The densest lattice in twenty-four dimensions.
Every sequence of positive or negative homothetic copies of a planar convex body whose total area does not exceed times the area of can be translatively packed in .
Let S be a square and let S' be a square of unit area with a diagonal parallel to a side of S. Any (finite or infinite) sequence of homothetic copies of S whose total area does not exceed 4/9 can be packed translatively into S'.