Thursday, March 16, 2017

[cheinley] Kissing tiles

Inscribe within a polygon a closed curve which is tangent at the midpoint of each edge.  Splines are probably the easiest.

Apply this to a polygonal plane tiling, not necessarily a tiling of only one tile type, and get a collection of closed curves that are tangent to each other, with gaps (surrounding the vertices).  No practical purpose.

Could also be done with polyhedral tilings (honeycombs).

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