  What is the zero-temperature ordering pattern of a Heisenberg antiferromagnet
with large spin length $S$ (and possibly small dilution), on the kagome
lattice, or others built from corner-sharing triangles and tetrahedra? First, I
summarize the uses of effective Hamiltonians to resolve the large ground-state
degeneracy, leading to long-range order of the usual kind. Secondly, I discuss
the effects of dilution, in particular to {\it non}-frustration of classical
ground states, in that every simplex of spins is optimally satisfied. Of three
explanations for this, the most complete is Moessner-Chalker
constraint-counting. Quantum zero-point energy may compete with classical
exchange energy in a diluted system, creating frustration and enabling a
spin-glass state. I suggest that the regime of over 97% occupation is
qualitatively different from the more strongly diluted regime.
