The Nieuwland number 
of a bounded convex polyhedron 
with nonempty interior is the
supremum of the scale factors 
for which a copy of 
scaled by the factor 
can pass, without turning, through a straight tunnel
in 
.
Boundary contact is allowed when defining this limiting ratio
(Steininger and Yurkevich 2023).
Equivalently, if 
is a three-dimensional rotation, 
is an orthogonal projection
onto a plane, and 
is a vector in that plane,
then
 |
Every such convex polyhedron has 
since identical aligned copies have identical orthogonal projections. It is a Rupert
polyhedron iff 
, and a nopert polyhedron iff 
(Steininger and Yurkevich 2023, Hervay 2026).
For the unit cube, Prince Rupert's cube gives
 |
The noperthedron and small rhombicosidodecahedron have Nieuwland number 1 (Steininger and Yurkevich 2025, Hervay 2026).
