Abstract
A convex polyhedron
P is
equiprojective if, for some
k, the orthogonal projection (or “shadow”) of
P in every direction, except those directions parallel to faces of
P, is a
k-gon. We address an open question posed by Shepherd and reported in Croft, Falconer, and Guy's “Unsolved Problems in Geometry”, by characterizing equiprojective polyhedra, and giving an
O
(
n
log
n
)
-time recognition algorithm.