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In this paper, we present two related results on curves of genus 3. The firstgives a bijection between the classes of the following objects:  * Smooth non-hyperelliptic curves C of genus 3, with a choice of an element ain Jac(C)[2]-{0}, such that the cover C/|K_C+a|^* does not have an intermediatefactor; up to isomorphism.  * Plane curves E,Q in P^2 and an element in b' in Pic(E)[2]-{0}, where E,Qare of degrees 3,2, the curve E is smooth and Q,E intersect transversally ; upto projective transformations.  We discuss the degenerations of this bijection, and give an interpretation ofthe bijection in terms of Abelian varieties. Next, we give an application ofthis correspondence: An EXPLICIT proof of the reconstructability of ANY smoothplane quartic from its bitangents.Comment: 24 pages, LaTeX 2e amsart, xypi

Any smooth plane quartic can be reconstructed from its bitangents