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Published in:
2004 | OriginalPaper | Chapter
Touching simplices
Authors : Martin Aigner, Günter M. Ziegler
Published in: Proofs from THE BOOK
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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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 $$f(2) = 4$$.