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The paper is one of a series devoted to the classification, the moduli spaces and the classification of surfaces of general type with \(p_g=0\). Here we generalize a classical construction due to P. Burniat (revised by M. Inoue). Among other results we construct a family of surfaces of general type with \(K_S^2 = 3\), \(p_g(S) = 0\) realizing a new fundamental group of order 16.

Burniat-type surfaces and a new family of surfaces with $$p_g = 0, K^2=3$$