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Convex bodies with non-convex cross-section bodies

Published online by Cambridge University Press:  26 February 2010

Ulrich Brehm
Affiliation:
Technische Universität Dresden, Fachrichtung Mathematik, Institut für Geometric01062 Dresden, Germany. e-mail: [email protected]
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Abstract

It is shown that the regular n-dimensional simplex has a non-convex cross-section body for all n ≥ 4.

MSC classification

Type
Research Article
Copyright
Copyright © University College London 1999

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References

1.Gardner, R. J.. Geometric Tomography (Cambridge University Press, New York, 1995).Google Scholar
2.Makai, E. and Martini, H.. The cross-section body, plane sections of convex bodies and approximation of convex bodies I. Geom. Dedicata, 63 (1996), 267296.CrossRefGoogle Scholar
3.Makai, E. and Martini, H.. On bodies associated with a given body. Canad. Math. Bull., 39 (1996), 448459.CrossRefGoogle Scholar
4.Makai, E. and Martini, H.. The cross-section body, plane sections of convex bodies and approximation of convex bodies II. Geom. Dedicata, 70 (1998), 283303.CrossRefGoogle Scholar
5.Martini, H.. Extremal equalities for cross-sectional measures of convex bodies. Proc. 3rd Geometry Congress, Aristoteles University, Thessaloniki (1992), 285296.Google Scholar
6.Martini, H.. Cross-sectional measures. Intuitive Geometry, Coll. Math. Soc. János Bolyai, 63 (Szeged 1991). eds. K. Böröczky and G. Fejes Tóth. North Holland, Amsterdam (1994), 269310.Google Scholar
7.Meyer, M.. Maximal hyperplane sections of convex bodies, Mathematika (this volume), 131136.Google Scholar