Spheres in 24 Dimensions in Leech Lattice

Theorem

Let a set of identical spheres in a $24$-dimensional space be arranged in a Leech lattice.

Then each sphere will touch $196 \, 560$ other spheres.

This is believed to be the densest possible sphere packing in $24$ dimensions.

Proof

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Sources

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

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $24$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $196,560$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $24$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $196,560$