Znak Politechniki Warszawskiej

K-dron: an incredible geometric shape


In 2009 a monument of K-drona stood in Kole, photo: Kolanin, Wikipedia, CC BY 3.0

It was small hours of the morning of January 11, 1985 in New York City. The life of Janusz Kapusta, graduate from the Faculty of Architecture, Warsaw University of Technology, was about to change forever; he had just discovered a new geometric shape. 

As Łukasz Lubański recalls in his feature for the Rzeczpospolita daily, all started back when Kapusta was studying the history of philosophy at the Academy of Catholic Theology. He had already had a diploma from our University (awarded in 1977). On the way to his lecture, the young architect started to ponder on how to actually draw infinity. Back home, he put his ideas on paper. This is how a drawing of two symmetric pyramids was created. One pyramid seemed to go inside the sheet and the other seemed to come out of it.

More or less infinity

This story might have taken a completely different path were it not for some incredible twists of fate. In the fall of 1981, Kapusta went to the United States. He was going to make the artwork for a book by Andrzej Pastuszek and come back. But fate decided otherwise as the Martial Law was declared in Poland.

The architect and illustrator stayed in New York City, where he started to pursue his career. Preparing one of his exhibitions, he got down to analyzing printouts of his old drawings of infinity. He himself dubbed them suggestively: “Plus minus nieskończoność” – “More or Less Infinity.” At that point, in the US, he was examining his works, matching and compiling. Something seemed to come out of it but it took several weeks more for a new geometric shape to emerge. Kapusta called it a K-dron.


Incredible properties

K-dron has 11 faces (hence the name: ‘dron’ means ‘face’ in Greek, and ‘K’ is the eleventh letter of the Latin alphabet). However, drawing it is quite a tricky task, even after thorough observation. It has unusual optical, aural and structural properties. Apparently, two K-drons put together make a cube, and if there are more shapes of the type, incredible space arrangements can be created.

Łukasz Lubański writes in his feature for the Rzeczpospolita daily: “If you divide a cube with planes through all of its symmetry axes, you will get 48 pyramids. Interestingly, if you place four cubes so divided side by side, a K-dron will be found in the middle. Prof. Stanisław Kwapień, a mathematician, discovered another relation of the new shape with science, having observed that a spatiotemporal model of the vibrating string equation is the K-dron surface area.”

Rektor PW i Janusz Kapustka

In 2016, Janusz Kapusta received the Medal of the Warsaw University of Technology, photo: BPI

Where is the shape applied?

But what would be the worth of the best of inventions if they were not in use? Kapusta patented his shape in 1987. He has found as many as 168 applications for his invention. K-dron can be used in designing building façades, roof tiles, ceilings, furniture, toys, games or jewelry. The shape has found its way into solutions for transporting column loudspeakers and car wheel hubcaps. A concrete block and a logic game based on a K-dron as well as a globe made of two K-drons went into mass production.
His 1985 invention earned Kapusta not only recognition but also a doctoral degree. The graduate in Architecture from Warsaw University of Technology was awarded the degree in 2010 from the Academy of Fine Arts in Warsaw. “I jokingly say that a master’s degree holder used to discuss the K-dron and the K-dron has made the K-dron a thing discussed by a doctor,” said Kapusta in an interview for NDTV.
Agnieszka Kapela
Promotion and Information Office
Łukasz Lubański, Janusz Kapusta wymyślił nową figurę geometryczną – k-dron [Janusz Kapusta invented a new geometric shape: k-dron], http://www.rp.pl/Plus-Minus/304279906-Janusz-Kapusta-wymyslil-nowa-figure-geometryczna--k-dron.html#ap-1, accessed October 12, 2017
Bronisław Pabich, K-dron, http://www.interklasa.pl/pabich/s5e.htm, accessed October 12, 2017
Janusz Kapusta, http://culture.pl/pl/tworca/janusz-kapusta, accessed October 12, 2017
K-dron. The shape of things to come, http://www.k-dron.com/, accessed October 12, 2017
Janusz Kapusta w programie „Kanapa” [Janusz Kapusta on the “Kanapa/Couch” show], https://www.youtube.com/watch?v=QnOMM6zKM1w, accessed October 12, 2017