E₈ root lattice

A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795.

This packing consists of a lattice in 8 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.

8 × 8 Gram matrix

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