Triangulations of orientable surfaces by complete tripartite graphs

Orientable triangular embeddings of the complete tripartite graph image correspond to biembeddings of Latin squares. We show that if n is prime there are at least image nonisomorphic biembeddings of cyclic Latin squares of order n. If image, where p is a large prime number, then the number of nonisomorphic biembeddings of cyclic Latin squares of order n is at least image. Moreover, we prove that for every n there is a unique regular triangular embedding of image in an orientable surface.