  Distance-based methods such as UPGMA (Unweighted Pair Group Method with
Arithmetic Mean) continue to play a significant role in phylogenetic research.
We use polyhedral combinatorics to analyze the natural subdivision of the
positive orthant induced by classifying the input vectors according to tree
topologies returned by the algorithm. The partition lattice informs the study
of UPGMA trees. We give a closed form for the extreme rays of UPGMA cones on n
taxa, and compute the normalized volumes of the UPGMA cones for small n.
  Keywords: phylogenetic trees, polyhedral combinatorics, partition lattice
