Aperture 3 Hexagon Subdivision
Also known as the Square Root Three Subdivision. A mathematical method for subdividing the plane with multi-resolution hexagon tessellations.
the PYXIS Index takes advantage of some properties of the division to produce an elegant hierarchical address label for each hexagon. A hexagon can be subdivided into seven smaller hexagons (Centroid Child and Vertex Child cells). There will be one 1-rosette on each vertex (a Vertex Child hexagon), and one in the centre (a Centroid Child hexagon). When the subdivision is performed again, another smaller hexagonal grid appears, rotated another 30 degrees. Thus, the total rotation is 60 degrees. Because hexagons have 60-degree rotational symmetry, this new grid is aligned with the original grid (often called the "grandparent" hexagon).
External Reference: SQRT 3-Subdivision, Leif Kobbelt, Max-Planck Institute for Computer Sciences http://www.subdivision-summerschool.uni-kl.de/HandOut/LeifKobbelt2.pdf