The Discovery of the Nobertherion: A New Geometric Shape

For centuries, scientists and thinkers have been intrigued by the question of geometric shapes and their ability to interlock. In the 17th century, Prince Rupert of the Rhine posed a question about whether a hole could be drilled in a cube so that a similar cube could pass through it. At the time, the answer was yes. Over time, scientists discovered other three-dimensional shapes that could achieve the same property, later called “Rupert shapes.” However, it was recently proven that there exists a geometric shape that does not possess this property, known as the “Nobertherion.”

The Story of the Nobertherion’s Discovery

In 2017, researchers hypothesized that all three-dimensional shapes with flat, non-hollow sides, known as convex polyhedra, possessed the Rupert property. Until now, no one had been able to refute this hypothesis. In 2025, researchers Sergei Yurkevich and Jakob Steininger introduced a new shape called the “Nobertherion,” which is the first of its kind not to have the Rupert property.

The Nobertherion consists of 90 vertices, 240 edges, and 152 faces. What makes this shape unique is that it was specifically designed to prove that no similar cube can pass through it. Its validity was confirmed using special computer software, which demonstrated that no matter how the two similar shapes are rotated or moved, one cannot pass through the other.

Challenges and Innovations

It took years of research and study to arrive at this discovery. Yurkevich and Steininger began their journey studying the Rupert property when they were university students. After watching a YouTube video about Prince Rupert’s cube, they found that the prevalent shapes were an open problem in mathematics. In 2020, they were the first to publicly propose that not all convex polyhedra possess the Rupert property.

The researchers used a combination of mathematical thinking and computer programming to identify all possible regions in the five-dimensional cube, representing all possible movements of the Nobertherion. This creative and precise approach has impressed many researchers in the field.

Scientific Reactions

Mathematician Pongpunthit Thonpho from Chulalongkorn University in Thailand, a specialist in studying the Rupert property, described this discovery as unexpected. The hypothesis that all convex polyhedra are Rupert shapes had been standing for years, and it was not anticipated that it would be refuted so quickly.

This discovery is a significant achievement in the field of mathematics, illustrating how creative thinking and scientific collaboration can lead to new discoveries that change our understanding of the world.

Conclusion

The discovery of the Nobertherion marks a turning point in the study of three-dimensional geometric shapes. It opens a new door to understanding how geometric shapes interact with one another, prompting scientists to rethink old hypotheses. This achievement highlights the importance of continuing scientific research and collaboration among scientists from different disciplines, which can lead to new discoveries that contribute to the advancement of science and human understanding.