Creation process for the transparent Clebsch surface

The Clebsch surface made in plaster is a very interesting figure, with its three "ears" upside and three holes downside... but in its interior, the surface is not visible, and you can not appreciate the other four holes that forms a "grullere maze".

The actual mathematic shape of the Clebsch figure is a surface, not a solid, but due to the extreme dificulty involving actually making it, you can not find such a figure in any university world wide.

Here we have a render of the surface as it is, done with pov-ray using this script.

The goal of this proyect is to create a Clebsch figure, including its twenty seven visible tangent lines, about one meter tall, thin as a surface should be (about 2 mm) and transparent, so you can observe the inside of the figure.

Previus to the actual process, several test figures where made as material tests, obtaining several imperfect Clebsch surfaces with almost the desired finish.

In the final surface, especial care was taken to assure a almost-perfect mathematical surface, instead of focusing on the materials like in the test figures.

The process start by creating a perfect model in plaster, that will then be used as a base and covered with liquid polyester resin and cristal fiber like in the boat hulls.

Instead of creating such a big figure all in plaster, it is far more convenient to make it with high density expanded poliestirene foam (the white foam used to pack a fridge or a TV set) and then cover it with a plaster film to obtain a perfect finish.

To be able of cutting the poliestirene easily and precisely, we hand built some resistance hot-wire tools.

This material use to be bought on perfect blocks with paralell faces of your choice, but we decided to reuse an old block, the one shown in the previous image, with the added problem of not having its faces paralell.

Cutting a cilynder form the block was tricky: we built a rotational tool in witch we could rotate the cube on its major axis, while the hot-wired tool was cutting away the outside as the wire was parelell to the axis.

The hot-wire tool at work.

The resulting cilyndre is almost perfect, except for the top and bottom circles that could had been if we had use a brand new block for the work.

Next step was to assure the intersection of cilynder and surface was as perfect as possible, aided with a real scale print of the revolution of such intersection. We used a had-ock program to do this, surely there are other options, but...

Once printed it was fixed to the cilynder surface and copied down to the material. Every half a radius a horizontal line was added to aid in the later stages, plus the heights at with every tangent line intersected with the cilynder, so the final coloured lines could be easily placed.

Before the figure could came out from the block, a top-down slice of it was also printed and cutted from wood to be used as a stencil.

With those bare tools we started carving, checking it every now and then against the up-down stencil.

After the stencil fits on all 3 axis, the figure it self can be guessed.

Now we will take advantaje of the fact that the lines intersect perfectly so we can safely carve more and more material after almost all remanents are off.

Once it was adjusted to all the lines, the rest of the surface was hand sanded until it was "nice curved to the hand", then it is "painted" with light plaster -more water than usual- so it can be finally sanded to the final shape.

An antiadherent has to be added in order to avoid the resine to get jammed with the plaster.

Thin layers of cristal fiber are added using transparent polyester resin as glue. Small pieces of fiber sheets are used to avoid tensions. Avoid using to much resin not to get dropings: The more and thiner the layers are, the better.

About 5-6 layers were used, the more in the weakest parts of the surface, until we felft is was not going to misserably break at the first movement.

In the middle of adding layers, coloured lines are lied down to a perfect fit. Any kind of line could be used provided it is visible enuoght and don't disolve with the resine.

The skirts are cuted off using a small rotational tool. Scissors are not a good idea, by the way. Note the added formula: In one midd layer, it was printed on a transparent film using a laser printer and then embeded into the resine.

The orginal mold material have now to be carved out, it is not possible to use it another time, even if the mold was made of any harder material, the shape itself doesn't admit extracting the mold from its interior outside without breaking it all.

Finally, the borders are sanded until we get a smooth finish.