A building or a statue? A BME student's thesis defence drew international attention

It is rare at any university in the world for a thesis defence to attract not only an audience of several dozen people, but also viewers from around the globe following the event via an online stream. On June 19, this is exactly what happened at the Faculty of Architecture at BME: Kinga Kocsis, a master’s student, presented her twofold focus excellence diploma project (thesis), which drew significant interest both on-site and online.

In this case, the term "twofold focus" means that the subject of the thesis is an architectural design, the mathematical foundation of which is at least as important as the product itself. Its more specific area is the field of geometry, and within that, the class of shapes known as soft cells.

Soft cells are formations that, when fitted together, fill the space seamlessly despite having no vertices at all. They occur in a surprisingly large number of places in nature. Their discovery was featured in Nature magazine last year, as well as on the cover of Scientific American, and even made it to the International Space Station through an experiment conducted by Hungarian astronaut Tibor Kapu. One of their discoverers is Gábor Domokos, a full professor at BME, also known as the creator of the “Gömböc”, who served as one of the thesis advisors for the diploma project (thesis). The other two thesis advisors were Ferenc Répás, an architect awarded the Ybl Prize and also a professor at BME, and Lajos Hartvig, the founder of Bánáti & Hartvig Architects.

Kinga Kocsis originally undertook the task of determining how many different types of soft cells can be generated from a simple cube according to defined principles by eliminating the vertices. It has been revealed that exactly 26 such items can be produced using an edge-bending algorithm – which, incidentally, is exactly the sum of the number of edges (12), vertices (8), and faces (6) of a cube, although it remains unclear whether there is any correlation behind this correspondence or if it is merely accidental.

Do they fit?

The next step was to ask the question: is it possible to assemble these shapes into a large 3×3 cube so that their faces and edges fit together perfectly all around? Although the number of possible variations is unimaginably large, she managed to find a solution – whether there are more remains to be seen – thus obtaining a Rubik's Cube-like shape (from which, of course, one element is absent, since there are not 3x3x3=27 small cubes, but one less).

She designed this formation for a specific location: a cliff face called Muley Point, situated beside the San Juan River in Utah, where the rock fractures into nearly regular cubes without any human intervention. The building, conceived as a lookout point, consists of two parts: a path known as the Hamiltonian Path leads to the large cube; this path winds its way through the 26 smaller cubes, touching each one only once. The material of the structure is copper, harmonising with the colour of the landscape; the cubes are connected by stone steps, and the pattern of the enclosing surfaces consists of planar soft cells.

The members of the evaluation committee were able to examine all of this while wearing VR headsets, entering the digital world created by the graduate. Virtual reality was therefore not an illustration, but one of the settings for the presentation. The defence was graded as excellent, thus Kinga Kocsis will receive a degree with honours.

Math gives the depths

One of the two opponents, Flórián Kovács, associate professor at the Department of Structural Mechanics, described the thesis as a "combinatorial problem solved with architectural inspiration." The external opponent, Richard Hőnich, an architect awarded the Ybl Prize, considered that the design straddled “the boundary between building and sculpture”. “A unique mathematical result has given rise to a unique architectural concept, which would stand on its own, but it is the mathematics that gives it its depth,” he stated.

“I began the design process with the aim of ensuring that the building was not defined by its function; in other words, the architectural concept came first, then it found a site, and finally the elements were put in place. It thus became clear that it could serve as a vantage point, as well as a route enabling visitors to experience the mountain’s natural network of fissures,” Kinga Kocsis told bme.hu.

Word of her design has already spread: she has been asked by the California Institute of the Arts to help with a design competition. 

In January, she will therefore be joining a design project in the Maldives which aims to curb local coastal erosion by embedding appropriately shaped protective structures in the sand. "The team always draws inspiration from such natural forms; hopefully, we will be able to develop a soft cell for the purpose," she added.

Meanwhile, she was also invited to National Tsing Hua University in Taiwan. “It is a matter of great significance; full-time students are not usually invited to prestigious universities in the Far East with all expenses paid,” remarked Gábor Domokos. The Head of the Doctoral School there, Ray-Kuang Lee, was one of those who followed the defence live. The other spectator was Marjorie Senechal, Professor Emerita at Smith College, former editor-in-chief of the Mathematical Intelligencer journal, and a distinguished authority in the theory of tessellations, but there were also spectators from the Institute of Mathematics at the University of Oxford and the Pratt Institute in New York.

A 25-minute summary of the defence

The Taiwanese professor is currently working on projects that straddle the boundary between science and art. "Such topics are becoming increasingly popular because rapid advancement of artificial intelligence is not expected in this field, which also accounts for the international interest," explained Gábor Domokos. 

“I, too, would like to maintain this duality in my life; I am looking for ways to do so.

Whether they are architectural projects or even art installations, we will see what the future brings. I believe that in order to create a relevant and authentic work of art, I need to understand the mathematics behind it – or, in fact, work it out for myself,” said Kinga.

International invitations notwithstanding, she already knows that she wants to continue her studies at the Pál Csonka Doctoral School at BME. “This topic could be explored further. 

I have just solved a problem, which has created a closed universe of forms, but the same problem can be formulated without certain constraints, and then a new universe opens up.”

Tamás Varga, Dean, stated in his speech following the defence that it is no coincidence that this thesis was created precisely at the Faculty of Architecture at BME. “He is very right. Here, one can engage in high-level academic work alongside art, which, as can be seen, also attracts international attention. Even back in secondary school, I did not give much thought to where I would go on to study, and I made the right decision," said Kinga Kocsis in response.

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