The study of self-duality has attracted some attention over the past decade.A good deal of research in that time has been done on constructing and classifying all self-dual graphs and in particular polyhedra.We will give an overview of the recent research in the first two chapters.In the third chapter, we will show the necessary condition that a self-complementary self-dual graph have n ≡ 0, 1 (mod 8) vertices and we will review White;;s infinite class (the Paley graphs, for which n ≡ 1 (mod 8)).Finally, we will construct a new infinite class of self-complementary self-dual graphs for which n ≡ 0 (mod 8).
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