Hexagonal symmetry examples are all over the natural world, but are also quite frequent in the fabricated world of technology as well. Here I present the main archetypes of hexagonal symmetry, and 6 concrete example templates, plus some bonus.

Themes Hexagonal Symmetry Examples are Based On

Hexagonal symmetry is when you can divide the image up radially, into six parts, such that each 1/6 slice is identical to the others. This would be like cutting a circular cake in half, and then cutting each half into thirds.

This shape provides stability and six-fold symmetry also contains 2-fold and 3-fold symmetry at the same time.

Six-ness Archetype: Template for Hexagonal Symmetry Examples

Templates that have hexagonal symmetry carry with them the inherent archetype of “six-ness.” The archetype of six-ness, based on the inherent qualities of the number, is that of structure, function, and order.

6 is the most highly divisible number up to that point in counting. It also has a pyramidal structure made up of 3 + 2 + 1. The archetype of six-ness can be associated with taking the swirly magic of the archetype of fiveness, and laying some order, some ground-rules, over it.

This stack of six oranges is very stable.

Hexagram Star

When you look at the hexagram star what do you feel?

hexagonal symmetry examples — To form the hexagram star, we take two perfectly symmetrical triangles and overlay them, centers overlapping, and one inverted with respect to the other.

To accurately assess this, you will need to try to divorce yourself from all the cultural notions conditioned about this image. Everyone’s answer may still be different, but psychologically, I feel that it has a very rigid and organized structure. Being the flow-y person I am, this actually feels a bit threatening and takes some breathing to make peace with its image.

Virgo, Ruler of 6th House in Astrology

Another mode to understanding numerical archetypes is connecting with the archetypes used in the zodiac. The zodiac system was set up to assign 12 basic archetypes that followed a progression of a universal story. Virgo lies right before the halfway point of this story, representing the sixth out of the twelve houses in astrology.

The sixth house pertains to one’s physical health, routines and schedules, organizations, household chores, and pets. Virgo rules over this house, and mercury rules over Virgo. Mercury is the god of communication and the mental realm. Virgo communicates its organized plans. Virgo also has the “out damned spot” energy, where it wants to fix and correct. For example, cleaning up spills as they happen, or being a bit of a perfectionist, are often associated with this archetype. And of course the symbol is the virgin, who wants to maintain the purity and keep out any aberrations.

Hexagonal Symmetry Examples

Now we get into the concrete hexagonal symmetry examples. These I chose iconic symbols and examples from both the natural and fabricated worlds.

#1 Pennsylvania Dutch

These rosettes have a bit of a mysterious character to them and likely warrant a whole article on their own. This is one theory of where the word “hex” meaning to curse came about. People of colonial Pennsylvania would put these over their barn doors to provide protection. But since they became associated with witchcraft, it later got telephoned to basically mean to curse someone. And the hexagonal symmetry, not always so, there are many using 8-fold and 5-fold as the next most common I’ve seen, respectively.

#2 Snowflakes

Though each special snowflake is unique, they all exhibit 6-fold hexagonal symmetry due to the forces inherent to the water molecules.

If you want to know more about why water freezes hexagonally, this is a very good presentation on the topic. Additionally, this more technical study finds, using algorithms, why different structures appear in snowflakes varying on the hexagonal theme.

#3 Foams and Soap bubbles, lipid rafts

Soap bubbles and foams also exhibit hexagonal symmetry, because they form with six bubbles around each bubble. Because the edges can be distorted in ordinary circumstances and the bubbles themselves are all different sizes, this is tricky to notice. But, if you look for it, it will start to jump out at you in more uniform foam samples.

only a small fraction of the lore can be connected in this way, so might as well https://t.co/KEup5maxB9
— AbnormalWays (@AbnormalWaysWeb) May 7, 2023

Bubbles won’t always appear to follow this, but they do tend towards it. Soap films seek to minimize surface area to achieve a more stable energy state. Six around one minimizes the gaps that seek to close up. Since soap films have these properties from being lipids, we also see the six around one symmetry in the lipid membranes that make up living cells.

Adding to this,
soap does the same thing, soap is made with saponified fats. (Goat milk, olive oil, etc). The rainbow colors are due to the thickness of the film. pic.twitter.com/q6szqCltqE
— AbnormalWays (@AbnormalWaysWeb) April 30, 2023

Notice the hydrophobic heads all clustered together to form the boundary of cells. When you close pack spheres like that, you get the six around one, hexagonal symmetry.

#4 Beehives

Beehives are hexagonally celled for the same reason as the bubbles. The bees have adapted to make the most of the volume they are using. There is no better way to optimize the amount of honey stored in a volume other than this. If you ask a computer algorithm to do the same, it will reproduce this pattern.

You can really see the hexagonal symmetry in a beehive because they produce it so perfectly.

Look at all those perfectly aligned hexagons.

#5 Bubble wrap packings

Manufacturers copy this to optimize the amount of bubbles on a sheet of bubble wrap. Again there is no better way to fit more bubbles on the flat sheet than the six around one structure.

(biomimicing blood vessels!)

#6 Fly Eyes

With fly eyes, we have nature optimizing the amount of cells just like with the bees. Flies are small but rely on their vision heavily. So their eyes are optimized through their genes to fit photoreceptors in maximal amounts.

Looking up close at the fine structure of the fly eye shows the hexagonally positioned photoreceptors.

Bonus Hexagonal Symmetry Examples

Benzene – Six-membered Petroleum

Of course I wanted to leave it at 6 for reasons, but I had to include Benzene, one of the most important biomolecules!

"The discovery of the benzene ring C6H6 […] came to German chemist Friedrich [August] Kekule [1829-96] after he dreamed of the ouroboros, the snake biting its own tail." -Schneider, Constructing the Universe #hexad
Benzenes make up hydrocarbons, they are ubiquitous https://t.co/kcvkypwzOh pic.twitter.com/r9WkyYQurE
— AbnormalWays (@AbnormalWaysWeb) May 28, 2023

Benzenes are in gasoline and any petroleum product, glues, paints, wax, detergents,

Bonus: Gluscose Sugar Rush to Finish You Off

Glucose molecules are also famously arranged in six-membered carbon rings.

Hexagonal Symmetry Examples Pervade Structures of Function

Hexagonally symmetry are also found in many everyday fabricated things that need structural stability, for example hex nuts and hex bolts. These tried-and-true designs tend toward this shape due to its stability under the twisting pressure.

Now it is helpful to be away that hexagonal symmetry is more rare in flowers and fruits than pentagonal symmetry, its five-fold symmetric sister. But we can see hexagon shapes on the stem-cut site of carrots and tomatoes, for example. There are also the six-petalled flowers, such as asparagus, cucumber, and onion flowers.

Hexagonal Symmetry Examples For Easy Structure in Your Life

Themes Hexagonal Symmetry Examples are Based On