Geodesic
Pointed spherical tilings and hyperbolic virtual polytopes
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 157-171

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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. 
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     author = {G. Yu. Panina},
     title = {Pointed spherical tilings and hyperbolic virtual polytopes},
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G. Yu. Panina. Pointed spherical tilings and hyperbolic virtual polytopes. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 11, Tome 372 (2009), pp. 157-171. http://geodesic.mathdoc.fr/item/ZNSL_2009_372_a15/