First convex polyhedron found that can't pass through itself (quantamagazine.org)

Article summary

Mathematicians have discovered a convex polyhedron, called the Noperthedron, that cannot pass through itself, resolving a centuries-old geometric mystery. The Noperthedron has 90 vertices and 152 faces, and its discovery proves that not all convex polyhedra have the Rupert property. The proof required a combination of theoretical advances and massive computer calculations. The finding has implications for the study of convex polyhedra and their properties.

Main themes

• Convex polyhedra
• Rupert property
• Geometric shapes
• Mathematical proofs
• Computer calculations

What commenters say

• The definition of a shape being able to pass through itself is equivalent to having at least one orientation where all sides of one instance are at most as long as all sides of the other instance.
• The problem of finding whether two shapes collide in 3D space is related to the problem of determining the Rupert property.
• A sphere is not considered a convex polyhedron and therefore does not have the Rupert property, but as polyhedra approach a sphere shape, they may lose the Rupert property.
• The discovery of the Noperthedron suggests that there may be other convex polyhedra that do not have the Rupert property, and further research is needed to explore this area.
• The use of computer calculations and algorithms is essential in studying the Rupert property and discovering new shapes that do or do not have this property.
• The Noperthedron is a specially constructed shape, and it is unclear whether other, more natural shapes, such as the snub cube, also lack the Rupert property.