Nonorientable biembeddings of Steiner triple systems

Constructions due to Ringel show that there exists a nonorientable face 2-colourable triangular embedding of the complete graph on n vertices (equivalently a nonorientable biembedding of two Steiner triple systems of order n) for all n≡3 (mod 6) with n9. We prove the corresponding existence theorem for n≡1 (mod 6) with n13