Determination of all regular maps of small genus
Journal of Combinatorial Theory Series B
Modelling finite geometries on surfaces
Discrete Mathematics - Algebraic and topological methods in graph theory
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A biplane is a geometry corresponding to a symmetric (k2)+1, k, 2). block design. Noutrivial biplanes are known to exist only for k = 3, 4, 5, 6, 9, 11 and 13. Group difference set constructions exist for the unique biplanes having k = 3, 4, and 5, for all three biplanes having k = 6; and for one of the four biplanes having k = 9. We find models for these seven biplanes, using Cayley graph imbeddings on closed 2-manifolds.