Self-dual orientable embeddings of Kn

Whenever Euler's Formula does not exclude a self-dual embedding of K_n in an orientable 2-manifold, we construct one. This completes a problem partially solved by Lothar Heffter in 1898 and Arthur White in 1973. The method employs a more general type of current graph than that used to construct triangular embeddings. Self-duality does not follow directly from the index one nature of the constructed embeddings.