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Given an integer  b  and a finitely presented group  G , we produce a compact symplectic 6‐manifold with  c  1 =0,  b  2 > b ,  b  3 > b  and  π  1 = G . In the simply connected case, we can also arrange for  b  3 =0; in particular, these examples are not diffeomorphic to Kähler 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.

The diversity of symplectic Calabi–Yau 6‐manifolds