"One can imagine propping a cube up on its corner and boring a large-enough square hole vertically through it to fit a cube of the same size as the original. Later, mathematicians found more and more three-dimensional shapes that eventually came to be called Rupert: they are able to fall through a straight hole in an identical shape. In 2017 researchers formally conjectured that all 3D shapes with flat sides and no indents, known as convex polyhedrons, are Rupert."
"Enter the brand-new noperthedron. It has 90 vertices, 240 edges, 152 faces and one very special property: it's nopert, a word coined this year by independent computer science researcher Tom Murphy VII to mean not Rupert. Mathematicians Sergey Yurkevich of Austrian technology company A&R Tech and Jakob Steininger of Statistics Austria, the country's national statistical institute, introduced this new shape to the world recently in a paper posted on the preprint server arXiv.org."
"The noperthedron isn't the first shape suspected of being nopert, but it is the first proven soand it was designed with certain properties that simplify the proof. Using a bespoke computer program, the researchers managed to verify that no matter how each of two identical noperthedrons is shifted or rotated, one could not possibly fall through a hole in the other."
Prince Rupert's cube question asks whether an identical cube can pass through a straight hole bored in a cube; many three-dimensional shapes were later found to have that Rupert property. A 2017 conjecture proposed that every convex polyhedron is Rupert. The noperthedron is a convex polyhedron with 90 vertices, 240 edges and 152 faces that lacks the Rupert property. The noperthedron was designed to simplify verification, and a bespoke computer program exhaustively checked all relative shifts and rotations of two identical copies to confirm that no orientation permits one to fall through the other, disproving the 2017 conjecture.
Read at www.scientificamerican.com
Unable to calculate read time
Collection
[
|
...
]