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We prove that for n > 3 every STS(n) has both an orientable and a nonorientable embedding in which the triples of the STS(n) appear as triangular faces and there is just one additional large face. We also obtain detailed results about the possible automorphisms of such embeddings.doi:10.1016/j.ejc.2004.01.014 fatcat:i3rp3awda5dr7feyqo4kzljea4