Abstract
The centrally symmetric convex polytopes whose images under orthogonal projection on to any pair of orthogonal complementary subspaces ofE d have numerically equal volumes are shown hare to be certain cartesian products of polygons and line segments. Ford≥3, the general projection property in fact follows from that for pairs of hyperplanes and lines. A conjecture is made about the problem in the non-centrally symmetric case.
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McMullen, P. Volumes of complementary projections of convex polytopes. Monatshefte für Mathematik 104, 265–272 (1987). https://doi.org/10.1007/BF01294650
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DOI: https://doi.org/10.1007/BF01294650