Find Open Problems
Find Open Problems
Search for open problems in our database
Submit a Problem
Submit a new open problem to our database (not available yet)
Dice Question Streamline Icon: https://streamlinehq.com

Certifying optimality and Nieuwland numbers

Construct a rigorous method to certify that a given solution to Rupert’s property is (locally) optimal by achieving the largest (local) Nieuwland number, and, more generally, develop techniques to prove conjectured Nieuwland numbers for specific polyhedra.

References

Find a method to prove that a solution to Rupert's property is (locally) optimal, i.e. it has the (locally) the largest Nieuwland number. More generally, how to prove the conjectured Nieuwland numbers?

— A convex polyhedron without Rupert's property (Steininger et al., 25 Aug 2025) in Section 9.2, Open Problems