Geodesic
Intersection of plane boundaries of a polytope with acute angles
Matematičeskie zametki, Tome 8 (1970) no. 4, pp. 521-527.

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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. 
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     author = {E. M. Andreev},
     title = {Intersection of plane boundaries of a polytope with acute angles},
     journal = {Matemati\v{c}eskie zametki},
     pages = {521--527},
     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_4_a11/}
}
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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/