Packing Cube Nets into Rectangles with O(1) Holes

Abstract

We show that the 11 hexomino nets of the unit cube (using arbitrarily many copies of each) can pack disjointly into an \(m \times n\) rectangle and cover all but a constant c number of unit squares, where \(4 \le c \le 14\) for all integers \(m, n \ge 2\). On the other hand, the nets of the dicube (two unit cubes) can be exactly packed into some rectangles.