copyright universaljoint.NU (Jonathan Chertok)

What happens when the sublime beauty of mathematical concepts meets modern technology? The result is a set of objects lovely to behold.

Rudolph Clebsch

Rudolf Clebsch, a German mathematician and important figure in the development of algebraic geometry and invariant theory, was working with Paul Gordan when the pair created what are known as Clebsch-Gordan coefficients used in spherical harmonics. That work is now a cornerstone of quantum mechanics, but the models of their work are art as much as they are math.

One of Clebsch's postulates, the icosahedral cubic surface, is a cubic surface all of whose 27 exceptional lines are often defined over real numbers. Historically the first cubic surface that was ever modeled is the Clebsch Diagonal Cubic.

It was the lovely curves of the Clebsch cubic which captivated designer Jonathan Chertok. In an effort to understand their underlying logic and mathematical beauty, Chertok began using one of the few software packages for simulating surfaces using meshes of tiny triangles to reproduce the classical mathematical models via the emerging process of rapid prototyping techniques.


copyright universaljoint.NU (Jonathan Chertok)

Chertok, who holds a BA in Political Science from the University of Michigan and a Masters of Architecture from the University of Texas at Austin, once worked in the office of the Pritzker Prize winning Architect Renzo Piano and at a number of commercial architecture firms. His work has been exhibited, recognized and published internationally.

In 2000, he founded Universal Joint, a research-based architectural practice in Austin, Texas. But it's his work on a research project he began in 1998 developing a digital recreation of the classical mathematical model collection housed in Goettingen, Germany which resulted in the images you see here.

Chertok used computed, numerical cross-sections and ZCorp hardware to arrange layers of plaster powder and glue to build up the 3D shapes of the models. The resulting models, taken from the collection, were originally created by hand in plaster in the 1800s.

According to Chertok, his recreation of the famous collection was originally modeled by Carl Rodenberg who was, at the time, working with renowned mathematician Felix Klein, another collaborator of Rudolf Clebsch.

Architekton with A2 and 2 - A1 singularities
copyright universaljoint.NU (Jonathan Chertok)

You can purchase some of these historically significant models on Shapeways.