# Cross-Sections of Leech Lattice

Jump to navigation
Jump to search

## Theorem

Except for dimensions $10$, $11$ and $13$, the densest possible sphere packing in all dimensions lower than $24$ can be obtained by cross-sections of the $24$-dimensional space Leech lattice arrangement.

## Proof

## Sources

- Jan. 1984: N.J.A. Sloane:
*The Packing of Spheres*(*Scientific American***Vol. 250**,*no. 1*: 116 – 125)

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $24$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $24$