The world’s most cited scientific journal, the Proceedings of the National Academy of Sciences (PNAS) published an article by four scientists (three Hungarian, one American). The researchers bring mathematical, mechanical and geological arguments to vindicate Plato‘s theory according to which the Earth is made of cubes.
The granite wall in the image above shows a fracture pattern which can be well approximated by a so-called primitive mosaic. According to the paper, this pattern is very common in Nature and results in fragments, having, on average, 6 faces and 8 vertices.
Relying on the theory of convex mosaics, large-scale discrete element simulations,
analysis of images about fragmenting icebergs,
the tectonic plates,
and images from space missions (surface of asteroid Bennu illustrated above) as well on measurements of 4000 natural fragments the research team concluded that Plato’s theory may have been more than mere speculation.
According to the study, natural abraison processes start with fragments with N~20 static balance points and end with ellipsoidal beach pebbles with N~6 static balance points. In this process the number N of static balance points is decreasing montonically, so the cube with N=26 balance points (repesenting the ideal average of fragments) and the Gömböc with N=2 balance points may be regarded as geometric brackets to this natural process.
The article was broadly reported in the media, over 400 news appeared in over 50 countries worldwide.
The original article can be accessed at the following link:
The story of the discovery is described in Quanta Magazine: