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 Mobius 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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