D₄ root lattice

A. Korkine and G. Zolotareff, Sur les formes quadratiques positives quaternaires, Math. Ann. 5 (1872), 581–583, doi:10.1007/BF01442912.

This packing consists of a lattice in 4 dimensions. A Gram matrix for the lattice is given below as comma-separated values. See the table of densities for how this packing compares with other dimensions.

4 × 4 Gram matrix

2,1,-1,1
1,2,-1,1
-1,-1,2,0
1,1,0,2