Auxetics are structures or materials that have a negative Poisson’s ratio. When stretched, they become thicker perpendicular to the applied force.
from Wikipedia’s entry on Auxetics
Is “auxetic packaging” really a thing? Most of the references I’ve found to packaging applications seem to be nano-scale. (Auxetic cushioning foams and the like.)
But there are others (artists and researchers) who are experimenting with folded paper and cardboard. And some of these models look (to me) like an intriguing new frontier in structural packaging design.
We have videos and information about two projects in particular (shown above), after the fold.
1. Taneli Luotoniemi’s 2015 “Jitterbox”
In our previous post, we were admiring Buckminster Fuller’s 1976 Jitterbug Atoms. Named after Fuller’s Jitterbug, the Jitterbox undergoes the same type of geometric transformation.
Taneli Luotoniemi is an artist and doctoral student at the Aalto University School of Art, Design and Architecture in Helsinki.
In 2015 he received a Fulbright scholarship as a visiting scholar to the University of Illinois at Urbana-Champaign for his doctoral dissertation research entitled, Visualizing 4-dimensional Geometry — An Artistic Research. It was around this time that Taneli designed the Jitterbox. If Luotoniemi’s research focused on “visualizing 4-dimensional geometry,” I wondered whether there was something inherently 4-D about the Jitterbox.
We contacted Luotoniemi in hopes of learning more about his transforming structure and the thinking behind it.
I’m doing doctoral research on the visual possibilities of 4D geometry at Aalto University in Helsinki, and I was looking at how to generalize Fuller’s jitterbug mechanism to higher dimensions. As a sidetrack, I examined the possibility to have the jitterbug not working only topologically on the surface of a sphere (like in Fuller’s original), but extend it to fill entire Euclidean 3-space. The Jitterbox is one possible solution for that problem.
Space-filling, but strictly Euclidean
Here at box vox, are always on the lookout for new ways of filling space, but I was actually reassured to learn that the Jitterbox is strictly Euclidean.
Still, when I tried to identify the polyhedral shape of the blocks in the video above, they looked to me like some irregular version of the rhombic dodecahedron. (And I’ve read that one of the 3-D projections of a hypercube is a rhombic dodecahedron…)
Extruded Cubes and Jitterbox Belts
Other designers have also given boxes the jitterbug movement. Around 1960 Hiroshi Tomura designed a polyhedral toy called the “Tom Cube” using strings to hinge the corners of adjacent cubes.
Luotoniemi, however, did not use cubes at all. He describes what he used instead as “cubes that are extruded along the direction of their space diagonals”. And he says that “the length of the extrusion is a free parameter.” (I wonder what effect changing that parameter has on the Jitterbox’s shape and transformation.)
He hinged his “extruded cubes” together with triangular flaps. These hinges work to constrain the angle of movement, in the same way that Dennis Dreher‘s “constant dihedral hinges” stabilized Fuller’s Jitterbug Atom.
All of these observations, however, are a little misleading. Luotoniemi generously shared the die-line/net of his basic module. To my surprise, he did not construct his model by hinging together separate polyhedrons. Instead, he designed a “belt” which, when combined in groups of six, collaborate to form the hinged blocks of the Jitterbox.
I like that Luotoniemi’s paper model is color-changing as well as shape-changing. I also like its pastel colors, which seem unusual compared to other polychrome polyhedral models. Which are often less subtle.
In his directions, Luotoniemi writes:
There are six colors (light hues of cyan, green, orange, purple, pink, yellow) … in this model each block is made from belts of every color, and all the belts … [of] the same color have also the same spatial orientation in the structure.
Luotoniemi also advises us “to use light hues or pastel colors, which do not prevent the appreciation of geometry through light and shadow.”
Complexity and the chained polyhedral portion pack
One reason that Luotoniemi’s design struck a cord with me, is that it reminded me of our “Gumball Puzzle Cube Pack.” Our design, based as it was on the existing “magic cube” novelty, was much more simplistic. We made our pack from 8 cube-shaped boxes, so the rotations were all at perpendicular right angles. Luotoniemi’s Jitterbox, on the other hand, consists of 64 boxes (made from “belts”) and hinged at angles that allow for a more surprising range of motions.
I’ll grant you, that my impulse to apply this type of auxetic complexity to a package design might not be practical. (A bit like a solution in search of a problem.) Never-the-less, I think that a simplified, smaller version of the Jitterbox structure could make a fascinating multi-pack.
2. “Toolkit for Transformable Materials”
A couple of months ago, researchers from SEAS and the Wyss Institute at Harvard University, published a paper in Nature. The “researchers” include Katia Bertoldi, Johannes Overvelde, Chuck Hoberman & James Weaver.
… we introduce a robust design strategy based on space-filling tessellations of polyhedra to create three-dimensional reconfigurable materials comprising a periodic assembly of rigid plates and elastic hinges.
Rational design of reconfigurable prismatic architected materials
Nature, January 18, 2017
The research began in 2014, when Hoberman showed [Katia] Bertoldi his original designs for a family of foldable structures, including a prototype of an extruded cube. “We were amazed by how easily it could fold and change shape,” said Bertoldi. “We realized that these simple geometries could be used as building blocks to form a new class of reconfigurable metamaterials but it took us a long time to identify a robust design strategy to achieve this.”
Leah Burrows, A toolkit for transformable materials
Another “extruded cube”
They published another paper last year in which they cited Heinz Strobl’s snapology as their starting point. The “family of foldable structures” mentioned above must be the “snapolgy” models shown below.
The Harvard team noticed, however, that not all of these structures were equally foldable. The extruded cube, for example, was highly deformable, while the extruded icosahedron was not.
This multiple extruded cube is deformable in the same ways as the single module. At one point in the video below, they show it completely collapsed.
Odd coincidence that, like Luotoniemi, they’ve also chosen to describe their basic module as an “extruded cube.”
Their “extruded cube,” of course, is quite different. It looks very much like the regular skew apeirohedron (as shown on the right) which was named “mucube” (multiple cube) in 2008 by John Conway in The Symmetries of Things.
Of course, even if their “extruded cubes” are “mucubes” once you start folding them, they become something else, entirely.
They also experimented with air-activated hinges on plastic models to power the transformations.
Reconfigurable prismatic packaging?
If the complexity of Luotoniemi’s Jitterbox seemed impractical for packaging applications, how can we even think of using this type of re-configurable structure as a package?
We generally design packages to contain stuff and these “reconfigurable prismatic architected materials” are more like malleable networks of open pipes. What possible packaging application can there be?
While you could move the Jitterbox into different positions without changing the volume of its individual compartments, these “reconfigurable” structures are different.
With these structures, every movement you make completely changes the interior volume.
For the moment, let’s set aside the appealing kinetic features demonstrated in the video.
Imagine a similarly “reconfigurable” package. Take the extruded cube structure, for example, and give each of its 6 openings a tuck flap. You can still manipulate this folding carton in the same way as shown in the video. Once you’ve filled the package and capped the openings, however, it will no longer be so kinetic.
Even so, it’s useful that our extruded-cube folding-carton can be packed flat. Manufacturers will often transport their packaging somewhere else before filling.
They also save money when they can use a generic package for different products. Let’s consider how our new “reconfigurable” package now has the ability to, in effect, change size. A manufacture might use the same basic package (in different configurations) for different quantities of a product.
A further possibility, if the product were a liquid or a colloid, might be to design a container in such a way that the contents could be poured or extruded by simply flexing the package towards one of its less voluminous states.
Reconfigurable prismatic sculptures
Chuck Hoberman also exhibited some kinetic sculptures last year based on the group’s research.