Apollonian sphere packing

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, doi:10.1142/S0218348X94000739, retrieved 2008-09-15
↑ ApolFrac

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 Close-packing Kissing number problem Sphere-packing (Hamming) bound

Other packings	Bin Tetrahedron Set

Puzzles	Conway Slothouber–Graatsma

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