Double lattice

In three dimensions, a double lattice is a space group of the type 1, as denoted by international notation.

In many cases the highest known packing density for a body is achieved by a double lattice.

Examples include the regular pentagon, heptagon, and nonagon[1] and the equilateral triangular bipyramid.

[3] In a preprint released in 2016, Thomas Hales and Wöden Kusner announced a proof that the double lattice packing of the regular pentagon has the optimal density among all packings of regular pentagons in the plane.

[4] This packing has been used as a decorative pattern in China since at least 1900, and in this context has been called the "pentagonal ice-ray".