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.

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.

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.

Homage to Pars

When I came across the website of Marcelo Pars, a Dutch tensegrity artist, I knew that my explorations wouldn't find an end soon. The site looked a bit different at the time, but had already some fantastically inspiring pieces on display. I had the impression that he builds models on a larger scale than I do, and much more with 'redundant' struts that I explored so far.

Besides exploring basic geometry, he managed to give his objects a solidity in appearance (and potentially in mechanical behaviour) that eluded me. I totally enjoy the ethereal appearance of some of my own structures, and managed to resist the call for more solid struts.

Parsed Rastafarian (12 strut tetrahedron)

While I consider the tetrahedron (in some educated believe in Fuller that the tetrahedron comprises the smallest unit in universe) a very appealing shape, most people exposed to my work prefer the icosahedron when it comes to 6 strut structures.

Parsed Rastafarian (sitting on a tetrahedral face)

While playing with the Java tensegrity viewer by Bob Burkhardt, a pioneer of constructing tensegrity structures, I realised have easy it should be to build a 12 strut tetrahedron like Pars did. I had a small colourful tetrahedron lying around, and decided to transform it. 

Parsed Rastafarian

The tetrahedron 'proves' that one and one add up to four, and it hides 3 pairs of orthogonal edges in it. Three colours suffice to show this twisted pair of edges. While I love many visual aspects of the small version, it's tricky to balance it on all corners, and the relative large diameter in relation to the length of the struts brings the struts nearly into contact.

Homage to Marcelo Pars (12 strut tetrahedron)

The proximity of the struts could easily be changed by upsizing. The corners are held together in a single spot, I'm tempted to connect the corners to the center. Well, as the first emanation with 60 cm struts already has quite a large prestress, I might delay this idea until the next build. 

Homage to Marcelo Pars

The larger build unveiled the space in between the intricate weaving patterns in the center of the sculpture. I'm still hesitant to play it hard, I had some accidents during the build and it feels so taut that I fear to break some of the flimsy struts used.

Genesis revisited (4 strut x-modul)

My attempts to scale the classic 4 strut x-module up didn't succeed. The 30 cm strut version, very taut with only nylon string, can easily be held in balance by slotting into a relatively heavy base. I hope my lungs didn't take damage from drilling the fibreglass base...

Double plus good

Using two colours for the tendons allows to show the 'centre' and 'periphery' of the x-module. Using two colours for the four struts will enhance the polarity of the struts, could be fun be find out how a chain of x-modules behaves. I did this before, very early in my tensegrity exploration, certainly worth doing again.

Pented up

The small 30 strut dodecahedron I had lying around didn't really invite for playing, so I thought in combination with a basis its wobbly qualities come into good use.