Matematičeskie zametki, Tome 8 (1970) no. 4, pp. 521-527
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E. M. Andreev. Intersection of plane boundaries of a polytope with acute angles. Matematičeskie zametki, Tome 8 (1970) no. 4, pp. 521-527. http://geodesic.mathdoc.fr/item/MZM_1970_8_4_a11/
@article{MZM_1970_8_4_a11,
author = {E. M. Andreev},
title = {Intersection of plane boundaries of a polytope with acute angles},
journal = {Matemati\v{c}eskie zametki},
pages = {521--527},
year = {1970},
volume = {8},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_4_a11/}
}
TY - JOUR
AU - E. M. Andreev
TI - Intersection of plane boundaries of a polytope with acute angles
JO - Matematičeskie zametki
PY - 1970
SP - 521
EP - 527
VL - 8
IS - 4
UR - http://geodesic.mathdoc.fr/item/MZM_1970_8_4_a11/
LA - ru
ID - MZM_1970_8_4_a11
ER -
%0 Journal Article
%A E. M. Andreev
%T Intersection of plane boundaries of a polytope with acute angles
%J Matematičeskie zametki
%D 1970
%P 521-527
%V 8
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1970_8_4_a11/
%G ru
%F MZM_1970_8_4_a11
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.
