Kisrhombille grid. It's worth a look. It's free scaling, like triangles and squares. Has 6 axii. Nice.
https://en.m.wikipedia.org/wiki/Kisrhombille
https://github.com/johnalexandergreene/Geom_Kisrhombille#rea...
https://en.m.wikipedia.org/wiki/Kisrhombille
https://github.com/johnalexandergreene/Geom_Kisrhombille#rea...
I've prototyped the 3D equivalent, which is composed of tetrahedrons and 13 axes (I wonder if that 3D tiling has a name). The tetrahedrons aren't the same size, so it's a bit awkward to work with but might be suitable for 3D models/art.
Yes it makes the map a bit ununiform and awkward. But.
Another way to use it would be to treat it as a substrate for a tesselation composed of a set of tiles. Like 2 or 5 or whatever basic shapes, all based on that awkward tessellation, arbitrarily fitted together to fill the space.
The image at that third link takes an approach like that. An alphabet of approximately 20 shapes. (A "self tiling system" I think.)
I'm not sure how useful that is but there you go