Sounds like maybe too much? Please bear with me. My post yesterday about Cull Nth (Hex_In_2025Jul3d.gh) was perhaps the most relevant to getting a reciprocal structure from these hexagons because it addresses the problem of duplicate edges.
I was curious though. Cull Nth leaves edges 0, 2 and 4 but what if three different edges are used instead? I searched the forum to find this:
And adapted that code to get this"
Combos_2025Jul4a.gh (9.8 KB)
Then internalized ‘combos’ and copied it here:
Hex_In_2025Jul4a.gh (40.5 KB)
It isn’t necessary to understand all of this code. The first yellow group allowed me to examine all 20 of the ‘combos’, one by one. When a combo looked “good” (six sides), I clicked the button to collect indexes (slider values) of “good combos”. When done, I internalized that list in the magenta group (eight “good combos”) and copied it to the bottom yellow group.
Which of the eight “good combos” is best? To be determined. What are the criteria 
P.S. Simplified:
Hex_In_2025Jul4b.gh (37.4 KB)