Seven seven seven

I build already a few versions of (truncated) chestahedra, one of them most likely still on display in Queensland, the rest of them embellishing my home. My "quick and dirty" way of transforming a geometric structure into a tensegrity basically cuts off the corners, with as many struts as the geometry had edges. The network of strings therefor doesn't properly reflect the original geometry, with the exception of the 4-strut tetrahedron.

4 strut tensegrity tetrahedron

6 strut (truncated) tetrahedral tensegrity

Truncation basically produces the "dual" of a Platonic solid. Cutting the corners of a cube creates the octahedron, cutting the corners of an octahedron brings back the cube. The number of faces becomes the number of vertices, while the number of edges remains the same. However, this beautiful relation does only really exist between hexahedron (cube) and octahedron, and between dodecahedron and icosahedron. Applying the same algorithm to non-Platonic solids creates still very interesting transformations.

The chestahedron, which can into human consciousness just very recently, also has a dual, the decatria. I'm surprised that it took me two years from finding out about the chestahedron to learn about its dual, which still is more than a mystery to me. I know it has 13 faces, 19 corners and 30 edges, mostly likely three different kind of faces. I still struggle to understand the 2d images I saw so far, how many different edge length are involved, so I delayed the ambition to "tensegrify" the decatria.

I got inspired, however, to build a chestahedron similar to the 4 strut tetrahedron, using the tension elements to outline the wireframe version of its geometry. I struggled a lot when tried this for the octahedron, failed completely for the cube so far. The six strut icosahedron doesn't need the additional six strings to unveil it's "true" geometry, my ten strut dodecahedron usually ends up slightly imperfect, with most pentagons not being really symmetric. 

10 strut dodecahedron

6 strut icosahedron

I ruminated a lot before getting hands on, using my experiences of building asymmetric structures to have a plan which made sense to me. I got frustrated on earlier attempts to construct things which seemed initially possible, but then turned out quite different. The idea to use seven struts for building a seven-sided object with seven corners kept me going. As the chestahedron has an unfolded tetrahedron at its base, the first tensegrity shape conceived in modern times might provide a great starting point.

This constellation was build in the 1920s before the term "tensegrity" was coined.

My first attempt followed my intuition. I chose three different length for the struts: 30cm for the base, 20cm for the vertical riser, and 15 cm for the middle section. The length for the outer tension network were simple, using the edge length relations Frank Chester published for the chestahedron. 9 strings were knotted to 30 cm, 3 more to 16cm, for a 0.53 ratio between top and base edge. In the truncated version, the top seemed to sink a bit in, distorting the beautiful relation of the solid object.

Healing heart (made of yarrow with suspended copper wire spiral) 

I started off as minimal as possible, connecting the three base struts with a string loop which served to received the three shorter struts for the middle section as well. The central riser was supposed to connect to the outer string network, and three pieces of elastic string connected to the top end of the base struts.

It was relatively straight forward to get everything together. All I needed to do was to connect the bottom of the vertical riser to the top of the base struts, creating an expansion from bottom to top through the inside which should be limited by the tension network on the outside. It got a bit fiddly, all seven sticks come together fairly close in the centre, but there were only two connections to go.... and then everything fell apart in a tangle of sticks and strings.

So decided to use some transparent elastic string to stabilise the base, making a classic nine string, three strut tensul out of it. It still took some dexterity to finish it, yet this the little deviation from making it as minimal as possible provided a satisfying prove of the concept which emerged less than 24 hours in my mind.

Very first seven strut tensegrity chestahedron as prove of concept

Elastic string always allows a bit of leeway, and I used it sometimes to draft models. Some of the four strut tetrahedra combine elastic string in the centre, and non-elastic on the outside. Non-elastic string requires much more precision than elastic, but besides this, I love the "invisibility" aspect of it. Frank Chester mentioned that geometric shapes act as scaffolding to manifest physical objects, so I'm perfectly happy to have some transparent scaffolding still in place.

I probably stopped using non-stretchy string for smaller objects after having some careless punters breaking my sculptures. I think it was Edison who mentioned that "you cannot make things foolproof, because fools are so damn inventive". I liked the idea to show the framework of a chestahedron with the outer tension network of a tensegrity, while hiding the supporting inside tension with transparent string. 

When I measured the draft I made, I noticed some variations of lengths, so I chose some very similarly prepared struts and dedicated some time to prepare my strings with as much precision as possible. The second model looked promising already in its early stages.

Unfolded tetrahedron, four equilateral triangles

All the supporting tension elements are now made with transparent string, symbolising the invisible forces. I still needed two attempts to find a good length for the strings supporting the vertical riser. The final version has a relaxed amount of tension. As it's not really meant to be stressed heavily, I'm quite confident that it will maintain its shape for years to come.

Seven strut chestahedron

Here you go. An object with seven vertices, seven faces made with seven sticks and seven supporting transparent strings. Can it get any better? Most certainly. I used three different length for the struts, introduced new length for the invisible support. The perceived centre moved up, although it still seems to divide the structure with the golden ratio.

Now that I know how to build a version of it, I'm curious how to explore this shape even more. It's close to my heart.... as it is the scaffolding needed to create a heart in first place. Stay tuned.

And on and on...

It's now nine month since I last busked out my tensegrities. While I accidentally sold a few pieces this year, I'd love the business to pick up again. Still, I took part of Polymer Dreams Lab installation in Coburg, and build a bit bigger.

I still haven't organised better camera gear, the mobile phone camera has many limitations, as well as my ageing IT gear. This made me a bit lazy in maintaining this site, as it has become a bit tedious to add decent photos in an acceptable time frame.

Goodbrew Vector Equilibrium

One of the first bigger pieces is based on the 24 strut cuboctahedron aka vector equilibrium. The struts are brush painted, an area where I can still improve my skills. The structure has survived some drops of a few metres and still hangs out in a large warehouse.

Garden decoration

I came across some nice looking broom handles, with a hole on one side, which I could quickly convert into a 4-strut tetra. I used the pre-existing holes for a continuos inner tendon, and guestimated the length for the outer tendons on the first shot. Unlike larger tetras with slightly flexible struts, the result behaves very sturdy and without the tendency to collapse through its centre. It's now an eye catcher in our front yard, surrounded with two brugmansias.

Eclectic tetra

I rediscovered some dowels I prepared for my very first tensegrity builds, when I still deployed hooks to secure the strings. The dowels probably had the larger diameter I used for small-size models, while the additional 12 sticks through the centre have about the smallest diameter I used. Unless I get another dremel, I can't prepare similar small diameter struts anymore, but combination of materials with different girths in larger scale are well worth contemplating.

Another lucky find were nicely carved bamboo chopsticks. Finding the right length for this one took much longer than building the larger version garden decoration, I nevertheless like the small version a lot.

I sourced some old trampoline springs, and a friend cut some old pipes to lengths for me. I totally underestimated the strengths of the springs, and had to settle down with a slightly asymmetric version of an icosahedron shape. I haven't dared to try to collapse the structure, as I realised how easily working with heavy struts and high tension can lead to serious injury. The springs and the weight allow any impulse to reverberate through the structure for a long time, hitting struts and springs produces quite some interesting sounds. 

Steampunk tensegrity

As the metal started rusting slightly, I decided to give the dull grey with bits of rust a colourful makeover. Different perspectives show now different colours dominating, yet I'm not too sure yet how long it'll survive outdoors.

Thingamabobs

I took up residency with my Magical Thingamabobs nearly a year ago, and many things happened in the open air shop in Melbourne's prestigious CBD since then. I encountered all four seasons now, and could observe the change in angle of the sun towards our planet.

Some people claim that my art work isn't 'emotional', which might hold true to a certain degree. Nevertheless, I experienced the gamut of fear, anger, grief, love, sadness and worry while patiently and persistently doing my work.

The 6 strut icosahedron and the 12 strut octahedron remain my most popular objects, but there's some shapes I discontinued, and a new set of objects to reassemble each time around. As my camera equipment doesn't work too well, I probably missed the opportunity to document some objects I haven't build since then.

Close encounter - 6 strut tetrahedron

I noticed that reassembling some of the objects creates some wear, and a loss of tension. The model above has reworked to have single-string connections to each corner. The 20cm Pars inspired tetrahedron has been painted a little bit to look even more distinct.

Japanese Butterfly - 12 strut tetrahedron

I love the shape of the 24 strut cuboctahedron, and build some colour variation with it. While four colours bring out the four intersection double triangles in the structure, using black as only colour works aesthetically well.

Checkerboard - 24 strut cuboctahedron

An icosahedron with suspended wireframe tetrahedron act as the current 'eye-catcher' for the front row. The transport made the doubled strings a bit weaker, the suspended centrepiece brings it back into good shape. 

Captured tetra - 6 strut icosahedron with suspended tetrahedron

The dodecahedron gets really wobbly as 30 strut structure. I found two variations for it, though. The first one consists of an 6 strut icosahedron, joined like the one above. By connecting the ends of the parallel sticks the strings outline 12 pentagonal faces. The other variation starts as 5 strut prism, with five more sticks outside the girth of it. 

10 strut dodecahedron

Painting the end of the sticks black adds another dimension to the structure, and works well for many basic shapes. The model below has already found a new home, but as I enjoy playing with this one most, it will have a rebirth soon.

12 strut octahedron with elastic and non-elastic string

The amount of 'un-playable' objects increases. The latest one of those offers plenty of potential for all sort of variation. The outer tendons shape a tetrahedron, the sticks are attached to its corner and miss each other in the central hub made of four tendons.

Black flag post 4 strut x-module based tetrahedron

I have two of 4 strut pyramids on display - the 15 cm version above, and a 30 cm one. And some more at home, one version with aluminium tube as struts. I want to explore whether I can use these tetrahedral modules to build a star tetrahedron, that might be a nice project for a rainy day.

I took some of the photos here from the blog Hello Mrs. Morris, who wrote a nice article about me and my work.

Intermezzo

I feel a bit tired after being out in City Square nearly every day for a week, rather in a positive way as I enjoyed the warmer weather and the interesting people which stopped by. Besides experimenting a bit with my structures, I also changed the 'shop' name from Antigravity Tensegrity several times - first to 'Magical Sticks'n'Strings', lately to 'Magical Thingamabobs.

Magical Sticks'N'Strings including Chinese translation

I tested also an alternative location in case of rain and/or too much wind, in a subway passage to Flinders Street Station. There's enough light to work, yet many really rushed people unlikely to take some time to stop by.

Melbourne's Smallest Art Gallery 

The signs consists of laminated A4 prints, easy to attach via blue tack to most surfaces. Thingamabobs seems to describe my sculptures best, and removes the stench of sciency stuff from them. When people start to handle them, the magical parts becomes much easier to understand.

Pointing towards seemingly impossible 3d objects

I want to improve the display of the sculptures. Arranging them in a not too overwhelming or chaotic way poses quite a challenge, especially when I have to consider wind, which often introduces complete chaos. Larger object like the one below wont stay 'up' in gusts, keeping me busy chasing after my sculptures.

Cup of Hope

This sculpture emerged from building larger objects mainly to attract attention, and isn't gone with the wind, but found a happy new home. Some structures lasted only for one or two days, until I decided to rebuild them in a different way.

4 colour Vector Equilibrium

Red green honey pot

The 24 strut Vector Equilibrium shape still fascinates me, and I have only realised a single four colour combination.

432 VE

One of my latest experiments were three 6-strut icosahedra with 10cm struts. Besides the added step of sawing sticks in half, the result looked quite amazing. As I tried them on a relatively windy day, the juggling suitable didn't turn out too well, the cuteness factor meant two were gone before I closed shop.

Icosa Fence

Joined with only four additional strings, the three icosahedra build a stable structure. With equal tension, four sticks build a compression rectangle, three of them with three modules connected. The idea invites itself to be extended in 2d with 5 modules, and 3d with seven.

Without people appreciating my work enough to take it home, I wouldn't have come across some of the structures build lately. I found new material, and more inspiration which shapes to materialise. I get the impression that my art is multi-dimensionally interactive - the exposure in public extended the range of shapes, and kept me busy exploring colour variations for more familiar geometries.

So I'd like to say thank you to all those who supported my work, by keeping me company, having a chat, donating or buying. Your interaction became my inspiration, so you're only playing with art but also with the artist. 

Is this street art?

You can touch this has been rebranded for the street market. As I still want to popularise the concept of tensegrity, I started busking my work in a public place, at City Square in Melbourne's CBD. 

Besides bringing about 10 build up structures along, I have string, scissors, ruler and sticks to build more. It's still only few sculptures per day that change hands for money, yet so far I haven't had any no-sales day.

Working in public is fun, and gains quite some attraction. I had plenty of inspiring conversations, and witnessed mass outbreaks of awe when school classes passed by. From of those, I heard the most interesting question so far: Is this street art?

My answer was simple: "If you think it's art, and it's definitely on the street, so yeah, you can call it street art." It has a bit the character of an exhibition as well, a temporary of course, with new objects every day.

I made friends with a chalk artist who is quire regularly nearby, and enjoy that he shares his experience on the street. It must be about the worst time to start this experiment - short daylight hours and not really pleasant weather. Especially the wind keeps me busy, but with a limited amount of models on display I still managed to chase up anything blown away.

The 6-strut icosahedron, plain or in 3 colours, and the octahedron go best, but I sold also the 12 strut tetrahedron, and some 9 strut joined tetras.

Besides some chalking, my setup is very basic. I still would like better display options. I could probably chalk some info, but a good looking solution that portable and easy to transport could improve my sales.

Sunny days bring out interesting patterns casted by the structures, and generally bring more smiles and interactions. I'm still hoping for the rain to cease, I build a tetrahedron as donation hat, and crave to try it out.

Revival

Although I didn't want to continue this blog, I picked up on an idea I rejected for some years now. It happened quite often to me that visitors to my market stall suggested making lamps out of my structures. Besides the problem of electrical safety, I didn't like the idea of the 'skin' part for a lamp.

Now I'm sitting in a friend's house, with many bare light bulbs hanging from the ceiling. I asked whether the house mates here want some cover for their lamps, and made a colourful icosahedron as test run. While they liked the structure, it doesn't do much as lamp shade - it just surrounds the bulb, and certainly looks best while its switched off.

The energy saving bulbs won't get too hot, so I wasn't worried about the plastic strings melting away. I remembered from the childhood a kind of craft paper which we used to make lanterns. Translucent paper, or vellum paper, is still available and should do exactly what is desired - blocking the harsh light, and giving it a warmer glow.

The icosahedron with 15cm struts looks small enough to probably fit two A4 sheets of paper in it - which would add another geometric configuration to it, yet could work. But while looking where I could get vellum paper locally, I revised my plans how to put 'shades' on, which might even save money for material (well, at least one...).

Option one would need a printer, or at least a printed template for some folding fun. The network outline of an icosahedron on A4 potentially fits nicely into the centre of a tensegrity sphere. It shouldn't really be needed to have a complete paper icosahedron inside, at least one triangle needs to be left out to allow the light bulb in.

While the basic shape of a tensegrity structure corresponds to the Platonic Solids, the crossings (corners) inflate to another opening (face), ie instead of having 20 openings and 12 crossings the tensegrity icosahedron has 32 openings (and more crossings I'm willing to count now). From a construction point of view, the 12 openings typical for a dodecahedron, the dual to the icosahedron, are more apparent than 20 openings describing the actual icosahedron.

Now I wish I still had the abundance of models and a printer around - even without suitable paper at hand, I could figure out how well folded A4 sheets, either as dodecahedron or icosahedron, would fit into my spheres with different strut lengths.... which is why I took some time to write down the ideas about finally giving a use to my structures.

Hanging around

Guerilla tensegrities have an unpredictable lifespan. Not necessarily by decomposition, that happened only twice as far as I can say, but rather due to their accessibility. If it's easy for me to install them, it's easy for anyone to take them, whether for their own enjoyment or as part of their paid jobs.

I released 13 objects into the wild so far, with only two or three still in place. I still wonder if my motivation reflects more narcissism or exercises in letting go. However, I cannot regret the experiences I made, the bits of adrenaline rush while doing it, and about how to increase the positioning to appeal at least to me when I cruise through the neighbourhood to check whether they're still in place.

The first object I released took the most effort and excitement, and it lasted for nearly a year. A three strut minimal tensegrity made of pencils, attached to a power wire with an elaborate mounting mechanism. It survived many periods of wild weather, and I found it on the ground after the attachment broke, still intact.

Yet I wonder if it was ever noticed, being tiny and in a place the usual gaze would wonder about to find something unexpected. Two objects of similar size in plain eyesight were gone quite fast, and lately I went to much bigger sculptures for outdoor installations - I ran out of space, and I hoped to increase their visibility.

The first sculpture put up in a place for its splendid visibility didn't even last 24 hours, installed in a stealthy night action it was gone before I could take any photo during daylight. Another one, which I placed in the trunk of cut-off tree, survived some flooding from the creek next to it, and I adjusted it several times for maximum viewing pleasure, is gone now as well.

My attempts to attached some medium sized octahedra on top of wooden poles might have gone with the wind - I found one of it next to the pole after a stormy day, yet I'm sure now that the way of attaching them is simply not viable.

One of the objects that is still happily hanging around, provided me a flood of synchronicities. I met someone living just about 50 metres away from where I hung it out, having one of the most amazing sunday afternoons, a day after it got into place.

Initially, it hung much closer to the branch it's suspended from than I intended. I wanted to give it visibility and freedom of movement, and instead pulled it very tightly to the branch. I still have no idea how it lowered itself down, the elements might have helped me in giving it a more prominent position. One day, instead of being snuggly close to the branch, it had at least the little bit of clearance to rotate in the wind, became more visible, and is now affected by the slightest breeze.

It's now about seven weeks that it's hanging around, and I haven't got a name for it. Hold on, I just found one: Louise, please. As it's along one of my favorite bike paths, I will have ample opportunity to check on its longevity.

Louise, please (6 strut icosahedron)

Filling the void

I started experimenting with combining tensegrity structures from the very start of my explorations. Most of the results used models of similar dimension and base geometry and some sort of quick and dirty approach. It took me a while, and some larger sculptures to deviate from this idea, and the initial set of combined structures had a clear defined orientation in space.

The idea of core and shell allowed me to create more complex structures which still can be placed in a variety of orientations. It also taught me experimentally that Buckminster Fuller's idea about the tetrahedron as smallest 'building block' of the universe can be demonstrated with tensegrity models.

Although I haven't attempted yet to exactly model the volumetric relations between the Platonic Solids as described in Synergetics, the 'compatibility' of all these highly symmetric structure becomes very apparent. Tetrahedra fits easily into 6-strut icosahedra, 12 strut cubes and octahedra, and 30 strut dodecahedra. Most likely also in 30 strut icosahedra (the most common tensegrity sphere), I just haven't bothered yet to build one.

Cubic merkaba

Octa Octa

Icosa Icosa

Explorations

After building a relatively large number of tried and tested icosahedra and octahedra, which so far exceeded the demand by far, I went back to the fun of exploring other shapes and build methods. Floating Spell is an adapted pentagonal prism, with the top struts connecting across the center.

Floating Spell (20 struts)

Five Elements creates different views from each angle, with two of the twelve pentagonal corners appearing copper from the outside, and black from the inside. Each strut looks basically identical, nevertheless a variety of pattern appear throughout the structure.

Five Elements (30 strut tensegrity icosahedron)

12 Meridians belongs to the recycling projects among my latest explorations. After deploying the centrally joined corner tendons, I rebuild a dodecahedron with black and white struts, which failed to impress me in its first incarnation.

12 meridians (30 strut tensegrity dodecahedron)

Balanced Infinity is a 12 strut cube with centrally joined corner tendon, and elastic string for the tendons along the edges. The model feels very floppy, yet when handled gently balances on each of its eight corners. It can go through quite some interesting before losing balance.

Balanced Infinity (12 strut tensegrity cube)

Star Icosa stems from the ambitious idea to build a 30-strut icosahedron entirely with non-elastic string. So far, my attempts usually lacked the precision in tendon length for satisfying stability in 30 strut models. The star connected corners looks especially interesting under UV light.

Star Icosa (30 strut tensegrity icosahedron)

Redfaced Revisited is another recycling project. The original Redfaced had transparent elastic tendons, It has a cuboctahedral shape (Vector Equilibrium), and handles nicely.

Redfaced Revisited (24 strut cuboctahedron)

Polar Symmetry belongs to the experiments with scaling up. Although the nylon string has only little elasticity, the model can collapse on itself and bounce back.

Polar Symmetry (6 strut tensegrity icosahedron)

The next three objects a variations of the same structure, utilising central corner joints. Green Bridge shows the pure concept: 4 20cm struts rising near vertical, two 30cm struts crossing in the center along a horizontal plane. 

Green bridge

Fiercely occupied uses different colours for the different tendons, and has a Pokemon as inhabitant.

Fiercely occupied

Gargoyled Tetra is also inhabited by a Pokemon, and also outlines a tetrahedron with the four orange tendons in its center. The tetrahedral pull towards the center contributes to the overall stability.

Gargoyled Tetra

After finding some many 'merging' structures in my latest tensegrity experiments, I revisited also the idea of the merkaba. The study has some flaws to it, yet it would like see a much larger build to dismiss this concept.

Merkaba study