  The Coulomb phase of spin ice, and indeed the Ic phase of water ice,
naturally realise a fully-packed two-colour loop model in three dimensions. We
present a detailed analysis of the statistics of these loops, which avoid
themselves and other loops of the same colour, and contrast their behaviour to
an analogous two-dimensional model. The properties of another extended degree
of freedom are also addressed, flux lines of the emergent gauge field of the
Coulomb phase, which appear as "Dirac strings" in spin ice. We mention
implications of these results for related models, and experiments.
