  I consider the class of "depleted pyrochlore" lattices of corner-sharing
triangles, made by removing spins from a pyrochlore lattice such that every
tetrahedron loses exactly one. Previously known examples are the "hyperkagome"
and "kagome staircase". I give criteria in terms of loops for whether a given
depleted lattice can order analogous to the kagome \sqrt{3} \times \sqrt{three}
state, and also show how the pseudo-dipolar correlations (due to local
constraints) generalize to even the random depleted case.
