Kissing Numbers

(Image: Tkdeason, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons)

The kissing number of a lattice structure is the number of other spheres that a sphere can touch. The maximal kissing number has been determined for dimensions up to 8. These kissing numbers are part of the On-line Encyclopedia of Integer Sequences as A001116 (0, 2, 6, 12, 24, 40, 72, 126, 240, 272).

For example, in the 2-D lattice shown above, the simple cubic arrangement has a kissing number of 4, while the hexagonal packing arrangement has a kissing number of 6 (the maximal number for 2-D). In a 3-D lattice, the maximal kissing number is 12

This blog has explored lattice structures in multiple dimensions in prior posts. See:

Atomic interstitial sizes in higher dimensions

Book Review – Instant Mathematics by Paul Parsons and Gail Dixon

Fields Medal Awarded to Maryna Sergiivna Viazovska (Марина Сергіївна Вязовська)

David Hilbert Problems