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Let S be a minimal surface of general type with p  g (S) = 0 and K   S  2  = 4. Assume the bicanonical map ϕ of S is a morphism of degree 4 such that the image of ϕ is smooth. Then we prove that the surface S is a Burniat surface with K 2 = 4 and of non nodal type.

A characterization of Burniat surfaces with K 2=4 and of non nodal type