Leech Lattice Questions

Many questions arise and might be answered by these tools. I want to compare this lattice with the laminar lattices I study here using oblique coördinates. Here is a list of inner products with neighbor points with (4, 4, 0, 0, 0, ...).

(4, 4, ...	32
(4, 0, ...	16
(3, 1, ...	16
(3, −1, ...	8
(2, 2, ...	16
(2, 0, ...	8
(2, −2, ...	0

And all of the negatives. Here is code to enumerate all of the neighbors. It checks LL membership via this program. A variation verifies that there is no overlapping between balls that touch the origin ball. Further, all distances between neighbors have the same distribution. E.g, every neighbor of the origin ball touches 4600 other neighbors of the origin.