Covers by polars of arrangements
B. Curtis Eaves, Alan J. Hoffman · 1990
For a collection of hyperplanes passing through the origin in euclidean space let S be the induced subdivision. Let T be the collection of polars of the full cells of S. If only the origin lies in all hyperplanes, T forms a {kappa} {approximately} fold cover of euclidean space. If, in addition, the collection of hyperplanes is of size m and is regular, then {kappa} is m {minus} 1 choose n {minus} 1. Other similar results relate to spheres, hemispheres, and linear programming.