Monday, 22 August 2016

Even more chestahedron

The last post about the chestahedron called "Mottled Heart" went a little bit all over the place, as I wrote it in multiple stages before the piece went to its final destination. So let's rewind and start at the beginning.

The artist Frank Chester set out on a mission to find a geometric structure with 7 equally sized faces. After many explorations he discovered the chestahedron, an object with 7 faces (four equilateral triangles, three kites) and 7 vertices. The structure does not qualify as Platonic Solid, as it has two different edge lengths and two types of faces.

As the structure bases on a tetrahedron folded open, it elegantly relates to all Platonic Solids, as well to a sphere surrounding it. According to Chester, the structure represents the geometry of our heart, please check out his talks for a more in depths explanation for this. When I followed a presentation about the genesis of this shape, my mind got blown several times, inspiring to seek some hands-on experiences with it.

In my first experiments I got the length for the top three struts wrong with only slightly satisfying results. Luckily, I found out the proper numbers, so that the latests builds give me better ideas about the qualities of this unique structure.

My 'standard' way of building tensegrities follows this simple algorithm:
1) All edges of the wireframe model become struts.
2) Each strut gets a string roughly 10% longer than the strut length.
3) The string network reflects a truncated version of the base geometry, eg the strings of my 6 strut "tetrahedron" create a truncated tetrahedron.
4) The number of struts converging in a corner determines the slicing, three edges create a triangle, four edges create a square, etc
5) Building of the tensegrity starts with a 'corner', eg connecting three struts with the strings shaping a triangle to begin building tetrahedron, cube or dodecahedron.
6) Each string connects to two more stick ends.
7) Repeat building 'corners' at the second string attachment position and continue until structure completed.

This simplified version works out fine for all Platonic Solids, it seems to fail for complex intersecting geometries like star tetrahedron. It worked well for the chestahedron, although, if you're really pedantic, the strings represent of truncated chestahedron. While geometrically interested people can perceive and identify the Platonic Solids in its representation as truncated tensegrity, the names of these geometric shapes evades a majority of people.

Our consciousness seems to resonate with geometry. The symmetry of it appeals to our perception of beauty, and it doesn't really matter whether we can put a name to a structure we experience. Architecture and engineering rely traditionally on squares, we have on overabundance of distorted cubes arounds us.

Mobile architecture utilises triangles much more, and geodesic domes offer a nice relieve of the geometrical desert which most urban landscapes offer. The chestahedron hides the numbers 1 to 7 in an elegant and surprising way. 1 object created from 2 base structures, a 4 sided tetrahedron, and 3 slices of a 5 pointed pentagram shows 7 corners and 7 faces. 6 edges shape a perfect hexagram through the centre of a sphere surrounding the chestahedron.

I played around a little bit with less symmetrical structures, but the majority of objects I build and sold showed multiple symmetries. I build some bases for spheres, there's often no clear up and down in my objects. The chestahedron breaks this mould - it commands like an obelisk to be put on its base. It invites to have something suspended from the apex.

The effect of a counterweight can be compared to someone pushing the object to the ground. As long as the counterweight doesn't move, which will happen. Without anchoring I could easily topple the structure over by moving the pendulum much out of centre, yet there was quite a lot of range of movement in a stable state possible.

With only about 80 cm height, "Mottled Heart" stands in a relatively sheltered space, surrounded by a planter box and equally high plants. 3 plastic tubes, fitting snugly over the bamboo sticks, anchor it about 10cm into the ground. Most of the time I saw it moving. I wonder how weathering will effect the stretch in the material, I anticipate a vast visual improvement. As I recycled the struts from a first experiment to paint on bamboo, the paint will wash and weather off. The strings will bleach off, the spot will get more and more sun exposure the closer summer gets.

I know how to improve the immediate visual appeal of the materials involved. While I was busking, I experimented a lot with colour, just a learn more about the fierce Australian sun than I wanted to. If something looks good outdoors over time, it works with nature and not against it. Oiling plant surfaces can provide interesting graceful ageing of material.

Instead of being the trickster, stunning by the immediate shineyness of their illusion, I let Mother nature do her part of trickery. If the "Mottled Heart" still beats a year from now, it will look quite different. Until then, I can enjoy seeing the calming movement reminding me of eternal change.

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