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A new view on some characterizations of simplices

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References

  1. T.Bonnesen und W.Fenchel, Theorie der konvexen Körper. Berlin-Heidelberg-New York 1974 (reprint).

  2. G. Butler, An extremal property of simplices. Proc. Amer. Math. Soc.30, 556–560 (1971).

    Google Scholar 

  3. R.Fourneau, Choquet simplices in finite dimensions. Ed. by J. Goodman et al.: Discrete Geometry and Convexity, Annals N. Y. Acad. Sci.440, 106–112, New York 1985.

  4. R. J. Gardner andP. McMullen, On Hammer's X-ray problem. J. London Math. Soc. (2)21, 171–175 (1980).

    Google Scholar 

  5. P. Gritzmann, Ein Approximationssatz für konvexe Körper. Geom. Dedicata19, 277–286 (1985).

    Google Scholar 

  6. B.Grünbaum, Convex Polytopes. New York 1967.

  7. H. Martini, Some characterizing properties of the simplex. Geom. Dedicata29, 1–6 (1989).

    Google Scholar 

  8. H.Martini, Convex polytopes whose projection bodies and difference sets are polars. Discrete Comput. Geom., to appear.

  9. H. Martini, Determining classes of convex bodies by restricted sets of Steiner symmetrizations. Geom. Dedicata30, 247–254 (1989).

    Google Scholar 

  10. H.Martini and B.Weissbach, On quermasses of simplices. Studia Sci. Math. Hungar., to appear.

  11. P. McMullen, R. Schneider andG. C. Shephard, Monotypic polytopes and their intersection properties. Geom. Dedicata3, 99–129 (1974).

    Google Scholar 

  12. C. M.Petty, Isoperimetric problems. Proc. Conf. Convexity and Combin. Geom., University of Oklahoma (Norman 1971), 26–41, Norman 1972.

  13. C. A. Rogers andG. C. Shephard, The difference body of a convex body. Arch. Math.8, 220–233 (1957).

    Google Scholar 

  14. C. A. Rogers andG. C. Shephard, Some extremal problems for convex bodies. Mathematika5, 93–103 (1958).

    Google Scholar 

  15. R. Schneider, A characterisitc extremal property of simplices. Proc. Amer. Math. Soc.40, 247–249 (1973).

    Google Scholar 

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The author wishes to thank Professor R. Schneider for helpful discussion, especially for referring his attention to the useful notionincluded double cone.

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Martini, H. A new view on some characterizations of simplices. Arch. Math 55, 389–393 (1990). https://doi.org/10.1007/BF01198479

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  • DOI: https://doi.org/10.1007/BF01198479

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