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Geometric Engineering is an important tool to construct interesting and non-Lagrangian theories in various dimensions. If a gauge algebra admits discrete automorphisms, there is the possibility to twist by them when performing a circle reduction. Since F-theory is related to M-theory by circle reductions, this begs the question which geometries capture such twisted gauge algebras in geometry. In this talk I will argue that so called genus-one fibrations are the key ingredient to engineer such twisted algebras in five dimensions. I use the algebraic description of the threefold to compute multiplicities of BPS states, perform conifold transitions to untwisted algebras and outline further applications if time permits. This talk is based on upcoming work with L. Anderson and J. Gray.