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Apollonian sphere packing is the three-dimensional equivalent of the Apollonian gasket. The principle of construction is very similar: with any four spheres that are cotangent to each other, it is then possible to construct two more spheres that are cotangent to four of them.

The fractal dimension is approximately 2.473946 (±1 in the last digit).[1]

Software for generating and visualization of the apollonian sphere packing: ApolFrac.[2]
References

Borkovec, M.; De Paris, W.; Peikert, R. (1994), "The Fractal Dimension of the Apollonian Sphere Packing" (PDF), Fractals, 2 (4), pp. 521–526, CiteSeerX 10.1.1.127.4067, doi:10.1142/S0218348X94000739, archived from the original (PDF) on 2016-05-06, retrieved 2008-09-15

ApolFrac

vte

Packing problems
Circle packing

In a circle / equilateral triangle / isosceles right triangle / square Apollonian gasket Circle packing theorem Tammes problem (on sphere)

Sphere packing

Apollonian In a sphere In a cube In a cylinder Close-packing Kissing number problem Sphere-packing (Hamming) bound

Other packings

Bin Tetrahedron Set

Puzzles

Conway Slothouber–Graatsma