This article is cited in 21 papers

Intersection of plane boundaries of a polytope with acute angles

E. M. Andreev

M. V. Lomonosov Moscow State University

Abstract: It is proved that the planes of nonadjacent faces of a polytope with angles not exceeding $90^\circ$ 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.

UDC: 513.83

Received: 06.08.1969

 English version: Mathematical Notes, 1970, 8:4, 761–764

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