Abstract
Abstract Toric Ricci--flat metrics in dimension four correspond to certain holomorphic vector bundles over a
twistor space. We construct these bundles explicitly, by exhibiting and characterising their patching matrices, 
for the five--parameter family of Riemannian ALF metrics constructed by Chen and Teo. The Chen--Teo family contains
a two--parameter family of asymptotically flat gravitational instantons. The patching matrices for these 
instantons take a simple rational form.
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