Platonic Passages

  title={Platonic Passages},
  author={Richard Jerrard and John E. Wetzel and Li-Ping Yuan},
  journal={Mathematics Magazine},
  pages={87 - 98}
Summary It is well known that a hole can be cut in a cube large enough to permit a second cube of equal size to pass through, a result attributed to Prince Rupert of the Rhine by J. Wallis more than three centuries ago. C. Scriba showed nearly 50 years ago that the tetrahedron and the octahedron have this same property. Somewhat surprisingly, the remaining two platonic solids, the dodecahedron and the icosahedron, also have this property: each can be passed through a suitable tunnel in another… Expand
5 Citations
Rupert Property of Archimedean Solids
It is shown that among the 13 Archimedean solids, 8 have this property, namely, the cuboctahedron, the truncated octahedrons, thetruncated cube, the rhombicuboctahedral, the icosidodecahedral, and the truncation dodecahedron. Expand
Cubes and Boxes Have Rupert’s Passages in Every Nontrivial Direction
It is proved that cubes and, in fact all, rectangular boxes have Rupert's passages in every direction that is not parallel to the faces, not only for the cube, but also for all other rectangular boxes. Expand
The Truncated Tetrahedron Is Rupert
Abstract A polyhedron has the Rupert property if a straight tunnel can be made in it, large enough so that a copy of can pass through this tunnel. Eight Archimedean polyhedra are known to have theExpand
The n-Cube is Rupert
It is shown that the n-cube is Rupert for each n ⩾ 3, because a straight tunnel can be made in it through which a second congruent oval can be passed. Expand


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Flexagons are paper polygons, folded from straight or crooked strips of paper, which have the fascinating property of changing their faces when they are “flexed.” Had it not been for the trivialExpand
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In modern terms, Euler's result stating that in three dimensions every rotation of a sphere about its center has an axis is formulated in terms of rotation matrices as follows. Expand
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Most convex bodies pass through a circle smaller than the section of their circumscribed cylinder. Most continua pass through arbitrarily small circles. In this paper we prove these and other similarExpand
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