Periodica Mathematica Hungarica

, Volume 57, Issue 2, pp 131–141 | Cite as

On edge-antipodal d-polytopes

  • Tibor Bisztriczky
  • Károly Böröczky


A convex d-polytope in ℝ d is called edge-antipodal if any two vertices that determine an edge of the polytope lie on distinct parallel supporting hyperplanes of the polytope. We introduce a program for investigating such polytopes, and examine those that are simple.

Key words and phrases

convex polytope edge-antipodal 

Mathematics subject classification numbers

52B11 52B12 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    K. Bezdek, T. Bisztriczky and K. Böröczky, Edge-antipodal 3-polytopes, Disc. and Comp. Geometry (J. E. Goodman, J. Pach and E. Webzl, eds.), MSRI, Cambridge University Press, 2005, 129–134.Google Scholar
  2. [2]
    T. Bisztriczky and K. Böröczky, On antipodal 3-polytopes, Rev. Roumaine Math. Pures Appl., 50 (2005), 477–481.MATHMathSciNetGoogle Scholar
  3. [3]
    B. Csikós, Edge-antipodal convex polytopes — a proof of Talata’s conjecture, Discrete Geometry (A. Bezdek, ed.) Pure Appl. Math. 253, Dekker, New York, 2003, 201–205.Google Scholar
  4. [4]
    L. Danzer and B. Grünbaum, Über zwei Probleme bezüglich konvexer Körper von P. Erdős und von V. Klee, Math. Z., 79 (1962), 95–99.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    B. Grünbaum, Convex Polytopes, Springer, New York, 2003.Google Scholar
  6. [6]
    P. McMullen, Polytopes with parathetic faces, Rev. Roumaine Math. Pures Appl., 51 (2005), 65–76.MathSciNetGoogle Scholar
  7. [7]
    C. M. Petty, Equilateral sets in Minkowski spaces, Proc. Amer. Math. Soc., 29 (1971), 369–374.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    A. Pór, On e-antipodal polytopes, submitted.Google Scholar
  9. [9]
    A. Schürmann and K. Swanepoel, Three-dimensional antipodal and normequilateral sets, Pacific J. Math., 228 (2006), 349–370.MATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    K. Swanepoel, Upper bounds for edge-antipodal and subequilateral polytopes, Period. Math. Hungar., 54 (2007), 99–106.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    I. Talata, On extensive subsets of convex bodies, Period. Math. Hungar., 38 (1999), 231–246.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Dept. of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.Department of GeometryEötvös Loránd UniversityBudapestHungary

Personalised recommendations