How to use 3d geometry to solve problems

Buckminster Fullers’s Design Science, 3d Printing, and the future of engineering

by Shaun D. McMillan

Most of the objects we see today are manufactured on a massive scale. The shapes we most often see are squares, rectangles, and simple forms that can easily be reproduced. But now that 3d printing is becoming more accessible, we are seeing more sophisticated geometry like fractals, hexagons, and organic flexible shapes. Is this just a trend, or will we continue to see more interesting geometry in our everyday lives? How can we use these more sophisticated shapes to solve problems?

Here is a simple way that geometry can introduce new solutions. PLA plastic is one of the most common materials used for 3d printing, but it is quite rigid and stiff. So how could we make flexible wearible 3d printed clothing and accessories? We could try to create hinge joints like we often do with metals, but actually we achieve a lot more flexibility and reduce the amount of material used by simply modifying the geometry.

3d geometry lowREs

These geometric patterns have their own design appeal and aesthetic, but first and foremost it emerged from its usefulness and efficiency.

Can this be taken further?

In this ted talk an innovative engineer, Skylar Tibbits, is trying to solve an old infrastructure problem. We often see traffic building up because of heavy construction being done to fix old infrastructure like drain pipes, colverts, buried concrete for sewers that run underneath our streets. All concrete structures decay over time. This innovator is working with 3d printed materials that automatically take on new forms based and a simple set of programming embedded into the materials. The geometry and the programming is simple, but the possibilities and solutions that could emerge from it are profound.

The earth is not flat, but most of our maps of the earth are. Globes are the only truly accurate maps, but all other maps are considered “projections” because in order to make a flat map of a spherical surface we must distort the images to make them fit our rectangle screens.

Which of the following 3 map projections has the most realistic proportions between nations? The mercator projection used by google maps, the Goode homolosine projection, or the dymaxion map by Fuller?

Google maps uses the most common of these maps referred to as the, “mercator projection,” but this map is extremely distorted at the top [northern regions] and bottom [southern regions]. Buckminster Fuller designed a map called the “dymaxion,” map to solve this issue. He create a sphere made up of triangles, and divided up the triangles and put them back together unfolded out onto a flat surface. This map has a small amount of distortion, but the proportional distortions are distributed evenly throughout the map. The map also lays out completely differently than any other map creating an entirely different perception of the earth. This new perception often inspires new creative solutions to ancient problems. We always think of America and Russia being so far apart, but the dymaxion map shows that actually we are only a pole away from Russia. Some of Buckminster Fuller’s students have proposed that America and Russia could share a power grid among other resources that previously no one ever considered.

example of rounded designs

Efficient manufacturing and uninspired design has left the world filled with square structures, but innovative new designers often try to implement rounder designs or even organic shapes and forms that do not follow such rigid structures but follow the patterns inspired by nature. Apple computers was one of the first computer companies to get away from designing rectangular computers opting for rounded corners and round spherical shapes where possible. These forms are arguably much more friendly or approachable, more attractive having their own unique aesthetic appeal, and spherical forms can often be more flexible without loss of structural integrity.

ALLIANCE Last Days Map
ALLIANCE World Peace Game Board which uses hexagons to allow for strategical movements

Hexagonal and triangular shapes are far more sophisticated than rectangular ones making them more difficult to design for, but they have potential we have yet to see. Hexagons in board games allow for much more dynamic interaction between players and allow for far more realistic simulations while still being simple enough to allow for game designers to program their desired probabilities and limitations needed for the implementation of rules.

Many of Buckminster Fuller’s designs utilized hexagonal polyhedrons which also proved to have far more structural integrity than your typical rectangular forms. Just like his dymaxion map allowed for distortion to be evenly distributed across the entire form, his bio-desic dome, which is a hexagonal or triangular framework, allows for weight, pressure, and stresses to be even distributed across the entire sphere. He made structures that used tension to hold the form’s shape together allowing for flexibility and referred to this as, “tensegrity.”He could make buildings that were easy to build using extremely light materials that would hold up to extreme weather without falling apart.

How could we use 3d geometry to solve even bigger or smaller problems?

How could we accomplish more for more people using less materials that cost less? Buckminster Fuller referred to this principle of doing more for less as, “ephemeralization.” Some innovators in India are trying to create extremely affordable mobile devices and cars for poor people who previously had no access to such technology. Their massive population is raising their standard of living and demanding the same amenities and transportation that we have in the west. But how can every Indian family have a car when resources are so scarce and the population so big? Indian engineers have set a goal to create a car for less than $1000! As minimalist designer philosophies often say, “less is more.” They are trying to simplify their car designs by removing absolutely every piece of metal and accessory that is not absolutely critical to the purpose of the device, which in this case is a bare minimum car that can get a family safely from part a of a city to another part.