Packing Cones and Their Negatives in Space

Let C be a cone in R3 whose base B is a planar convex body in a horizontal plane π and whose tip is a point v /∈ π. Let C be a packing formed by translates of C and −C in R3 . We exhibit an explicit constant c > 0 such that the density of any such C is is smaller than 1−c, answering a question of Wlodek Kuperberg.

• Type: Journal
• Year: 2007
• Where: DCG
• Authors: Imre Bárány, Jirí Matousek
• Keywords: DCG 2007, Horizontal Plane, Planar Convex Body