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Mat. Zametki, 1970, Volume 8, Issue 4, Pages 521–527 (Mi mz9616)  

This article is cited in 10 scientific papers (total in 13 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.

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

Bibliographic databases:

UDC: 513.83
Received: 06.08.1969

Citation: E. M. Andreev, “Intersection of plane boundaries of a polytope with acute angles”, Mat. Zametki, 8:4 (1970), 521–527; Math. Notes, 8:4 (1970), 761–764

Citation in format AMSBIB
\Bibitem{And70}
\by E.~M.~Andreev
\paper Intersection of plane boundaries of a polytope with acute angles
\jour Mat. Zametki
\yr 1970
\vol 8
\issue 4
\pages 521--527
\mathnet{http://mi.mathnet.ru/mz9616}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=279680}
\zmath{https://zbmath.org/?q=an:0209.26506}
\transl
\jour Math. Notes
\yr 1970
\vol 8
\issue 4
\pages 761--764
\crossref{https://doi.org/10.1007/BF01104379}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. È. B. Vinberg, “Discrete linear groups generated by reflections”, Math. USSR-Izv., 5:5 (1971), 1083–1119  mathnet  crossref  mathscinet  zmath
    2. V. V. Nikulin, “On arithmetic groups generated by reflections in Lobachevskii spaces”, Math. USSR-Izv., 16:3 (1981), 573–601  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. V. Nikulin, “On the classification of arithmetic groups generated by reflections in Lobachevsky spaces”, Math. USSR-Izv., 18:1 (1982), 99–123  mathnet  crossref  mathscinet  zmath  isi
    4. È. B. Vinberg, “Hyperbolic reflection groups”, Russian Math. Surveys, 40:1 (1985), 31–75  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. A. A. Felikson, “Coxeter decompositions of hyperbolic simplexes”, Sb. Math., 193:12 (2002), 1867–1888  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. O. V. Shvartsman, “Gruppy otrazhenii i gruppy Kokstera”, Matem. prosv., ser. 3, 7, MTsNMO, M., 2003, 64–81  mathnet
    7. V. O. Bugaenko, “Klassifikatsiya mnogogrannikov Kokstera”, Matem. prosv., ser. 3, 7, MTsNMO, M., 2003, 82–106  mathnet
    8. P. V. Tumarkin, A. A. Felikson, “Reflection Subgroups of Reflection Groups”, Funct. Anal. Appl., 38:4 (2004), 313–314  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. V. O. Bugaenko, “Ob ostrougolnykh mnogogrannikakh”, Matem. prosv., ser. 3, 8, Izd-vo MTsNMO, M., 2004, 123–126  mathnet
    10. A. A. Felikson, “Lambert Cubes Generating Discrete Reflection Groups”, Math. Notes, 75:2 (2004), 250–258  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. A. A. Felikson, “Coxeter Decompositions of Compact Hyperbolic Pyramids and Triangular Prisms”, Math. Notes, 75:4 (2004), 583–593  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. D. A. Derevnin, “Prizmy v $H^3$”, Vestn. NGU. Ser. matem., mekh., inform., 5:4 (2005), 14–31  mathnet
    13. Felikson A., Tumarkin P., Zehrt T., “On Hyperbolic Coxeter N-Polytopes with N+2 Facets”, Adv. Geom., 7:2 (2007), 177–189  crossref  isi
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