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Six-dimensional theories provide a unification of four-dimensional theories via dimensional reduction together with access to some of the novel features arising from M-theory. Ambitwistor strings directly generate S-matrices for massless theories in terms of formulae that localize on the solutions to the scattering equations; algebraic equations that determine n points on the Riemann sphere from n massless momenta. These are sufficient to provide compact formulae for tree-level S-matrices for bosonic theories. This talk introduces their extension to the polarized scattering equations which arise from twistorial versions on ambitwistor-strings. These lead to simple explicit formulae for superamplitudes in 6D for super Yang-Mills, supergravity, D5 and M5 branes and massive superamplitudes in 4D. The framework extends also to 10 and 11 dimensions. This is based on joint work with Yvonne Geyer, arxiv:1812.05548 and 1901.00134.