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We embed neighborhood geometries of graphs on surfaces as point-circle configurations. We give examples coming from regular maps on surfaces with a maximum number of automorphisms for their genus, and survey geometric realization of pentagonal geometries coming from Moore graphs. An infinite family of point-circle \(v_4\) configurations on p-gonal surfaces with two p-gonal morphisms is given. The image of these configurations on the sphere under the two p-gonal morphisms is also described.

Isometric Point-Circle Configurations on Surfaces from Uniform Maps