Each vertex is an admissible diamond. Each leaf is a degeneration, then pivots a irreducible sl₂×sl₂ representation + it's conjugate (if it has one) onto its limit (in the sense of lie theory). We call these objects piles, because analogously to sand piles they populate adjacent cells as soon as the pile has enough sand. They differ from sandpiles in that the possible ways to “fall” is not unique, and in fact all paths are taken (all the ways to decompose a diamond into piles). Drag / wheel to navigate; click nodes in graph view.