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Geometric Realization of a Triangulation on the Projective Plane with One Face Removed

Abstract

Let M be a map on a surface F 2. A geometric realization of M is an embedding of F 2 into a Euclidean 3-space ℝ3 such that each face of M is a flat polygon. We shall prove that every triangulation G on the projective plane has a face f such that the triangulation of the Möbius band obtained from G by removing the interior of f has a geometric realization.

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Author information

Correspondence to Atsuhiro Nakamoto.

Additional information

This research was partially supported by the Ministry of Education, Science, Sports and Culture of Japan, Grant-in-Aid for Young Scientists (B), 18740045, 2005.

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Bonnington, C.P., Nakamoto, A. Geometric Realization of a Triangulation on the Projective Plane with One Face Removed. Discrete Comput Geom 40, 141–157 (2008). https://doi.org/10.1007/s00454-007-9035-9

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Keywords

  • Triangulation
  • Geometric realization
  • Möbius band
  • Projective plane