This piece combines printmaking and sculpture, resulting in a piece of art that also travels well.

Truchet tiles

If you are new to Truchet tiles, read Kerry Mitchell’s paper Generalizations of Truchet Tiles first. He explains the concept with beautiful original examples. I actually keep a copy of this paper with my sketchbook and refer to it from time to time.

The aspect of this type of tile that I was focusing on was the ability to arrange and rotate tiles arbitrarily.

Here are the basic tiles I used:

You can use this random tile loader to see what a plane filled with a random selection of these tiles looks like. Zoom out to see more and reload the page for an updated sample. The white lines appear to continue across tiles no matter how the triangles are rotated.

tiling deltahedra

A triangular tessellation will work even if the triangles are not coplanar (so, in three dimensions). In fact, any deltahedron (a polyhedron made up of triangles, and yes, they are called that simply because a delta looks like a triangle) will work.

So what shape is this? It’s very close to the stella octangula and the Escher solid, but it is made up of an octahedron with a tetrahedron on the center of each face. Hence the name “tetrahedron-augmented octahedron.”

randomness

For the record, randomness relates to decision making with no intended outcome, not distribution of results.

I wanted to break up the uniformity of the tiles a little without adding too much more visual information. The base layer for each triangle (the colored part of the tiles above) was printed first. I made smaller blocks for overprinting layers on top of the base layer.

This made some areas of each tile darker while preserving the large white lines.

I started out using a spinner to determine which component to print where, but I quickly realized it was going to significantly add to the amount of time spent on the project, so… I used Excel to pick random values for me. This gave me a list of instructions I could quickly follow. I got some slow head shakes at the print shop for the spinner and the instructions, which made it worth it.

portability / assembly

One of the constraints with this piece was portability. How do you get a sculpture with a 30cm diameter over the Atlantic ocean without paying a fortune? Make it into a kit!

This was the arrangement I decided would be the best for carrying and packaging the components for minimal damage.

assembly

The basic tiles are triangles, but the sides of the main octahedron are three attached triangles. This let me attach loops of paper to the undersides which I could slide a small painted wooden rod through. Slight imperfection in the straightness of the dowels gives just enough friction to hold everything together without tension.

presentation

Unfortunately, the piece is unlikely to be exhibited in zero gravity, so a stand is needed. The same tile designs were used to make 8 unique strips which fit together to make the stand.

the finished piece

fashion

Obviously I had to make a shirt too. The back of the shirt and right sleeve use different colors for the triangles behind the white lines, creating another layer of pattern.