There are 9 non-isomorphic incidence geometries on 6 points, having 6 to 15 lines each. Find the incidence geometry with 6 points and 6 lines, find the one with 6 points and 15 lines, and find at least two other incidence geometries on 6 points and that are not isomorphic to any of the other geometries. Each additional non-isomorphic incidence geometry will count as extra credit.

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