Geometriae Dedicata

, Volume 117, Issue 1, pp 47-64

First online:

On the Number of Tubes Touching a Sphere or a Tube

  • Eugene L. StarostinAffiliated withMax Planck Institute for Physics of Complex Systems Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


A problem is formulated about how many unit-radius tubes can touch a ball of given radius from the outside and from the inside. Upper bounds for the maximum numbers of contacts are obtained for both interior and exterior contacts. It is also shown that the maximum number of unit-radius tubes touching the same orthogonal cross-section of a particular tube of radius P is [π (arcsin(P+1)−1)−1] and if the number of contacts takes on its maximum, then all tubes are locally aligned.


packing tube bialy kissing number spherical codes Tammes’ problem

Mathematics Subject Classifications (2000)