136 research outputs found
Flexible polyhedra in the Minkowski 3-space
Given a polyhedral surface, assume that it is prohibited to change the shape
and size of any face but it is permissible to change the dihedral angles
between the faces. A polyhedral surface is said to be flexible if it is
possible to change its shape under the above restrictions. We prove that
flexible polyhedral surfaces without boundary do exist in the Minkowski 3-space
and each of them preserves the (inclosed) volume and the (total) mean curvature
during a flex. To prove the latter result, we introduce the notion of the angle
between two arbitrary non-null nonzero vectors in the Minkowski plane. The
latter notion may be of some independent interest.Comment: 13 pages, 4 figures, LaTeX 2.0
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