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Apr 21, 2011 at 7:16 comment added Mario Stefanutti I made a correction to the question (as pointed out by jc). I was interested in "regular maps" without forcing 3-vertex-connectivity. Sorry for the mistake. The abstract of the paper reports: "In the paper, we enumerate three classes of cubic planar maps with no loops or multiple edges: 1-connected; 2-connected; 3-connected and triangle-free." The results I found manually give these results for 3, 4 and 5 faces: 1 maps, 3 maps, 20 maps.
Apr 19, 2011 at 20:54 history answered Igor Rivin CC BY-SA 3.0