Abstract
In this paper, we construct three numerical Burniat surfaces as desingularizations of double planes of degree >10. Two are surfaces having the bigenus P2=4 and the third is a surface having the bigenus P2=5. In addition, another surface of general type is constructed as a desingularization of a double plane of degree 12 having the birational invariants: q=p g =1, P2=4. One of the numerical Burniat surfaces with P2=4 is obtained as a desingularization of a double plane of degree 22 with an irreducible branch locus, so it is a good candidate for having torsion zero. Moreover, its bicanonical transformation seems to be birational.
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