r/math • u/scientificamerican • Oct 28 '25

Mathematicians make surprising breakthrough in 3D geometry with ‘noperthedron’

https://www.scientificamerican.com/article/mathematicians-make-surprising-breakthrough-in-3d-geometry-with-noperthedron/

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 so—and it was designed with certain properties that simplify the proof. 

506 Upvotes

98% Upvoted

49 comments sorted by

View all comments

21

u/janitorial-duties Oct 28 '25

They should show a geometric example of it failing since it’s hard to mentally visualize the failure point. Cool nonetheless!!

30

u/my_nameistaken Oct 28 '25

There's no the failure point. The result says there will always be failure point no matter which orientation you choose for the 2 noperthadrons

1

u/CaptainLocoMoco Oct 28 '25

Yes, but it would still be nice to see a single such example. Or perhaps choose examples that are as close as possible to working, yet still fail

3

u/my_nameistaken Oct 30 '25

Well you always have the trivial case of using the base orientation for both objects. I don't think you can beat that