The noperthedron is the 90-vertex convex polyhedron constructed by Steininger and Yurkevich (2025) as the first proved example of a nopert polyhedron. It is a centrosymmetric set that cannot pass with positive clearance, without turning, through a straight tunnel in a congruent copy of itself.
One exact construction starts with the points
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
If 
is the rotation
about the 
-axis
through angle 
, then the noperthedron is
 |
(4)
|
where 
denotes the convex hull (Steininger and Yurkevich
2025).
The proof excludes every possible passage by covering the symmetry-reduced configuration space with regions verified using rigorous rational bounds. The construction disproves the conjecture that every bounded convex polyhedron has Rupert's property (Steininger and Yurkevich 2025).
