Acta Mathematica

, Volume 121, Issue 1, pp 293–302 | Cite as

Grassmann angles of convex polytopes

  • Branko Grünbaum
Article

Keywords

Convex Polytopes 

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References

  1. [1].
    Bourbaki, N.,Intégration, Ch. 7 (Mesure de Haar). Actualités Sci. et Ind., No. 1306. Hermann, Paris 1963.Google Scholar
  2. [2].
    Fáry, I., Sur la courbure totale d'une courbe gauche faisant un nœud.Bull. Soc. Math. France, 77 (1949), 128–138.MATHMathSciNetGoogle Scholar
  3. [3].
    Frostman, O., En sats av Fáry med elementära tillämpningar.Nordisk Mat. Tidskr., 1 (1953), 25–32.MATHMathSciNetGoogle Scholar
  4. [4].
    Grünbaum, B.,Convex polytopes. Wiley, New York 1967.Google Scholar
  5. [5].
    Hadwiger, H.,Vorlesungen über Inhalt, Oberfläche und Isoperimetrie. Springer, Berlin 1957.Google Scholar
  6. [6].
    Perles, M. A. & Shephard, G. C., Angle sums of convex polytopes. To appear inMath. Scand.Google Scholar
  7. [7].
    —, Facets and nonfacets of convex polytopes.Acta Math., 119 (1967), 113–145.CrossRefMathSciNetGoogle Scholar
  8. [8].
    Petkantschin, B., Zusammenhänge zwischen den Dichten der linearen Unterräume imn-dimensionalen Raum.Abh. Math. Sem. Hamburg, 11 (1936), 249–310.MATHGoogle Scholar
  9. [9].
    Shephard, G. C., Angle deficiencies of convex polytopes.J. London Math. Soc., 43 (1968), 325–336.MATHMathSciNetGoogle Scholar
  10. [10].
    Sommerville, D. M. Y., The relations connecting the anglesums and volume of a polytope in space ofn dimensions.Proc. Roy. Soc. London, Ser. A, 115 (1927), 103–119.MATHGoogle Scholar
  11. [11].
    —,An introduction to the geometry of n dimensions. Methuen, London 1929.Google Scholar

Added in proof (October 13, 1968): The following recent paper deal with topics related to Grassmann angles

  1. [12].
    Banchoff, T., Critical points and curvature for embedded polyhedra.J. Diff. Geometry, 1 1 (1967), 245–256.MATHMathSciNetGoogle Scholar
  2. [13].
    Hadwiger, H., Eckenkrümmung beliebiger kompakter euklidischer Polyeder und Charakteristik von Euler-Poincaré. To appear.Google Scholar
  3. [14].
    Mani, P., On angle sums and Steiner points of polyhedra. To appear inIsrael J. Math. Google Scholar
  4. [15].
    Shephard, G. C., An elementary proof of Gram's theorem for convex polytopes.Canad J. J. Math., 19 (1967), 1214–1217.MATHMathSciNetGoogle Scholar

Copyright information

© Almqvist & Wiksells Boktryckeri AB 1968

Authors and Affiliations

  • Branko Grünbaum
    • 1
  1. 1.University of WashingtonSeattleUSA

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