Pointed spherical tilings and hyperbolic virtual polytopes

The paper presents an introduction to the theory of hyperbolic virtual polytopes from the combinatorial rigidity viewpoint. Namely, we give a shortcut for a reader acquainted with the notions of Laman graph, 3D lifting, and pointed tiling. From this viewpoint, a hyperbolic virtual polytope is a stressed pointed graph embedded in the sphere $S^2$. The advantage of such a presentation is that it gives an alternative and most convincing proof of existence of hyperbolic virtual polytopes. Bibl. – 20 titles.