The paper "Evidence that no liquid equilibrium process is involved in the comb building of honey bees (Apis Mellifera)" Naturwiss. Zeitschr. 2017, 67: 8-27 missed the mark on several levels.
First, the bees clearly chew away and place individual scales of wax, and do generate significant heat while doing so, but there is never a point at which wax becomes liquid.
Second, the fact that bubbles of equal size, blown between two glass sheets form INDENTICAL shapes does not require the bees to use liquid wax to end up with the same shapes.
Third, variation within combs built by the same hive show clearly that the bees less-than perfect construction techniques result in variations that show the impact of infinitesimally thicker walls, in that the resulting shapes vary enough to verify that the bees are simply fitting cells as best they can, and are not doing any "math" or "design" at all.
A sufficiently-chewed away wall of wax will be thin enough to react "as a soap bubble does", to the same sort of forces of tension and compression. The bees help, as they also want minimal-thickness walls.
So, the bees do NOT build the optimal structure of Fejes Toth (better than Kelvin's solution)
https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-70/issue-4/What-the-bees-know-and-what-they-do-not-know/bams/1183526078.full
https://tinyurl.com/392fnmnr
and...
https://doi.org/10.1007/s13592-022-00915-8
Instead, Weaire and Phelan found that they could easily switch between the theorical "perfection" of the Toth structure, and the very slightly less perfect shape of honey bee comb by simply adding a little more soap to their bubble solution, and making the film thicker.
https://doi.org/10.1080/09500839408241577
So, the bees do the best they can with the materials at hand, and in actual practice, only about 20% of their cells end up as approximations of the Toth or Weaire-Phelan structures, as their building process is chaotic, with many workers contributing to each and every surface, and some working at cross-purposes.
Further detail in this recent (2022) paper shows the level of variation, and verifies that physics is doing the heavy lifting here, bees are just doing their best to make the most cells from the least wax:
https://link.springer.com/article/10.1007/s13592-022-00915-8
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