Abstract
It is proved that the planes of nonadjacent faces of a polytope with angles not exceeding 90° cannot intersect. It is also proved that the dimension of the intersection of any set of hyperplanes is equal to the maximum dimension of a boundary lying in this intersection.
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H. S. M. Coxeter, “Discrete groups generated by reflections,” Ann. of Math.,35, No. 3, 588–621 (1934).
É. B. Vinberg, “Discrete groups generated by reflections in Lobachevskii spaces,“ Matem. Sb.,72, No. 3, 472–488 (1967).
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Translated from Matematicheskie, Vol. 8, No. 4, pp. 521–527, October, 1970.
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Andreev, E.M. Intersection of plane boundaries of a polytope with acute angles. Mathematical Notes of the Academy of Sciences of the USSR 8, 761–764 (1970). https://doi.org/10.1007/BF01104379
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DOI: https://doi.org/10.1007/BF01104379