3 papers
math.MG2026
The Nieuwland number of the Octahedron
Jakob Steininger, Sergey Yurkevich
We prove that the Nieuwland number of the Octahedron is . Along the way, we provide an elementary proof that Rupert's problem for the Octahedron admits no solution in…
math.MG2025
A convex polyhedron without Rupert's property
Jakob Steininger, Sergey Yurkevich
A three-dimensional convex body is said to have Rupert's property if its copy can be passed through a straight hole inside that body. In this work we construct a polyhedron which i…
math.MG2021
An algorithmic approach to Rupert's problem
Jakob Steininger, Sergey Yurkevich
A polyhedron has Rupert's property if a hole can be cut into it, such that a copy of can pass through this hole. There are several wo…