15d packing

Laminated lattice Λ15

E. S. Barnes and G. E. Wall, Some extreme forms defined in terms of Abelian groups, J. Austral. Math. Soc. 1 (1959), 47–63, doi:10.1017/S1446788700025064.

This packing consists of a lattice in 15 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.

15 × 15 Gram matrix

4,2,-2,2,2,2,2,2,0,2,2,1,1,-2,2
2,4,-2,2,2,2,2,2,0,2,2,1,2,-1,1
-2,-2,4,0,0,0,0,0,0,0,0,-2,-1,1,-1
2,2,0,4,2,2,2,2,1,1,1,0,1,0,1
2,2,0,2,4,2,2,2,1,1,1,0,2,-1,0
2,2,0,2,2,4,2,2,1,1,1,1,1,-1,0
2,2,0,2,2,2,4,2,1,1,1,1,2,-2,1
2,2,0,2,2,2,2,4,1,1,1,1,2,-2,0
0,0,0,1,1,1,1,1,4,-3,-3,2,2,0,-2
2,2,0,1,1,1,1,1,-3,6,4,-1,-1,-1,3
2,2,0,1,1,1,1,1,-3,4,6,-2,0,-1,3
1,1,-2,0,0,1,1,1,2,-1,-2,4,2,-2,0
1,2,-1,1,2,1,2,2,2,-1,0,2,4,-2,0
-2,-1,1,0,-1,-1,-2,-2,0,-1,-1,-2,-2,4,-1
2,1,-1,1,0,0,1,0,-2,3,3,0,0,-1,4