Bi-embeddings of the projective space PG(3, 2)
A bi-embedding of a pair of Steiner triple systems \(S\), \(S'\) in an (orientable or nonorientable) surface is a face 2-colourable triangulation of the surface in which the triangular faces of the two colours form Steiner triple systems isomorphic to \(S\) and \(S'\), respectively. The authors determine all bi-embeddings in which both \(S\) and \(S'\) are isomorphic to the design of points and lines of the projective space \(\text{PG}(3, 2)\). There is up to an isomorphism a unique bi-embedding in an orientable surface, and exactly three nonisomorphic bi-embeddings in a nonorientable surface.
scientific article; zbMATH DE number 1471117