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.

Heart Space

Once I started understanding the slightly irregular geometry of the Chestahedron, I grew fond of it. Two variations of it now decorate the Neurophysics Functional Movement Centre in Queensland, as well as being used to demonstrate complex processes.

Even without anything suspended from the top, the Chestahedron favours an upright position in relation to gravity. 'Chiming Heart' was sized to fit into a 50cm cube, made of non-elastic string and Tasmanian Oak. It has a Chinese Bell as attachment, introducing more moveable elements to a relative sturdy structure.

'Fiery Heart' needed to be more moveable, even the small weight of a bell (ca. one ounce) put too much stress on a similar structure with elastic strings. I decided to use non-elastic string for the lateral 'corners' to maintain the overall shape after distortion, and to make the non-elastic attachment point part of the tension network.

While I used whatever I could find as attachments so far, I needed now something of decent size, low weight and potentially bell-shaped. A small 6-strut tensegrity tetrahedron fits the bill perfectly, creating pleasing size relations. Some dashes of colour high light this centre, combining the shape for Fire with its colour red.

Meanwhile, 'Mottled Heart' gets taken over a by tomato, rosemary and mustard. The dodecahedron on the roof suffered a bit with the stormy weather lately, but 'Mottled Heart' shows only slight fading of the strings. I wonder whether its attachment will interfere with the mustard underneath, it won't take long before I find out.

Chestahedron

I came across a very interesting geometric shape, an object with 7 openings (faces). It is composed out of 4 equilateral triangles and 3 kite-shaped openings. The kite is composed by cutting a similar sized in half and arranging the parts along their longest sides.

Mathematically speaking, it would be classified as diminished trapezoid, or as a heptahedron. You can find 7 a lot of times: Number of openings, number of crossings (vertexes), it's entire surface area is 7 times that of an equilateral triangle, there are 3 crossings with 4 trajectories, and 4 crossings with 3 trajectories.

I build it easily as tensegrity structure, with my simplest construction method. 3 of the 12 edges are shorter (with a factor of sqr(3)/2 ), which I guesstimated for the first build. The model tends towards a circular shape, the elegant elongation of Frank Chester's models gets a bit lost. I experiment with using different spins of the 4- and the 3-trajectory crossings, yet set on its triangular base, it tends to 'go bubbly'.

A larger model, with a better approximation of the strut length comes closer to the desired appearance of an elongated object when suspended from the top corner. Maybe there's a simple way of keeping it 'slim' by ways of an internally suspended structure.

 Chester demonstrates in his presentation how his chestahedron relates to 4 of the 5 Platonic Solids, embeds the Golden Ratio and how it fits into the Flower of Life.

PS: I found a document having the angles and strut length relationships. The shorter struts have a 0.53 factor in relation to the base length. The latest models use a 0.5 factor, which increased their optical appeal and structural stability. The slimness I missed once I found in the proper proportions.

I recycled 75cm bamboo struts for the largest version so far. Standing on its triangular base, the structure resembles an obelisk. A teardrop shaped former bed post top is suspended from the top three struts. At the moment, it's suspended using the same type of string used overall. I will replace it with fishing line, and adjust the length so that the centre of the object indicates the centre of the hidden hexagram.

PPS: While the teardrop/bell shaped centre piece isn't probably in the centre of hidden hexagram, it attached it already in a 1:1.61 relationship (height from ground:length to the top). As the object has three points of contact with about 30 degree from vertical I plan to use some hollow plastic tubes as support anchors for them in the ground. The relatively high mount point of the bell will topple the object if it is too far from the centre.

It's fun to play a bit with this piece - the pendulum creates interesting patterns of movement, even in a still state of the pendulum. The visual effect of white paint peeling off, combined with pink string, appears very harsh. In outdoor conditions, the original bamboo will reappear, the strings will bleach. It will grow over as well - the patch I want use is fertilised with three mouse corpses, mulch and saw dust, with heaps of mustard seeds.

The 4-strut tetrahedron in my front yard turned invisible. A ranking plant took it over, and attacked the two brugmansias next to it. I expected this plant to die back in winter, but I noticed only the comfrey and chamomile to die back. I want to prune the rosemary next to the patch where the 'Mottled Heart' will live.

Most of my outdoor creations didn't survive more than some months. The first 'garden model' still lives, more than I want to. Mold has taken hold of the repurposed broomsticks, so I need consider treatment for materials meant to sustain outdoor conditions. The fierce sun bleaches lots of colour, which is why I'm curious curious about the change in colour especially with the pink string.

The dodecahedron above the office block still twirls around on a string. The prevailing wind often nails it to the eastern wall, but a change in wind direction brings it back to a floaty space. The nylon string I use mostly stretches a little bit over time, yet it still looks sufficiently tense. I use the same string for 'Mottled Heart', which might need readjustment over time. My estimations for string length meant it's not too easy to take a cm out of the overall length.

I already fell in love with the interactivity of this object. Anchors will hopefully provide a minimalist way of preventing being blown away by the wind, or toppled over by over ambitious experimentalists. The wind can mainly attack from one side, so the movement shouldn't get out of control. With spring on the door step, plants will use the support to grow intro different spaces.

The last garden sculpture was destroyed during a party. The project gained some useful insights, yet even without the destructive effort it wasn't meant to last. Replacing the stinky compost place with a beating heart appeals to me.

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. 

Modular

The triangle seems most obviously the most stable configuration, and it can be found in a lot of my tensegrity structures. Three trajectories building the eight intersections of a cube would be one example, which transform into eight triangular opening of an octahedron. Two triangles that add up to four triangles in three dimensions of the tetrahedron would be another.

While showing my tensegrity structures in the street I skipped the 30-strut structures for pragmatic reasons. I carry about 13 items around - 3 six strut icosahedra in different sizes, 2 octahedra, 2 tetrahedra, 2 cubes, 2 joined tetrahedra, 2 pentagonal prisms that build some donation vessel.

While it's easy enough to perceive the octahedron as a kind of spherical object, it's much less obvious than a 30 strut icosahedron, or the 24 strut vector equilibrium, or it's dual, the rhombic dodecahedron. Just to keep me busy, I started building the latter two while I'm sitting around, and discovered some interesting quality.

Vector equilibrium

Instead of building strut by strut, the VE and its dual invite themselves to be composed of triangular modules. Actually, the same applies to the cube and octahedron.

Rhombic dodecahedron

The triangular module used to build the above model connects the struts in the middle of the attached string, which works easy enough to build the VE and the dodecahedron. The dodecahedron balances quite easily on its 'square' corners, the VE on its 'rhombic' corners.

Usually, the triangles are rather located on a one third/two third ratio, at least when I aimed for maximum symmetry. While the half configuration works quite satisfying for the larger structures, building cube and octahedron from the same 3-strut modules produces rather skewed results.

Skewed octahedron

The four 'modular' triangles are larger than those that emanate by connection, and instead of having square corners, they are rather rhombic. The same applies to the cube - four intersections have the size of the original modules, the other four end up much smaller.

Skewed cube

The reduced symmetry in the skewed versions still has lots of aesthetic appeal, and invites itself to be build in multicolour. I appreciate more and more the opportunity to experiment with different ratios of tendon lengths that elastic string allows for.

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.

Busking tensegrities

Since I started building tensegrity structures, I got hooked. When I succeeded for the first time, I experienced something I couldn't have imagined before. In a way, I encountered the difference of what is called 'book wisdom' and 'experienced wisdom', and it blew my mind.

Now I'm certain that the concept of tensegrity will be part of my life. It is, scientifically speaking, anyway - from the way the cells in my body maintain their shape, to the interaction of the musculo-skeletal system, it's just a fact of life.

As I enjoy the process of building physical tensegrity structures, in various sizes and shapes, using different materials and strategies, I soon ran out of space to keep or at least collect my own work. For more than two years, I managed to tackle this challenge partly by going to a market and sell some of the structures I build.

I even went to live in the bush for a while with the hope to fill space with bigger things. This only meant limiting the amount of audience - instead of familiarising a larger part of my community with this beautiful way of representing fundamental principles within the universe, I engaged in some sort of (not really satisfying) form of artistic wanking.

Being involved in the Friday Free Shop in Melbourne's City Square gave me a better opportunity to gage the attraction of my work - I donated some of my structures each week I went there, and usually all of them found some new owners. Success! Even without knowing the term tensegrity, about thirty or forty tensegrity toys ended up in unknown curious hands.

Encouraged by the ease to sell my work for free, I decided to make City Square my new market place. As often as the weather permits, I will offer a variety of tensegrity structures there, as well as building new ones while I'm there.

The short time of sunlight restricts the amount of time I can spend there, nevertheless I will do my best to be available for a chat, and a build to customers preferences at City Square in Melbourne. Pick up a sample of my work for free on Fridays, or meet me, weather permitting, trying to get some of your hard-earned money for my honest craft on any other day without rain.

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.

Rainbow Buckyball

After a quite disappointing season on the Rose Street Artists Market, I had a break to reconsider the direction I want to take my tensegrity work to. I want to increase the size of sculptures, but with only limited space available, and no marketing opportunity for bigger things it's not something very feasible at the moment.

So I came up with the idea to make my third buckyball, a truncated icosahedron requiring 90 struts, this time using 6 colours. With the two colours versions I already found out how to structure different colours, and I had at least a plan. There's 12 pentagons in the buckyball shape (which is basically the same layout as a soccer ball), and 20 hexagons. Using six colours means each hexagon can contain all colours.

I thought if I start out with the pentagons, each build in a single colour, it should work out in this way. It still turned out as some tricky puzzle, and the actual build took me as long as the preparation of all the elements.

After building the twelve pentagons, 60 struts were gone, and 5 five struts of each color left. Each hexagon in this tensegrity consists of the struts from a adjacent pentagon, and three that connect to another hexagon. I had to figure out a build algorithm that allowed the hexagons contain all colours, which took me only two attempts.

There are two pentagons of each colour, and as expected, they appear on opposite poles of the finished structure. To my surprise, the remaining five struts of the same colour form an equator, only this configuration warrants that each hexagon contains all colours. This symmetric distribution of colour doesn't continue with the hexagons, all of them seem to have a different variation in the way the colours are arranged.

While I expected to have at least two hexagons in 'rainbow configuration' (yellow, orange, red, purple, blue, green), it might not be possible to achieve this, but I really can't be bothered to reassemble this sphere, or to transform this into a mapping problem. The weight means it's best to suspend this sphere, which measures roughly 45 cm from pole to pole with 20cm struts.

Rainbow buckyball (90 struts)

Caught in the act

I have too many larger sculptures that want to be seen. As I haven't found a gallery, and carrying more than one of them around doesn't work too well, I outsourced some of them. Three of them vanished so far, two of them disintegrated, and four are currently on display in the neighbourhood.

Tet-a-tet

Installing my sculptures in the middle of the night has some trade-offs. One that I really liked vanished in less than 24 hours, without me having any chance to see it hanging in daylight. Another one hangs much closer to the branch its dangling from than I wanted, I couldn't see my progress in lifting it up and so it ended up too high for my liking.

My last attempt to install something on top of one of the wooden posts failed as well, not too mention the bruises I got in the process. As I fail to notice any illegal thing in placing tensegrities in the wild, I simply decided to use a break in rain to do my work.

I wanted to use a tetrahedron made of string within a tensegrity tetrahedron as mount point, which meant 'squaring a triangle. My rough measurements worked out okay, a tighter fit is still possible.

I admit, I used anti-stealth mode. As the winter came back with a cold spell, I wore my space jacket. Lazy as I can be, I rode with my unicycle, carrying a relatively large sculpture in front of me.

At my target, I saw a young woman contemplating on the bench next to the post. I smiled over to her, leaned my unicycle to the post to easily reach the top, and to my pleasure, my idea how to slip the string tetra above the post worked well.

Tet-a-tet a bit closer

I didn't wait for the sun to come back for better shots, did my best to adjust the sculpture as balanced as I could, and happily cycled back. I passed a group of people that had seen me before, one of them asked me: Where's your little thing? I just shrugged my shoulders, with a big smile, and another one commented: "Very Brunswick". Indeed.

I still have to have a second look in sunlight. The visibility seems fine, but the tetrahedral shape has least appeal. A square within a tensegrity square can use the same mounting technique, and might look much more stunning. I still need to make a choice about the strut length, I think 30 cm could be too small for a dramatic effect.

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