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2-Periodic self-dual tilings are important in fields ranging from crystal chemistry to mathematical physics. They have been systematically enumerated using combinatorial tiling theory, and 1, 5 and 62 uninodal, binodal and trinodal self-dual tilings have been found. This paper illustrates all uninodal and binodal self-dual tilings and selected trinodal self-dual tilings. Most of these structures are described for the first time. [ABSTRACT FROM AUTHOR]