Key Takeaways
- The honeycomb theorem: Hexagons are the mathematically optimal way to divide a plane into equal areas using the least perimeter—bees discovered this millions of years before mathematicians proved it.
- Bone wisdom: Your bones aren't solid—they're made of trabecular networks that put material only where stress occurs, achieving strength with minimal weight.
- Nacre's toughness: Mother-of-pearl is 3,000 times tougher than the chalk it's made of, thanks to a brick-and-mortar architecture that stops cracks cold.
- Real applications: From aircraft panels to crash helmets, biomimetic structures are saving weight and lives across industries.
The Mathematician’s Honeycomb
In 36 BC, Roman scholar Marcus Terentius Varro proposed what became known as the Honeycomb Conjecture: of all possible shapes that tile a plane without gaps, regular hexagons have the smallest perimeter relative to their area.
In other words, if you want to divide a surface into equal-sized cells using the least amount of dividing material, hexagons are the answer.
Varro was observing bee behavior. Bees construct honeycomb from wax, which is metabolically expensive to produce—it takes roughly 8 kilograms of honey to make 1 kilogram of wax. Any wasteful architecture would be ruthlessly selected against.
For over 2,000 years, Varro’s conjecture remained unproven. Mathematicians suspected it was true but couldn’t demonstrate it rigorously.
In 1999, mathematician Thomas Hales finally provided a complete proof. Hexagons are indeed optimal. Bees had been right all along.
Why Hexagons Win
The mathematics is elegant.
Consider the challenge: cover a flat surface with identical cells, leaving no gaps, using the minimum amount of wall material.
Only three regular polygons can tile a plane without gaps: triangles, squares, and hexagons.
| Shape | Sides | Perimeter for unit area |
|——-|——-|————————|
| Triangle | 3 | 4.56 |
| Square | 4 | 4.00 |
| Hexagon | 6 | 3.72 |
Hexagons win by about 7% over squares and 18% over triangles.
The saving seems small, but multiply it across millions of cells and thousands of generations, and the advantage compounds. Colonies that waste less wax on structure have more resources for honey, brood, and survival.
Evolution optimized the honeycomb millions of years before humans understood why it worked.
The Third Dimension
Real honeycomb isn’t flat—it’s a three-dimensional structure with cells on both sides of a central wall. The geometry becomes more complex, but the efficiency principle holds.
Each cell is a hexagonal prism, angled slightly backward from the opening. The back of each cell interlocks with three cells from the opposite side, creating a continuous structure with no wasted space.
The angle isn’t random: cells tilt at about 13 degrees from horizontal, which:
Prevents honey from dripping out before the cell is capped
Maximizes structural rigidity of the overall comb
Allows bees to access cells at a natural working angle
This geometry was analyzed by Charles Darwin, who called the honeycomb “absolutely perfect in economizing labor and wax.”
Aircraft Honeycomb
Engineers rediscovered honeycomb architecture in the early 20th century, initially for aircraft.
The challenge was familiar: aircraft structures need to be strong enough to survive flight loads but light enough to actually fly. Every gram of structure is a gram not available for payload or fuel.
Honeycomb sandwich panels solved this elegantly:
Two thin, stiff face sheets (aluminum, carbon fiber, or other materials)
A core of hexagonal cells oriented perpendicular to the faces
The whole assembly bonded together
The result is a panel that’s:
Extremely stiff — The face sheets resist bending, while the core prevents them from buckling
Very light — Most of the volume is empty air
Crash-resistant — The cells progressively crush under impact, absorbing energy
Modern aircraft use honeycomb panels extensively:
Floor panels in passenger cabins
Interior walls and partitions
Control surface structures (ailerons, rudders)
Fairings and aerodynamic surfaces
The Boeing 747 contains over 4 square kilometers of honeycomb panels. Without them, the aircraft would be too heavy to fly economically.
Beyond Hexagons
Honeycomb is efficient, but it’s not the only biomimetic structural solution.
Trabecular Bone
Your bones aren’t solid—and that’s essential to their function.
The interior of bones contains trabecular (or cancellous) bone: a network of thin struts and plates that look almost like a natural honeycomb. But unlike the regular hexagons of bee architecture, trabecular bone is adaptive.
The struts align themselves along the principal stress directions. Where loads are high, trabeculae are dense and thick. Where loads are low, bone is sparse or absent.
This was first recognized by Julius Wolff in the 1890s, who formulated Wolff’s Law: bone adapts to the loads placed upon it. Use a limb heavily, and the bone thickens. Immobilize it, and bone is resorbed.
The result is a structure that uses minimum material for maximum strength—but customized to each individual’s activity patterns.
Implications for engineering:
Generative design algorithms that mimic bone adaptation
3D-printed components with material only where stress requires it
Lightweight aerospace structures optimized for specific load cases
Modern software can simulate stress patterns and generate trabecular-like structures automatically. The results often look organic—because they’re following the same optimization logic that evolution discovered.
Nacre: Brick and Mortar
Nacre (mother-of-pearl) lines the inner surface of many mollusk shells. It’s beautiful—iridescent layers that shimmer with color. But its true wonder is mechanical.
Nacre is made of aragonite, a form of calcium carbonate—essentially chalk. Chalk is brittle; hit it with a hammer and it shatters.
But nacre is approximately 3,000 times tougher than the aragonite it’s made of.
The secret is architecture. Nacre isn’t solid aragonite—it’s a composite:
Microscopic aragonite tablets (the “bricks”) — flat, hexagonal plates about 5-10 micrometers wide and 0.5 micrometers thick
Organic protein layers (the “mortar”) — thin films of biological polymer between the tablets
When stress is applied, the organic layers act as shock absorbers. If a crack starts to propagate, it encounters a protein layer and is deflected sideways rather than continuing straight through. The crack has to work around each tablet, dissipating energy along the way.
This crack deflection mechanism transforms a brittle material into a tough one.
Engineering applications:
Synthetic nacre — Researchers have created nacre-inspired composites using aluminum oxide and polymer layers
Armor systems — Layered ceramics that stop projectiles by deflecting and dispersing crack energy
Impact protection — Helmets and protective equipment using brick-and-mortar geometry
The Eiffel Tower Connection
One of the most famous structures in the world may be biomimetically inspired—though the connection is debated.
The Eiffel Tower uses a lattice of iron struts arranged in a pattern that closely resembles trabecular bone. The design distributes load efficiently from the top to the broad base, using the minimum amount of iron.
The connection to biology comes through Karl Culmann, a Swiss engineer who studied with anatomist Hermann von Meyer. Meyer had documented the internal structure of the femur (thigh bone), showing how trabeculae align along stress lines.
Culmann recognized that the bone’s architecture followed the same mathematical principles as engineering truss design. His work influenced Maurice Koechlin and Émile Nouguier, the engineers who drafted the original Eiffel Tower design.
Whether the influence was direct or coincidental, the result is a structure that embodies nature’s approach to efficient architecture: material only where stress requires it, arranged along the natural flow of forces.
The Giant Reed Stem
Plants face their own structural challenges. They must stand upright against wind and gravity, support the weight of leaves and seeds, and do so while growing continuously.
The giant reed (Arundo donax) can grow up to 6 meters tall yet remain flexible enough to bend in storms without breaking. Its stem provides a masterclass in efficient structural design:
Hollow center — Most of the stem’s volume is empty, minimizing weight
Nodes at intervals — Solid partitions that prevent the hollow tube from collapsing
Fibrous walls — The outer layer contains dense fibers running lengthwise, providing tensile strength
Gradient density — The wall is denser toward the outside, where bending stress is highest
This structure achieves nearly the same bending stiffness as a solid rod but with a fraction of the material.
Engineers call this principle second moment of area optimization. Moving material away from the neutral axis (center) and toward the surface dramatically increases resistance to bending.
Bicycle frames, tent poles, and fishing rods all exploit this principle—but the giant reed perfected it millions of years before humans existed.
Auxetic Materials: The Anti-Intuitive Structure
Most materials get thinner when you stretch them. Pull on a rubber band, and it narrows in the middle. This is characterized by Poisson’s ratio—typically a positive number.
But some structures have negative Poisson’s ratio—they get fatter when stretched. These are called auxetic materials.
Nature provides examples:
Cat skin — Becomes thicker when pulled, resisting puncture wounds
Certain tendons — Expand under tension, locking joints in place
Some mineral crystals — Exhibit auxetic behavior due to molecular geometry
The geometry that creates auxetic behavior typically involves re-entrant structures—hexagons that fold inward rather than outward, or networks of connected bow-tie shapes.
When auxetic materials are compressed, they densify uniformly rather than bulging outward. This makes them excellent for:
Blast protection — Auxetic armor compresses and thickens under impact, absorbing energy
Medical stents — Tubes that expand when compressed, making insertion easier
Smart textiles — Fabrics that become thicker and more protective under stress
Airless Tires: Honeycomb Meets the Road
Conventional pneumatic tires are engineering marvels—but they fail catastrophically when punctured. For military vehicles, emergency responders, and remote operations, flats can be dangerous or even deadly.
Airless tires solve this by replacing air with structure. Several designs use honeycomb-like geometry:
Michelin’s UPTIS (Unique Puncture-proof Tire System) — Uses a flexible honeycomb structure that deforms under load but springs back
Bridgestone’s Air Free Concept — Features spokes arranged in a pattern inspired by bicycle wheel designs
Polaris’ TERRAIN ARMOR — Military-grade tires with internal honeycomb that can withstand gunfire
These tires sacrifice some of the ride comfort of pneumatic designs, but they’re virtually indestructible. A honeycomb tire can keep running even after significant damage—the distributed structure means no single failure is catastrophic.
Glass Sponge: The Deep-Sea Architect
At depths of 200-1,000 meters in the ocean lives the glass sponge (Euplectella aspergillum), also known as Venus’s flower basket. Its skeleton is one of the most sophisticated structures in nature.
The sponge builds a lattice of silica (glass) fibers arranged in a hierarchical pattern:
Nanoscale — Individual silica spheres with organic cement
Microscale — Spheres fused into spicules (tiny rods)
Mesoscale — Spicules bundled into larger beams
Macroscale — Beams woven into a diagonal lattice
The lattice geometry is remarkable: a grid of horizontal and vertical elements, with diagonal braces at 45 degrees. This is exactly the pattern that modern engineers use in tall buildings to resist wind and earthquake loads.
But the glass sponge evolved this design hundreds of millions of years ago.
Studies show that the sponge’s structure is more efficient than human-designed equivalents. The diagonal pattern handles stress from any direction, and the hierarchical construction stops cracks at multiple scales.
Architectural applications:
The Swiss Re Building (“The Gherkin”) in London uses a diagonal lattice inspired by similar principles
Research into bio-inspired facades and structural systems continues
The Lesson: Do More With Less
Nature faces a universal constraint: resources are limited.
Every gram of material a bee uses for honeycomb is a gram of honey not stored. Every gram of bone is a gram that muscles must carry. Every gram of shell is a gram of food not used for growth.
Evolution’s response is ruthless efficiency. Structures are optimized to use minimum material for maximum function. Nothing is wasted. Every element serves a purpose.
Human engineering historically took the opposite approach: make it strong by making it heavy. Add material until the problem goes away. Accept waste as the cost of reliability.
But we’re running out of resources for this approach. Climate change, energy costs, and material scarcity are forcing a rethink.
Nature’s architects—bees, bones, shells, reeds—have been solving the “less material” problem for millions of years. Their blueprints are freely available.
We just need to read them.
References
Hales, T.C. “The Honeycomb Conjecture.” Discrete & Computational Geometry, 2001.
Wegst, U.G.K. et al. “Bioinspired Structural Materials.” Nature Materials, 2015.
Meyers, M.A. et al. “Biological Materials: Structure and Mechanical Properties.” Progress in Materials Science, 2008.
Kapsali, V. Biomimicry for Designers. Thames & Hudson, 2016.
Gibson, L.J. and Ashby, M.F. Cellular Solids: Structure and Properties. Cambridge University Press, 1997.
Next in the series: The Whale Fin Revolution — How the bumpy edges of humpback whale fins are transforming wind energy and beyond.