The method used in Needles provides each cube with the part of its ``family tree'' comprising the direct line of descent from the root to itself. It therefore knows how it is related to its parent, how its parent was related to its grandparent, and so on. A cube knows only about its own ``branch'', which is passed down to it by its parent.
The relationship between parent and child cubes is contained in the child indices . Each cube therefore receives a list of such index triplets, detailing the relationships between ancestors of different generations. The list is linked backwards, i.e. from child to root. The formulae to calculate a cube's centre coordinates are simpler when the list is traversed in this direction. They are computational in nature, involving iteration when traversing the list, so we have not included them here, but they are given in the next section in procedure .