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I'm looking for a formula which determines the number of external (that is, non-touching) edges in multiple tiled hexagons.

By observation, there are 10 external edges when 2 hexagons are adjacent. There are 30 external edges in a pattern of 19 hexagons. But I would like a formula.

fonini
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ThomasDoe
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    Wouldn't the answer depend on just how the hexagons are joined? Three hexagons in a line give a different answer than three that have a common vertex. – Rory Daulton Jul 01 '15 at 19:53
  • @RoryDaulton Hmmm... I was wondering that - but from what I can see, there are always 14 external edges to 3 adjacent hexagons. Happy to be shown I'm wrong. – ThomasDoe Jul 01 '15 at 20:07
  • If the hexagons are in a line, there are $14$ external edges, but there are only $12$ if the hexagons have a common vertex. – Rory Daulton Jul 01 '15 at 20:21
  • @RoryDaulton Sorry, my bad. So I presume there's no common formula. Any ideas, anyone? – ThomasDoe Jul 01 '15 at 20:39

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