A Tree is a specific arrangement of a trio of pyramids, namely a stack with a small piece on top, a medium piece in the middle, and a large piece on the bottom. The hollow Icehouse pieces are designed with parallel inner walls and a rounded inner apex, so that they stack nicely, but do not get stuck together. The three-pyramid arrangement complementary to the Tree is the Nest.
Evidently, the pyramid "tree" is named after the roughly conical sort of pine tree, since it does not display the sort of branching that is usually characteristic of "trees" (e.g. genealogical trees and other tree diagrams).