Volumes of complementary projections of convex polytopes

Abstract

The centrally symmetric convex polytopes whose images under orthogonal projection on to any pair of orthogonal complementary subspaces ofEd 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.