Tuesday, 4 October 2011

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.

Thursday, 8 September 2011


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.


Monday, 29 August 2011

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.

Wednesday, 24 August 2011

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.

Wednesday, 27 July 2011


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.

Thursday, 14 July 2011

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.

Friday, 8 July 2011

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.

Wednesday, 22 June 2011

Bell Tower

I played around with models of orthogonal cubes, trying to stack them together. I'd love to build a mega-cube with 20 cubes connecting a larger one, yet I still doubt whether I could easily balance and tune such a large structure.

I would need three columns of tree cubes stacked on top of each other, so I experimented to find out how to stabilise three cubes. Four struts of each cube connect top and bottom vertically, and come very close with simple stacking. I decided to have four central struts, and complete them in the pattern of three stacked cube models.

Bell Tower early draft
The build turned out quite awkward, with some engineering challenges on the path. It took me some hours just to tune the model into a more symmetric shape, and achieved hardly any decent balance. Cubes without diagonal support are inherently instable, so I decided to add cross-bracing tendons to the sides of the structure.

Finally, I was getting more stability and balance, and I began marvelling how to finalise the now sturdy base in a satisfying way. I could easily stack my two cube model over the base, and have an octahedron to top it off.

Bell Tower last draft
Although this experiment created the first 6-level tower I ever made (if you count the base of three levels), balancing was rather unpredictable, and probably hardly stable over time. I had enough leaning towers, and an octahedron on top simply jumped the shark. Finishing the cube-based structure with a 'twisted' cube combined with half an octahedron rather mimics traditional building methods, no need for a wobbly extension on top.

I achieved the final bit of stabilisation by suspending a bell from the four central struts, bringing the centre of gravity down, and dampening lateral movements. I had all aspects together I wanted for that sculpture: a lean base with four central struts, a pointy roof, and a suspended weight. The devil hid in the detail. A cube combined with half of an octahedron can be build with 12 struts, using four joined corners, instead of simply wedging an 8 strut half octahedron on top of a 12 strut cube. Also, the bell had the right kind of weight, but not the looks I wanted.

Bell Tower nearly finished
I spend the first day on building the base structure, the second day with finding a top and suspension, as well as cleaning up the model and fine-tuning. On the third day, it was time to bring everything together. 

Once the bell was in place, the model stood easily balanced, and I installed the last struts without bothering about the wobbly base to work with. The top can now be bend, and the weight of the bell prevents the model from falling over on the rebound. Once in motion, top, base and bell swing in different, connected rhythms, with pressure from the top it rather bends away instead of collapsing.

Bell Tower
Even while blogging, I couldn't stop tinkering. The finishing touches included a cross-bracing of the central struts, similar to the sides, and a tip made with red struts, rotating opposite to the smaller half octahedron underneath. I like the distinct shapes emerging from the red struts from a distance, as well as the sturdiness with all sides cross-braced. 

I used four oak struts (60cm) and 44 bamboo struts with three different length (24 @ 20cm, 16 @ 16cm, 4 @ 28 cm), three types of elastic cord totalling about 12 metres in length, and about 6 metres of nylon cord. Bell Tower measures 90 cm, with a base of 20 x 20 cm, encapsulating a volume of about 35 litres with an estimated weight of about 300 grams. There's roughly at 2:3 ratio in the added length of struts and tendons.

Thursday, 16 June 2011

Leaving symmetry behind

I used a short stint of sunshine to spray paint a batch of struts to bring more colour to my market display. Then I left symmetry behind to experiment with more skewed tensegrities, and came up with five structures in which a splash a colour creates new interesting perspectives.

Disguised Rastafarian
Disguised Rastafarian represents another variation of my favorite octahedron build method, using nylon and elastic jewellery cord together. It's the forth or fifth octa with four green struts hinting at a square, and not the last....

Limejelly revives my old preference for transparent elastic, and for building the 'complementary' tensegrity. Limejelly displays clockwise rotating corners, so their at least two little differences to Disguises Rastafarian.

I think a tensegrity cube allows a symmetric distribution of two colours, yet I continued with a 2:1 ratio in colour distribution, with 4 out of 12 struts coloured green. Balanced on one corner, the green struts appear floating. The box character of the orthogonal tensegrity cube allows for a parallel arrangement for the coloured struts.

Skewed Jellycube
My experiments to transform 12-strut octa and cube into a cuboctahedron inspired Skewed Jellycube. I like the shape and stability of a 12-strut cuboctahedron, but it offers only little play. Skewed Jellycube can be pushed down to collapse in this orientation, although I'm not too sure whether it would survive to vigorous playing.

Skewed Jellyocta
Skewed Jellyocta repeats the idea of Skewed Jellycube, highlighting one of the four potential triangles in a 12-strut cuboctahedron. The structure doesn't collapse entirely, but can be squeezed easily.

With this 80ties retro series the market stall offers enough eye-catching colour, I just need to build some more small icosas and I have a decent collection for the next market day.

Saturday, 28 May 2011

Market preparations

Egg of Columbus
I got lazy since the last market, although I could replenish my stock of smaller sculptures after 5 pieces changed hands. I build two more 6-strut icosas, and have plenty of 12-strut octas in various sizes left. The new show piece is a slightly skewed 30-strut icosa, using two strut length and two colours, the Egg of Columbus.

Unfortunately, I can't get Triple Y in my old Volvo, and the larger structures don't like transport too much. The weather permits the use of more colour as well, so most preparations considered producing certificates, preselecting models for tomorrow and printing more business cards.

I'm overwhelmed by the space-filling character of these structures. My lounge room became an ecosystem of many variations of tensegrities. The heater ventilates hot air into the air, which moves Windspiel around, without ringing the chimes. At the basis of Windspiel, a pack of similar sized left-over experiments from the toolkit development lingers around. A short tetrahelix invaded a corner of Triple-Y, which itself seems to duck away from a large Class-2 tensegrity tetrahedron, which hooked itself into a band of x-modules. The modules connect like a vine the space between the lamp and the window, growing towards the artificial light.

The lamp also holds a cuboctahedron up, with a 6-strut suspended in its center. Windspiel repeats the theme, a small tensegrity suspended in a sphere. Out of seven basic geometric shapes an evolution of sculptures emerged, a constant recombination of materials and methods in different scales. Parts of this zoo will have the opportunity to find a new home, ending up in curious hands.

As I still have no idea which models to take, I simply will sleep the decision over.

Wednesday, 4 May 2011

Getting wild

I received the elastic cord I wanted to use for The Affordable Tensegrity Toolkit, and prepared the first 30 stick prototype with it. The diameter of the cord fits nicely to the groove width, it wedges in and form a stable connection (within limits).

I build first a 30-strut icosa with it, and was amazed about the bounce the final structure had. Instead of using a structure as template of the build, I had a generic weaving pattern in mind, following two simple rules. Once finished, I played with the icosa like a football, producing some domino effects with other structures.
30 strut icosahedron

The next test consisted of timing the transformation from icosahedron into dodecahedron. That meant disassembling the icosa completely, and reusing the components in a different pattern. Again, I navigated through the build by its pattern, creating triangular corners around pentagonal faces. The structure warped itself in shape already while completing the third of twelve pentagons, and after eight minutes the transformation was complete.

I threw the dodecahedron quite lot around, which opened sometimes a corner. Playing it hard goes the limits of the attachment technique. This time I decided to time the disassembly by itself, less than two minutes to undo the sixty connections.
30 strut dodecahedron

As expected, building the 6 strut tetrahedron proved most difficult, but cube and octahedron provided a fast, straight forward build. In a room without other sculptures, I started throwing the cube and octahedron quite hard against the wall. At some point, a tendon in the octahedron snapped, though I wasn't sure whether it was the impact or the way I held it before throwing.

After I replaced the tendon, I continued to bounce the models madly from wall to wall. This time I took care of holding the model mainly at the struts. I guess I limited the vigour I used for my experiments, although I used enough force to hear the tendons swishing during flight. Anyway, no more breakage occurred. The octahedron can safely be used for throwing games and bounced off walls. With all the fun I had finding out the stability limits by relatively brutal force, I look forward to more swishing, clicking and hitting sounds while doing some stress testing for the tensegrity toolkit.
30 struts in three different models

You can reconfigure the model easily. Each single cord gets used as three tendons, two for the corner and one for the connection between corners. While building a model, aiming for similar length makes building easiest. Of course, as there are no markers each connection has to be guesstimated. When I played with different configuration of cube and octahedron, I noticed the dual quality. As two struts connect to each cord, you can place them very close together. The model can't collapse any more, yet seems more robust when thrown around.

Effectively, the total number of tendons reduces from 36 to 24. I'm not certain whether the proximity of the struts converts the 'missing' tendon into a kind of joint, however, by ignoring this tendon the remaining 24 tendons outline a cuboctahedron, the intersection between cube and octahedron. Both physical models look and behave similar in this configuration. By moving the struts together, they shaped four entwined triangles, like faces of a tetrahedron twisted inside and around. Reminds me of the jitterbug transformation, so I don't think I discovered something 'new', just new for me.
Four intertwined triangles in a 12strut pseudo cuboctahedron


I think the tetrahedron represent the number 2, the basic duality in universe. It contains as well the number 3. I see more three-ness in the 6 faces of a cube and the 6 vertices of an octahedron, the 2by2-ness appears in 4 edges constituting a face (cube) or converging into an edge (octahedron).  Somehow, five-ness appears in the shapes observable. From a specific perspective, pentagonal outlines appear, all the while of hexagram and pentagram can be inscribed to some struts. Is there already the five-ness of the icosahedron in cube and octahedron?

In the 'orthogonal' cube, eliminating the 'middle' tendon doesn't create entwined triangles, yet brings two struts together along their length. The closer I moved the parallel struts together, the more familiar the structure appeared: it's a kind of 12-strut icosahedron.

Orthogonal cube morphed into 12-strut icosahedron
The new cord material requires a bit more work to prepare the toolkit elements, but so far looks extremely promising to combine easy build methods with lasting tendons.

Wednesday, 20 April 2011

And that's TATT!

Different times have different toys, different ways to explore constructive creativity. Mechano or Lego come to mind to name some of those amazing influences on the development of creative minds around the globe.

Lego provide the 'atomic' toolkit, solid pieces of matter, stacked together. The Affordable Tensegrity Toolkit brings us closer to the unpredictable nature of quantum mechanics. The regular structure come with a twist, or a wobble, a bit of surprise based on very simple rules of construction. You build atoms, which basically consist of plenty of empty space. The empty space and the lightness of 'solid parts of matter' become apparent in a finished tensegrity structure.

Two tetrahedra with opposing chirality
With six struts, you can build the first platonic solid, the tetrahedron.

Trigonal dypyramid 
With nine struts, a structure with surprising properties emerges. Three tensegrity prisms (or tensuls) stacked on each other form the trigonal dypyramid.

Flattened dypiramid
This structure flattens under pressure and bounces back happily.

Trigonal Prism

The trigonal prism offers less excitement, due to lack of symmetry across its corners. It squeezes down, but doesn't bounce back too spectacular.

The cube can be build in two ways. Above you see a cube where all the corners rotate in the same direction. The faces appear square, yet while lying on a face the vertical struts 'lean' to the side. With mixed chirality, the struts cross each other orthogonally, yet each face looks rectangular.

Two stacked orthogonal cubes
Of course, it takes 24 elements to stack to cubes together.

Octahedron (view onto triangular face)
Yet it just take 12 struts for the third platonic solid, the octahedron. Its symmetry in combination with elastic tendons provides lots of bounce.

Octahedron (corner view)
Pushing the corner towards each other flattens the model.

Cuboctahedron (view on triangular face)
With 24 struts you can build the cuboctahedron, or Vector Equilibrium. This structure shows the transition from cube to octahedron, and has thus six square and eight trigonal faces.

Cuboctahedron (view on square face)
All of that (and things I haven't thought of) can be constructed with a maximum of 24 toolkit elements. The remaining two platonic solids, icosahedron and dodecahedron, require 30 struts. The simple joining methods allows it to put smaller models together (like the two stacked cubes) to create larger ones.

How to build an octahedron with the Affordable Tensegrity toolkit

You can build an octahedron (eight triangular faces, twelve edges and six corners joining four edges each) out of twelve identical elements. The cord gives the strut an orientation, a back and front. The knotted end points in clockwise direction when viewed from the front.

Single toolkit element
This orientation determines the twist of the tension element, and helps following simple rules during the build phase. Here goes the first one:
Tendons go along the front of the strut, which means the 'outside' of the finished structure.

The first connection
First, an element connects to the tendon of another. The distance is about one third of the total tendon, for simplicity I call this the 'short end'. Both struts lie on their 'back', the knot in the connection points towards the short end, the knot in the short end points clockwise.

Continuing the pattern
The third strut repeats the same idea: The knot points towards the short end, the short end of the newly connected strut rests upon the strut it threaded in. The next rule becomes apparent:
The knots point towards the end of the strut, not the center.

Four struts form one 'corner'
With the fourth strut one corner of the octahedron is finished. All knots should now point towards the short end of the next strut in the square, and the struts intersect in clockwise direction like in the photo.

Two corners
Preparing top and bottom corner makes the final assembly easier. Simply connect four more struts exactly the way you did before. Put it aside until later

The next vital connection
From now on, things get more three-dimensional and require a bit confidence that everything holds together. Each of the tendons connects to two other struts in the final structure (hence short and long end). The next four struts connect to the long ends, and introduce the second rule of building tensegrities with TATT:
When viewed from the front, the two struts connecting to the tendon of a toolkit element, arrive from opposing sides.

The pattern for the second stage
The long end of the new connection connects to the nearest strut of the corner.

Two struts of the second level
The next strut follows the same idea: Connecting to the open long end of a corner strut, having the long end connected to the next corner strut.

Three struts of the second level
Connect the third strut, remember that tendons go outside, the knots point to the short end, struts connecting the same tendon come from opposite directions.

Eight struts of the octahedron connected
After connecting the second level of the octahedron, the structure slightly bends itself into shape. To get the final shape, more bending needs to be done for the final shape. Eight unconnected ends and eight spaces in tendons remain for the last few connections to be made.

Corner with second level turned around next to top corner 
After turning the eight stick module around, the top corner finishes the build.

First connection of the top corner
The first connection comes easy.

Second connection of the top corner
The second connection bends the model into a skewed shape, it follows the same pattern as before.

Three connection of the top corner
The tension increases while the connections aren't balanced, yet the model get more bounciness and stability during the final steps.

Model with four missing connections
The open ends of the top corner now connect to the rest of the structure, with four attachment spots remaining. The four remaining open ends (from the eight struts of the first build phase) connect into this open spots.

Three missing connections 
The same rules as before apply. The knots point towards the short ends, struts connect from opposing directions to a shared tendon.
Two missing connections
Due to the increased tension, unsecured connection might easily slip during this phase.

One step away from finishing
The increased tension makes building a bit trickier. At the same time, the tension guides you towards making the 'right connections'.

Tensegrity octahedron balancing on a corner
Once we last connection is made, you can test the symmetry by balancing the model on each of its six corners
Flattened model
The elasticity of the cords allows the model to squeeze down, the size of the squared loops in the corners determines to flat the model can get. You can adjust the model by reattaching one stick at a time in a more symmetrical way.

Don't take the rules for the build as eternal truth, for other models other rules (although similar) apply. There's more than one way of building any tensegrity structure, only experimentation can improve any construction method.

The Affordable Tensegrity Toolkit just has hatched and needs now good documentation. Please contact me via this blog if you're interested in more details, or have specific requests or comments.