Detour into the basics

I detected through a comment the work of George Mokray - he build a set of A and B quanta modules that connect via magnets, and form a tetrahedron and an octahedron, which then join together to a cube. I spend some time investigating his suggestion to build tensegrity quanta modules, and simply need to keep track of some important experiences I gained in this process.

Tetrahedron split into four volumetric quarters, bottom quarter split into 6 A-Quanta modules

My spatial imagination improved while working on my tensegrity structures, but I still have trouble conceptualising a 3d object from a 2d still image. Initially, I was unaware that the four quarters were identical, and that the same applied for the A-quantas - there's only one set of edge lengths which can be build in two orientations.

A Class-2 tensegrity tetrahedron requires only four struts, two joints and seven tendons. As the a-quanta module is an irregular tetrahedron, there are two different strut length and seven different tendon lengths that need to be calculated (or experimentally derived). Symmetry brings a lot of stability and balance two class-1 tensegrities, irregular objects belong to uncharted territory.

Nevertheless, I used my copy of Fuller's Synergetics to refresh my knowledge, and started creating a CAD file to have some plans with precise measurements. I plan to do some 3d printing in the future, which means I better familiarise myself with CAD software. And potentially I could design single struts with a bend, instead of using two struts and a join.

Besides building an irregular tetrahedron as Class-2 tensegrity, the challenge to join many of them remains tricky. George used magnets in the faces to link the modules together - magnetic polarity will still require face bonding. However, depending on the design of the strut end, three magnets could be installed at each end.

The next steps will be designing the strut ends to easily attach tendons, and deciding how much curvature I will use. Building has to wait for a while- first I will have to set up the printing environment,  which hopefully will solve of the technical problems I have with OpenSCAD.

Revisited

Red Star (Intertwined tensegrity tetrahedra)

I revisited my attempts to combine tetrahedra to build a tensegrity representation of the merkaba. Red Star comes so far closest to joining two tetrahedra in this fashion, yet I had to take two different sizes. The tendons of the red tetra are suspended from the struts of the larger one, it can vibrate while the outer structure is extremely solid.

Red Star

The tendons of the larger tetra connect to each other, instead of directly from strut to strut. I haven't tried out this way of connecting a corner with elastic string, with nylon it works really well, and is optically very appealing.

Merkaba (Tensegrity octahedron with 8 tensuls attached to form two tetrahedra)

With 36 sticks the sculpture Merkaba offered initially hardly any depth to it, as all struts had the same colour. I rebuild the structure using a green octahedron, and using bicolour struts for one of the surrounding tetrahedra. The model balances on each of its eight tetrahedral corners, and folds down along the axis connecting opposite corners of the octahedron.

Merkaba

Exploring other things...

I guess I'll need some more practise in producing videos, there's still some unclear instructions and a couple of hang-ups in it. I still hope for decent light conditions in my improvised video studio to shoot the how-tos for icosahedron and dodecahedron, with the potential to redo the intro part as well. However, this video gives you an impression how fast models can be build: Only seven minutes show what's happening between the first connection and last connections being made, without time lapse.

How to build a tensegrity cube

I started shooting some instruction videos for The Affordable Tensegrity Toolkit, which will be available via Big Cartel as soon as I finished documenting how to build the Platonic Solids with it. There's certainly room for improvement when it comes to the production quality of the videos, but so far I'm quite happy with the result. Contact me via this blog or via lutz (at) smart-at (dot) net for further information.

Tetrahelix

The first challenging build I did was the tetrahedron. The method differed from the ones I use now, and I got much more familiar with the chaos of sticks and strings that exists before finishing a structure. Although most likely the icosahedron plays a much more important role for biotensegrity, our vertebrae possess a very tetrahedra-like appearance.

I experimented lots with combining tetrahedra into larger structures. Two of them joined at a corner produce an hourglass shape. I build as well a tower of five stacked tetrahedra, which took me ages to balance, and still doesn't satisfy me much. Most of the time, I approached larger structures with tetrahedra in a more complex way than needed. When two 6-strut tetrahedra are joined at a face, the 'center' triangular consists of 6 struts, while only three are needed.

In a tetrahelix, faces of tetrahedra are joined. When enough tetrahedra are joined in this way, the corners seems to build a helix (hence the name....).  I hoped that five tetras would produce some interesting effect, yet joining pre-build tetras turned out more of a challenge than I hoped for. There's more than one way to connect modules to each other, and each yields different results.

Then I decided a new approach. Instead of perceiving the tetrahelix as compound of tetra modules, I tried to understand it as singular structure enclosing connected tetrahedral spaces. So if I take a tetrahedron and extend it to enclose to tetrahedral spaces, I get a tensegrity tetrahelix without a single tetrahedron remaining visible.

The first 5-stage tetrahelix required 30 struts, yet when my idea works out with only 21 struts I have six stages (6 struts for the 'seed' tetra, 3 for each additional stage). Instead of connecting an incomplete three-strut tensul 'somehow', I connected the extension into the corner loops. Although that meant some more steps per connection than usual, I found an easy way to do so. The first extension, however, brought the biggest surprise. I just build myself another trigonal dipyramid.

I used a magnetic model to figure out the corner configuration for the tetrahelix. Each additional tetrahedron adds only a single vertice to the helix. So the dipyramid has two tetras and five corners, lets make this a bit more systematic.

struts # tetra spaces # corners # type
6        # 1               # 4           # tetrahedron
9        # 2               # 5           # trigonal dipyramid
12      # 3               # 6           # 3-stage tetrahelix
15      # 4               # 7           # 4-stage tetrahelix
n*3+3 # n              # n+3        # n-stage tetrahelix

I'm not sure whether an object encompassing 3 tetrahedral spaces already deserves the name tetrahelix, it takes at least 5 tetrahedra to have all possible vertice configurations (3, 4, 5 and 6 struts converging in one corner). However, knowing that the maximum number of struts meeting in a single is six made extending the helix a breeze. The corner at the end has 3 struts, on the second level there are either four, five or six struts meeting. Thus there are three different constellation for the faces connecting to the 'top' (or bottom) corner: 3-4-5, 3-4-6 and 3-5-6.

So all I needed to do when extending the helix was finding the 3-4-5 face, and adding an incomplete tensul to the vertices of this face. I think I went up to 69 struts, creating something quite floppy which might connect into a torus.

Unlike most other models, I didn't manage to create something self-balancing. Up to about seven or eight stages, the model kept straight while I held one end, before the elasticity of the string made it bend a lot. While it's not too suitable for mere display, it's a lot of fun to play with. At the moment I have it hanging around, with an EL-wire threaded through the corners. In this constellation, the helical structure becomes visible, which otherwise remains quite hidden in the chaos of sticks and strings.

For real

Last century, it took months if not years to start a shop. In the 21st century, it took me the better part of an afternoon to do so. I admit, part of requirements is a PayPal account, and it might take some days to verify your details to have it fully activated. But then, unless you have a customer base before you start, you don't necessary expect anything happening in the first hours of operation.

Like a spider in its web, I can sit and wait for the first order to arrive per email. Luckily, this means I can spend my time in other ways. Like producing a how-to for The Affordable Tensegrity Toolkit. The free shop at Big Cartel serves as platform to manage internet sales. I have no idea how many random visitors come across, as all interesting features transform the free shop into paid one, a classical freemium business model. That means I will have to bang my own drum, in the shape of youtube videos.

So far, I offer only the models that can easily be mailed, but feel free to use the contact form of the shop if you're interested in something you see here, or to discuss specific projects. For of all you lucky enough to live in Melbourne, you can have a look and a chat when I'm on the Rose Street Artist's Market in Fitzroy.

PS: I mentioned spiders and their web before - Google has picked up the shop and included in its 'tensegrity' alert.

Playing around

While I still haven't solved the lack of space, restricting my ambitions to go bigger, I continue to experiment with new ideas. I build Tetroid some time ago, and had it with me at the market quite often, but I wasn't too happy with it overall. The tendon length didn't work out properly, so I decided to connect the three strut in a corner in a star shape instead of a triangular loop.

With more tautness than before, each strut could move laterally a lot more, and the network of tendons now distinctly outlines a tetrahedron. I wonder if an octahedron build like this could still collapse....

Marsupial (Large tetrahedron mounted on 3-strut tensul with small tetrahedron suspended)

The new corner configuration increased the appeal straight away, as next step I mounted the tetra on a tensul, using the 'edges' as mount point. Tapping on the top, the structure bounces and rotates a bit. When done carefully, you can rotate it on the spot. The size invited to suspend something in its middle, a 'traditionally' build tetrahedron. The 'baby' tetra swings in its own frequency when the model gets in motion, like a Joey bopping its head out of its mother's pouch. Well, at least with a lot of imagination.

United Duals (Octahedron with a cube intersecting the edges)

I still want to build a tensegrity merkaba, and discover how slight variation produce very amazing outcomes. I started with an octahedron, and added 3-strut moduls to the edges of each triangular face. I moved the strut close together, so that the 24 struts surrounding the octahedron appear like 12 struts in a cube. The struts of the octahedron are a bit less twice the length of the cube struts. The corners of the cube are too small to provide balance for the whole structure, but the model can be 'suspended' from each octahedral corner, which stands slightly out from the cubic faces.

Merkaba (stellated octahedron or octangula)

Having cube and octahedron united was nice, but unexpected. I went back to my small merkaba model and noticed that I had join the tensuls to the corner, and not the edges of an octahedron. It still folds along opposing corners of the octahedron, but the two intersecting tetrahedra remain hidden in the chaos of 36 struts. Having the octahedron in a different colour could bring out more interesting pattern, it's fun to play with, yet a bit visually overwhelming.

Hyper Tetra

Hyper Tetra has a green tetrahedron at its core, surrounded by four tensuls connecting to the edges of it. I made the corner triangles quite large to allow balance on each corner. Now I realise that this model comes closest to the idea of the merkaba: two intersecting tetrahedra. Of course, the 'outer' tetrahedron is roughly twice the size, same sized tetrahedra intersect along their edges. This idea invites to a bigger rebuild, using a 6 strut outer tetrahedron with center holes.