Touching simplices

  • Martin Aigner
  • Günter M. Ziegler

Abstract

This is an old and very natural question. We shall call f(d) the answer to this problem, and record f (1) = 2, which is trivial. For d = 2 the configuration of four triangles in the margin shows f (2) ≥ 4. There is no similar configuration with five triangles, because from this the dual graph construction, which for our example with four triangles yields a planar drawing of K4, would give a planar embedding of K5, which is impossible (see page 67). Thus we have
$$f(2) = 4$$
.

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References

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    M. A. Perles: At most 2 d+1 neighborly simplices in E d, Annals of Discrete Math. 20 (1984), 253–254.MathSciNetGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 2
  1. 1.Institut für Mathematik II (WE2)Freie Universität BerlinBerlinGermany
  2. 2.Institut für Mathematik, MA 6-2Technische Universität BerlinBerlinGermany

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