Friday, May 13, 2016

a tiling of regular nonagons and stars


When I found this nice nonagon and star tiling, I couldn't get They Might Be Giants out of my head. The underlying symmetry comes from hexagons though:


The relationship described in the previous post tells us that the next regular polygon that can be put around a hexagon like this is the dodecagon (see the line k = 6):


And sure enough, these dodecagons can also form a nice hexagon-based tiling, with somewhat pointier stars.



The k = 6 line above gives us a whole family of polygon and star hexagonal tilings that follow the relationship n = 3m + 3 - the stars don't start to appear until m = 2



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