  We find exact solutions to the Hamiltonian of a 16-site spin-1/2 pyrochlore
crystal with nearest neighbour exchange interactions. The methods of group
theory (symmetry) are used to completely block-diagonalize the Hamiltonian,
yielding precise details about symmetry of the eigenstates, in particular those
components which are {\em spin ice} states, in order to evaluate the spin ice
density at finite temperature. At low enough temperatures, a `perturbed' spin
ice phase is clearly outlined within the four parameter space of the general
model of exchange interactions. The quantum spin ice phase is expected to exist
outside these boundaries.
