  We give an explicit presentation for each lower bound cluster algebra. Using
this presentation, we show that each lower bound algebra Grobner degenerates to
the Stanley-Reisner scheme of a vertex-decomposable ball or sphere, and is thus
Cohen-Macaulay. Finally, we use Stanley-Reisner combinatorics and a result of
Knutson-Lam-Speyer to show that all lower bound algebras are normal.
