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 Mobius band obtained from G by removing the interior of f has a geometric realization.
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