tile pattern on an irregular grid

Hello all,

This is my first time posting, so I apologize if the task with which I am seeking help is complicated or unclear...

I have developed a triangulated grid, upon which I would like to generate a bunch of polygons with varying numbers of sides. I'd like to use the grid not as the centroids of the polygons, but as the sides so that they are adjoining. I suppose the simplest question would be, how do I go about defining these polygons along these gridlines? The grid itself is actually two sets of three-point surfaces; the definition was modified from the "Surface Diagrid" tutorial in the primer.

The second part is that I would like to make the number of sides of the polygons react to a set of attractor points. I have modified the "Attractor_2pt_circles" definition and gotten fairly close, but can only define polygons based on a centroid rather than vertices.

Help? Thanks!!