Partial generalizations of the theory of virtual polyhedra (sometimes under different names) appeared recently in the theory of torus manifolds look very different from the original theory of virtual polyhedra. Such generalizations are based on simple arguments from homotopy theory while the original theory is based on integration over the Euler characteristic. We explain how these generalizations are related to the classical theory of convex bodies and the original theory of virtual polyhedra. The paper basically contains no proofs: all proofs and details can be found in the cited literature.
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Dedicated to the 85th anniversary of my beloved teacher Vladimir Igorevich Arnold
Translated from Problemy Matematicheskogo Analiza 121, 2023, pp. 119-129.
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Khovanskii, A.G. Geometry of Generalized Virtual Polyhedra. J Math Sci 269, 256–268 (2023). https://doi.org/10.1007/s10958-023-06274-8
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DOI: https://doi.org/10.1007/s10958-023-06274-8