  We study a local ferromagnetic Ising model for classical spins on the
trillium lattice. The ground state of this model features two spins out(/in)
and one spin in(/out) on each triangle, and leads to a macroscopic ground state
degeneracy. Our Monte Carlo simulations find a ground state entropy
intermediate to that of spin ice on the kagome and pyrochlore lattices,
suggesting that trillium spin ice is highly frustrated. To motivate the search
for trillium spin ice, we calculate the magnetic susceptibility and structure
factor. We note the qualitative resemblance of the susceptibility to previously
published work on EuPtSi, which features local moments on the trillium lattice.
