Abstract
Let M ⊂ Rn be a compact, convex body. We consider the family T(M) of all its translates (Fig. 111) and denote by him M the Helly dimension of T(M): him M = him T(M). This chapter is devoted to the Helly-dimensional classification of compact, convex bodies. In other words, we are going to consider the following problem: to give a geometrical description of the compact, convex bodies M ⊂ Rn satisfying him M = r, where 1 ≤ r ≤ n. By reasons which will be mentioned in this section, this problem is said to be the Szökefalvi-Nagy problem.
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© 1997 Springer-Verlag Berlin Heidelberg
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Boltyanski, V., Martini, H., Soltan, P.S. (1997). The Szökefalvi-Nagy Problem. In: Excursions into Combinatorial Geometry. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59237-9_4
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DOI: https://doi.org/10.1007/978-3-642-59237-9_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61341-1
Online ISBN: 978-3-642-59237-9
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