We develop a way of seeing a complete orientable hyperbolic 4-manifold
M as an orbifold cover of a Coxeter polytope P⊂H4 that has a facet colouring. We also develop a way of finding
totally geodesic sub-manifolds N in M, and describing
the result of mutations along N. As an application of our method,
we construct an example of a complete orientable hyperbolic 4-manifold
X with a single non-toric cusp and a complete orientable hyperbolic
4-manifold Y with a single toric cusp. Both X and
Y have twice the minimal volume among all complete orientable
hyperbolic 4-manifolds.Comment: 24 pages, 11 figures; to appear in Proceedings of the London
Mathematical Societ