A tetrahedron is the simplest Platonic solid. Mathematicians have now made one that’s stable only on one side, confirming a ...

The results, published in the September issue of PNAS Nexus, reveal what Domokos and colleagues describe as soft cells—rounded forms capable of filling a space entirely thanks to specific ...

Prof. Gábor Domokos, mechanics, materials and structures, Budapest University of Technology and Economics, gave the University a gömböc, which was placed in the Math Library on Thursday.

Gabor Domokos, head of the department of Mechanics and Materials and Structures at Budapest's Technical University, shows his invention, "Gomboc," in Budapest. Laszlo Balogh / Reuters ...

That confirmed that cubes were indeed the 3D answer. Now Domokos had the average shapes produced by splitting a flat surface or a three-dimensional block. But then a larger quest emerged.

The development of a quantitative understanding of pebble shapes began with the work of Domokos, whose research was triggered by the discovery of the Gömböc, a curious three-dimensional object ...

Domokos et al., PNAS Nexus 2024 under CC BY-NC 4.0 In a cross-section of a chambered shell, the segmented shapes appear to have corners, but the 3D geometry of the chambers does not have any.

Intrigued, Domokos consulted with two theoretical physicists – Ferenc Kun, an expert on fragmentation, and János Török, an expert on statistical and computational models.

"It is very expensive (1000 euros or £790) due to the extreme precision that is needed (0.01mm)," says Prof Domokos. "We hope to make it cheaper in a couple of months." ...