The convex hull of the integer points in a large ball (Q1271225)

The ``integer convex hull'' of the \(d\)-dimensional ball of radius \(r\) centered at the origin (denoted \(rB^d\)) is defined as \(P_r=conv(Z^d \cap rB^d)\). In this beautiful paper the authors write lower and upper bounds for the number of \(k\)-dimensional faces of \(P_r\). This extends previous work for the two dimensional case.