Orientable biembeddings of cyclic Steiner triple systems from current assignments on Möbius ladder graphs

We give a characterization of a current assignment on the bipartite Möbius ladder graph with 2n+12n+1 rungs. Such an assignment yields an index one current graph with current group Z12n+7Z12n+7 that generates an orientable face 2-colorable triangular embedding of the complete graph K12n+7K12n+7 or, equivalently, an orientable biembedding of two cyclic Steiner triple systems of order 12n+712n+7. We use our characterization to construct Skolem sequences that give rise to such current assignments. These produce many nonisomorphic orientable biembeddings of cyclic Steiner triple systems of order 12n+712n+7.