Prince Rupert's Cube

The largest Cube which can be made to pass through a given Cube. (In other words, the Cube having a side length equal to the side length of the largest Hole of a Square Cross-Section which can be cut through a unit Cube without splitting it into two pieces.) The Prince Rupert's cube has side length $3\sqrt{2}/4=1.0606601\ldots$, and any Cube this size or smaller can be made to pass through the original Cube.

See also Cube, Square

References

Cundy, H. and Rollett, A. ``Prince Rupert's Cubes.'' §3.15.2 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 157-158, 1989.

Schrek, D. J. E. ``Prince Rupert's Problem and Its Extension by Pieter Nieuwland.'' Scripta Math. 16, 73-80 and 261-267, 1950.