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Prince Rupert's Cube

PrinceRupertsCube

Prince Rupert's cube is the largest cube that 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 that can be cut through a unit cube without splitting it into two pieces.

Prince Rupert's cube cuts a hole of the shape indicated in the above illustration (Wells 1991). Curiously, it is slightly larger than the original cube, with side length 3sqrt(2)/4 approx 1.0606601... (OEIS A093577). Any cube this size or smaller can be made to pass through the original cube.

See also

Cube, Cube Square Inscribing, Hole, Square

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References

Croft, H. T.; Falconer, K. J.; and Guy, R. K. "Prince Rupert's Problem." §B4 in Unsolved Problems in Geometry. New York: Springer-Verlag, pp. 53-54, 1991.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.Sloane, N. J. A. Sequence A093577 in "The On-Line Encyclopedia of Integer Sequences."Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 33, 1986.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 195, 1991.

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Prince Rupert's Cube

Cite this as:

Weisstein, Eric W. "Prince Rupert's Cube." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PrinceRupertsCube.html

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