Here are, it appears, two methods to attract a smaller grid of tiles from an preliminary hexagon:

On the left, we halve the facet size $s$ and create many of the new tiles centered on the midpoint of sides. The space of the brand new common shapes is one quarter as a result of the father or mother sees one and 6 halves youngsters. On the best, we use the vertices as facilities for the brand new hexagons; the facet size goes to $frac{sqrt{3}}{3}s$ and the realm a 1:3 ratio as a result of there might be one and 6 thirds youngsters reporting to the primary hexagon.

I hope we predict via the benefits of these programs. The first could also be of extra comfort and lowered overhead, which might be outweighed by inventive worth. But I believe there are different standards for my functions and it is also a common query. (For now feeling just a little bewildered by geometry.)

My undertaking is a recreation map (on this iteration, a globe; each subdivision strategies generalize to a beginning icosahedron I feel) which ought to have good “zooming” properties. I wish to use bigger tiles to summarize options below them which will be generated in additional element at will.