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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 "Diracdoi:10.1103/physrevlett.107.177202 pmid:22107573 fatcat:zwzpnoiee5emdev4m6rnpbaxyy