Abstract. Orientable triangular embeddings of the complete tripartite graphs Kn,n,n correspond to biembeddings of Latin squares. We show that if n is prime there are at least en.ln(n)-O(n) nonisomorphic biembeddings of cyclic Latin square of order n. If n=kp, where p is a large prime number, then the number of nonisomorphic biembeddings of cyclic Latin square of order n is at least e(n/k)ln(n)-O(n) . Moreover, we prove that for every n there is a unique (reflexible) regular triangular embedding of Kn,n,n in an orientable surface.