From Looney Pyramid Games Wiki
A Nest

::LMSE :Arrow ::LMS

A Nest is a specific arrangement of a trio of pyramids, namely a stack with a large piece on top, a medium piece in the middle, and a small piece on the bottom. The hollow Icehouse pieces are designed so that each piece fits neatly inside another piece of the next larger size. The three-piece stack complementary to the Nest is the Tree.

It is probably an accidental verity that you can put a Nest in your Tree, but you can't put a Tree in your Nest.