A084825 Maximum number of spheres of diameter one that can be packed in a cube of edge length n.

1, 8, 27, 66

Offset: 1

Author

Hugo Pfoertner, Jun 12 2003

Keywords

• hard
• more
• nonn

Comments

From an extrapolation of Dave Boll's numerical results a(4)~=66 and a(5)~=141 are estimated values for the next terms.

However, E. Specht's data suggest a(5)=135. - Hugo Pfoertner, Jul 08 2025

Examples

			a(3)=27 because there is no known better arrangement than the 3*3*3 cubic one that would allow packing more than 27 spheres into a cube of edge length 3.
		

Links

• Dave Boll, Optimal Packing of Circles and Spheres
• Hugo Pfoertner, Densest Packings of Equal Spheres in a Cube
• Hugo Pfoertner, How to pack 66 spheres of diameter 1 in 4 x 4 x 4 cubic box, YouTube video by Talabfahrer, 2016.
• Hugo Pfoertner, Observed number N of spheres in best packing known versus edge length x of cube, comparison against empirical lower limit N > 1.325*x^2*(x-1), (2025).
• Eckard Specht, The best known packings of equal spheres in a cube (complete up to N = 1000), 2013.

Crossrefs

Cf. A084824, A084828, A084617.

Extensions

a(4) from Hugo Pfoertner, May 21 2011