References
Aitken, A., Determinants and Matrices, Oliver and Boyd, London, 1956.
Bokowski, J. and Sturmfels, B., ‘Oriented Matroids and Chirotopes — Problems of Geometric Realizability’, Preprint, TH, Darmstadt, 1985.
Bonnesen, T. and Fenchel, W., Theorie der konvexen Körper, Springer-Verlag, Berlin, 1934.
Busemann, H., Ewald, G. and Shephard, G.C., ‘Convex Bodies and Convexity on Grassmann Cones’, Math. Annal. 151 (1963), 1–14.
Chakerian, G. D. and Filliman, P., ‘The Measures of the Projection of a Cube’, (Studia Sci. Math. Hungarica, to appear).
Coxeter, H. S. M., Regular Polytopes, Dover, New York, 1973.
Fejes Toth, L., Regular Figures, Macmillian, New York, 1964.
Griffiths, P. and Harris, J., Principles of Algebraic Geometry, Wiley, New York, 1978.
Grünbaum, B., Convex Polytopes, Wiley, London, 1967.
Hadwiger, H., Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer-Verlag, Berlin, 1957.
Hodge, W. and Pedoe, D., Methods of Algebraic Geometry, Vol. I, Cambridge Univ. Press, London, 1947.
Kramer, P. and Neri, R., ‘On Periodic and Non-periodic Space Fillings of E m obtained by Projections’, Acta Cryst. A40 (1984), 580–587.
Linhart, J., ‘An Upper Bound for the Intrinsic Volumes of Equilateral Zonotopes’, Coll. math. soc. János Bolyai 48, Intuitive Geometry, Siófok, 1985.
Linhart, J., ‘Extremaleigenschaften der regulären 3-Zonotope’, Studia Sci. Math. Hungarica 21 (1986), 94–98.
Martini, H. and Weissbach, B., ‘Zur besten Beleuchtung konvexer Polyeder’, Beiträge Algebra Geometrie 17 (1984), 151–168.
McMullen, P., ‘On Zonotopes’, Trans. Amer. Math. Soc. 159 (1971), 91–109.
McMullen, P., ‘Volumes of Projections of Unit Cubes’, Bull. London Math. Soc. 16 (1984), 278–280.
McMullen P., and Betke, U., ‘Estimating the Sizes of Convex Bodies from Projections’, J. London Math. Soc. (2), 27 (1983), 525–538.
Schneider, R. and Weil, W., ‘Zonoids and Related Topics’ in Convexity and its Applications, Birkhäuser, 1983, pp. 296–317.
Shephard, G. C., ‘Combinatorial Properties of Associated Zonotopes’, Canad. J. Math. XXVI, No. 2 (1974), 302–321.
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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