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Extremum problems for zonotopes

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References

  1. Aitken, A., Determinants and Matrices, Oliver and Boyd, London, 1956.

    Google Scholar 

  2. Bokowski, J. and Sturmfels, B., ‘Oriented Matroids and Chirotopes — Problems of Geometric Realizability’, Preprint, TH, Darmstadt, 1985.

  3. Bonnesen, T. and Fenchel, W., Theorie der konvexen Körper, Springer-Verlag, Berlin, 1934.

    Google Scholar 

  4. Busemann, H., Ewald, G. and Shephard, G.C., ‘Convex Bodies and Convexity on Grassmann Cones’, Math. Annal. 151 (1963), 1–14.

    Google Scholar 

  5. Chakerian, G. D. and Filliman, P., ‘The Measures of the Projection of a Cube’, (Studia Sci. Math. Hungarica, to appear).

  6. Coxeter, H. S. M., Regular Polytopes, Dover, New York, 1973.

    Google Scholar 

  7. Fejes Toth, L., Regular Figures, Macmillian, New York, 1964.

    Google Scholar 

  8. Griffiths, P. and Harris, J., Principles of Algebraic Geometry, Wiley, New York, 1978.

    Google Scholar 

  9. Grünbaum, B., Convex Polytopes, Wiley, London, 1967.

    Google Scholar 

  10. Hadwiger, H., Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer-Verlag, Berlin, 1957.

    Google Scholar 

  11. Hodge, W. and Pedoe, D., Methods of Algebraic Geometry, Vol. I, Cambridge Univ. Press, London, 1947.

    Google Scholar 

  12. Kramer, P. and Neri, R., ‘On Periodic and Non-periodic Space Fillings of E m obtained by Projections’, Acta Cryst. A40 (1984), 580–587.

    Google Scholar 

  13. Linhart, J., ‘An Upper Bound for the Intrinsic Volumes of Equilateral Zonotopes’, Coll. math. soc. János Bolyai 48, Intuitive Geometry, Siófok, 1985.

    Google Scholar 

  14. Linhart, J., ‘Extremaleigenschaften der regulären 3-Zonotope’, Studia Sci. Math. Hungarica 21 (1986), 94–98.

    Google Scholar 

  15. Martini, H. and Weissbach, B., ‘Zur besten Beleuchtung konvexer Polyeder’, Beiträge Algebra Geometrie 17 (1984), 151–168.

    Google Scholar 

  16. McMullen, P., ‘On Zonotopes’, Trans. Amer. Math. Soc. 159 (1971), 91–109.

    Google Scholar 

  17. McMullen, P., ‘Volumes of Projections of Unit Cubes’, Bull. London Math. Soc. 16 (1984), 278–280.

    Google Scholar 

  18. McMullen P., and Betke, U., ‘Estimating the Sizes of Convex Bodies from Projections’, J. London Math. Soc. (2), 27 (1983), 525–538.

    Google Scholar 

  19. Schneider, R. and Weil, W., ‘Zonoids and Related Topics’ in Convexity and its Applications, Birkhäuser, 1983, pp. 296–317.

  20. Shephard, G. C., ‘Combinatorial Properties of Associated Zonotopes’, Canad. J. Math. XXVI, No. 2 (1974), 302–321.

    Google Scholar 

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Filliman, P. Extremum problems for zonotopes. Geom Dedicata 27, 251–262 (1988). https://doi.org/10.1007/BF00181491

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  • DOI: https://doi.org/10.1007/BF00181491

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