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.

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.

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

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.

Neoncube

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.

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.

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

Intermezzo

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.