You're obviously not looking for the answer "tile the plane with regular hexagons", so what are the additional requirements you're making? Are you requiring all three types of polygons to appear (at least once? infinitely often?)? Are you looking for some notion of a randomly-generated tiling, with some sampling distribution properties over the space of all tilings? Etc. --Michael Kleber On Wed, Jun 18, 2008 at 9:41 AM, Guy Haworth <g.haworth@reading.ac.uk> wrote:
A colleague wants a computer to define a 2D-graph, a tiling of the plane if you will, which only has pentagons, hexagons and heptagons.
He's a chemist, which may give someone a clue what this is about, but that someone is not me.
I don't suppose the n-gons can all be convex (but don't have a proof of that) but concave n-gons are not necessarily an issue.
Anyone got an algorithm or even better, a program. My colleague did have the suggestion of just tiling the plane with triangles and then knocking sides out, but the problem then becomes one of inspecting what is left to see that it meets the requirements.
Thanks - Guy
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