  Given an integer b and a finitely presented group G we produce a compact
symplectic six-manifold with c_1 = 0, b_2 > b, b_3 > b and fundamental group G.
In the simply-connected case we can also arrange for b_3 = 0; in particular
these examples are not diffeomorphic to K\"ahler manifolds with c_1 = 0. The
construction begins with a certain orientable four-dimensional hyperbolic
orbifold assembled from right-angled 120-cells. The twistor space of the
hyperbolic orbifold is a symplectic Calabi-Yau orbifold; a crepant resolution
of this last orbifold produces a smooth symplectic manifold with the required
properties.
