Small volume closed hyperbolic 4-manifolds

Further examples of non-orientable compact hyperbolic 4-manifoldsof volume 32²/3 arising from torsion-free subgroups of the 5,3, 3, 3] Coxeter group are given. These are the smallest knownclosed hyperbolic 4-manifolds and arise by consideration ofmaps from the 5, 3, 3, 3] Coxeter group onto the simple simplecticgroup S₄(4).