Hexagons, from Bee Hives to our Solar System and Back
More than 30 years ago I attended a seminar whose topic was on researching the most effective areal design to monitor atmospheric pollutants. The speaker concluded by stating that tessellated hexagons would be the best choice. While I subsequently had opportunities to design several monitoring projects, none lent themselves to using hexagons. More recently, my curiosity was once again raised when I saw a photo of a bee hive, which reminded ones I had seen in jars of honey many years ago.
Soon I was seeing hexagons in most everything. While that may be an exaggeration, I have learned that this simple, regular, 6-sided polygon is part of the living physics in our solar system, such as the north pole of the planet Saturn (below)and has through organic evolution and Darwinian selection inserted itself into the very fabric of micro- and macro-organisms, higher plants, animals, including humans.
Creative human minds have observed nature and mimicked the hexagon in many constructions. The genius of Buckminster Fuller first comes to mind. The Biosphere (below) at Expo 1967, Montreal, was designed by Fuller. Each hexagon was designed for strength and beauty by inscribing the interior of each hexagon with 6 equilateral triangles.
It turns out that organic evolution over the past 3.8 billion years of our Earth’s existence has supported the belief that the ingredients for organic molecules arrived early on in the evolution of our Earth and its solar system. We’ve seen an advanced example above when looking at a bee hive. What about plants? Evidence is shown in a potato by these parenchyma cells, below. Both bee hives and these plant cells are “tessellated”: they provide strength and function.
Plant cells (above), geodesic domes, and let’s not forget our outer skin cells (epidermis), are constructed (tiled) as to not allow water to penetrate the interior of the organism/structure. The hexagon formation once again creates a tile-effect with no spaces exposed between the among adjoining cells.
“Now, a team from Keio University in Japan, working with a researcher at Imperial College London, have discovered that the shape of the epidermal cells combined with their ability to temporarily glue together, may explain how they form this strong barrier. The researchers suggest that a shape of an epidermal cell is actually a flattened version of a tetrakaidekahedron — a 14-sided 3D solid made out of six rectangular and eight hexagonal sides. “
If we drill down even farther into Earth’s evolution we discover that some of the most critical molecules to human existence are hexagons: first, glucose and benzene.
Today we know how critical these two molecules have been but we also know that each one has been selected over billions of years to create growth and energy for humans, inorganic and organic: glucose is the essence of life on earth via photosynthesis.
The James Webb Space Telescope (JWST) was commissioned in December 2021. If you have seen photos you will have noticed the configuration of its mirrors, shown in this photo.
Here is the rationale for the structural configuration as a hexagon:
“The hexagonal shape allows for a roughly circular, segmented mirror with “high filling factor and six-fold symmetry.” High filling factor means the segments fit together without gaps. If the segments were circular, there would be gaps between them. Symmetry is good because there need only be 3 different optical prescriptions for 18 segments, 6 of each (see above right diagram).”
Research about the formation of snow flakes requires patience and very sophisticated equipment. Their configurations vary depending upon several variables including the temperature, humidity and, of course, altitude.
Cloud formations, and their stability via nonlinear upward and downward flow described by atmospheric physics, were found to apparently be associated with the geometry of hexagons hexagons, see below (thanks to Prof. Chris Garrett for pointing me to this mss.: Krishnamuti, R. (1975). Journal of Atmospheric Sciences. vol. 32: 1353–1363).
Finally, below we see a dramatic photo of hexagons formed at the surface of a dry salt lake, such as found in Death Valley, California and below, “the world’s largest salt desert is Salar de Uyuni, in Bolivia, which boasts the spectacular honeycomb pattern found on salt deserts across the world. (Image credit: sara_winter via Getty Images).” The pattern is now believed to be caused by the physics of salty and less salty water in a loop , rising and falling, beneath the surface, followed by evaporation.
Personally, I have enjoyed this short journey that has explored the hexagon and the many ways, and places, where it my be found in nature, on Earth and beyond. If you agree, share your thoughts.
Thanks very much for using your time to read my writing.
Zack.
Further reading
Clay properties (hexagon): https://en.wikipedia.org/wiki/Clay_mineral : “Their structure is based on flat hexagonal sheets similar to those of the mica group of minerals.[9] Standardization in terminology arose during this period as well,[8] with special attention given to similar words that resulted in confusion, such as sheet and plane
