Almost convex groups and the eight geometries

IfM is a closed Nil geometry 3-manifold then π1(M) is almost convex with respect to a fairly simple “geometric” generating set. IfG is a central extension or a ℤ extension of a word hyperbolic group, thenG is also almost convex with respect to some generating set. Combining these with previously known results shows that ifM is a closed 3-manifold with one of Thurston's eight geometries, π1(M) is almost convex with respect to some generating set if and only if the geometry in question is not Sol.