  We calculate the integer cohomology ring and stable tangent bundle of a
family of compact, 3-Sasakian 7-manifolds constructed by Boyer, Galicki, Mann,
and Rees. Previously only the rational cohomology ring was known. The most
important part of the cohomology ring is a torsion group that we describe
explicitly and whose order we compute. There is a surprising connection with
the combinatorics of trees.
