The diversity of symplectic Calabi-Yau six-manifolds

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Given an integer b and a finitely presented group G we produce a compact symplectic six-manifold with c₁ = 0, b₂ > b, b₃ > b and fundamental group G. In the simply-connected case we can also arrange for b₃ = 0; in particular these examples are not diffeomorphic to Kähler manifolds with c₁ = 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.