In this paper we consider finding a minimum-sum dipolar spanning tree in R3, and present an algorithm that takes O(n2 log2 n) time using O(n2) space, thus almost match- ing the best known results for the planar case. To achieve this, we prove an interesting result related to the complex- ity of the common intersection of n balls in R3, of possi- ble different radii, that are all tangent to a given point p. The problem has applications in communication networks, when the goal is to minimize the distance between two hubs or servers as well as the distance from any node in the net- work to the closer of the two hubs, and could lead to reduc- tion in power consumption for devices like PDAs, sensors, cell phones and laptops.