12 sides are better than 6
Dodecagons offer a different shape that tessellates in a flagstone style with triangles and rhombuses.
It's not really all that different from an architectural perspective from hexagons. But it does create different silhouettes..
This is dodecagons connected by rhombuses.
Nothing mysterious here. Just two classic shapes playing nicely together.
Fits pretty well on a 32 pleat triangle grid.