Kallus, Y.
We consider the problem of identifying the worst point-symmetric shape for covering -dimensional Euclidean space with lattice translates. Here we focus on the dimensions where the thinnest lattice covering with balls is known and ask whether the ball is a pessimum for covering in these dimensions compared to all point-symmetric convex shapes. We find that the ball is a local pessimum in 3 dimensions, but not so in 4 and 5 dimensions.