|Packaging-wise, we live in a rectangular
world: big box stores with products stacked on square pallets... retail
space, measured in square and cubic units ... rectangular boxes on shelves,
stacked efficiently in rows with no wasted space.
But rectangular boxes are not the only
shapes that can stack efficiently. There are lots of other interesting
shapes that can do this.
Toblerone’s triangular prisms (above) will
fit together snugly in a packing carton. As will the hexagonal prisms of
Add a rectangular toothpaste-tube-box to these
two examples and you have the three regular prisms that fit together like
three dimensional tiles. But this is just the tip of the polyhedral iceberg.
The real story of close packing starts with spheres.
Maximum interior volume + minimum surface
area = the sphere. If that were our only calculation then all packaging
should be spherical. Put your “sphere packs” together, however, and right
away there are inefficient gaps! In the produce department: rectangular
arrangement = big gaps; triangular/hexagonal arrangement = small gaps.
For shipping and display purposes, how well
your packaged products fit together is good thing to keep in mind. Some
shapes — like spheres and tetrahedrons (the familiar triangular tetrapak
below) — will pack pretty close together, but still leave gaps in between.
What are the space-filling shapes that leave
no gaps in between? Of the polyhedral shapes with regular faces there are
only five that can do this:
1. Cubes (obviously)
5. Truncated octahedrons
The truncated octahedron is the basis of an
innovative packaging solution that protects and maintains the purity of
its content – Luso natural mineral water – while
seeking to optimize and ease storage, transportation and display, as well
as handling and consumption. What's next?
2. Triangular prisms (like the Toblerone
3. Hexagonal prisms (like the Droste boxes
4. Rhombic dodecahedrons