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Touching simplices

  • Martin Aigner
  • Günter M. Ziegler
Chapter

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 91).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 1
  1. 1.Institut für MathematikFreie Universität BerlinBerlinGermany

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