohama National University, 79-2 Tokiwadai, Hodogaya-ku, Yokohama, 240-8501, Japan
2. Department of Information Media and Environment Sciences, Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama, 240-8501, Japan
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| Abstract: | 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 ℝ3 with no self-intersection such that each face of M is a flat polygon. In Bonnington and Nakamoto (Discrete Comput. Geom. 40:141–157, 2008), it has been proved that every triangulation G on the projective plane has a face f such that the triangulation G−f on the M?bius 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. |
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