Orientable biembeddings of Steiner triple systems of order 15

A complete enumeration is given of orientable biembeddings involving five of the \( 80 \) Steiner triple systems of order \( 15 \). As a consequence, it follows that each of the \( 80 \) systems has a biembedding in an orientable surface, and precisely \( 78 \) of the systems have orientable self-embeddings.