This 5v design has just 5 unique panels and strut lengths rather than 9 for the standard 5v, I used a deltiodal hexacontahedron for the parent and subdivided each face with 5 equilateral triangles.

The equilateral triangles are shown in green and sit on a planar hexagon, this gives a couple of versions, a honeycomb version with pentagons, hexagons and a few scattered triangles

The fully triangulated geodesic structure has 5 unique panels and 5 strut lengths, I think that this design could be improved upon but it is still much more efficient than using standard subdivision. This design does have the advantage of being able to control the dihedral angles, I like to keep dihedrals as even as possible so I don''t have to keep changing the saw to make different bevel angles on the strut timber. This is the colour coded fully triangulated structure.

I have just finished rudimentary chord factors without adjustment for dihedral angles, call this a first draught, I'll post again when I have fine tuned.

This design was produced using Regular Polygon Subdivision

I also have a 4v design here.