Fleen is a system for doing stuff with this geometry. ALSO, and probably more importantly, we provide a shape grammar and associated machinery for creating complex geometries within a nested (eg infinite detail) kisrhombille geometry.
We address it as a mass of cells or as a graph of vertices. We provide all the expected methods : getDistance(), getVertex(), getCell(), getDirection(), etc.
The tessellation is "demiregular". We have 6 axii of freedom and straight lines are doable. Our intervals are 1, 2, sqrt3. Our angles are pi/2, pi/3 and pi/6. We can do rectangles, equilateral triangles, hexagons, funky magnet shapes, wings... you get the idea. Connect the vertices.
Our shape grammars look like this : 
We create complex systems of shapes by building trees of polygons (aka Bubbles) and kisrhombille tessellation definitions (aka Grids). We use rules that control symmetry and whatever.
WHAT IS IT GOOD FOR?
Art, generative or otherwise; 6-axis system of interacting 2D objects (like in a videogame); organizing and mapping, maybe for a GUI; fancy cellular automata.
Check out the various samples in the source and wiki. There's a grammar editor, generators for making compositions and animations; and various illuminating images and animations and stuff.
(site in progress. moving everything off the old site)
https://code.google.com/p/fleen/